dr Jakub Lengiewicz 

Doktorat
20090122  Analiza wrażliwości dla zagadnień kontaktowych z tarciem
 621 
Ostatnie publikacje
1.  Deshpande S.^{♦}, Bordas S.^{♦}, Lengiewicz J. A., MAgNET: A graph UNet architecture for meshbased simulations, Engineering Applications of Artificial Intelligence, ISSN: 09521976, DOI: 10.1016/j.engappai.2024.108055, Vol.133 B, No.108055, pp.118, 2024 Streszczenie: In many cuttingedge applications, highfidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on largedimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder–decoder geometric deep learning framework called MAgNET, which extends the wellknown convolutional neural networks to accommodate arbitrary graphstructured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph UNet architecture that is analogous to convolutional UNets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for nonlinear finite element simulations in the mechanics of solids. Słowa kluczowe: Geometric deep learning, Mesh based simulations, Finite element method, Graph UNet, Surrogate modeling Afiliacje autorów:
 140p.  
2.  Lavigne T.^{♦}, Bordas S.^{♦}, Lengiewicz J., Identification of material parameters and traction field for soft bodies in contact, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2023.115889, Vol.406, No.115889, pp.122, 2023 Streszczenie: We provide an optimization framework that is capable of identifying the material parameters and contact traction field from two measured deformed geometries of a soft body in contact. The novelty of the framework is the idea of parametrizing the missing contact traction field and incorporating it into the inverse+forward hyperelasticity formulation. We provide the continuum and finite element formulation of the framework, as well as the direct differentiation method of sensitivity analysis to efficiently obtain necessary gradients for the BFGS optimizer. The correctness of the formulation and the excellent performance of the framework are confirmed by a series of benchmark numerical examples. Słowa kluczowe: Hyperelasticity, Inverse form, Large strains, Contact, Calibration, Soft bodies Afiliacje autorów:
 200p.  
3.  Deshpande S.^{♦}, Sosa R.^{♦}, Bordas S.P.^{♦}, Lengiewicz J.A., Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics, Frontiers in Materials, ISSN: 22968016, DOI: 10.3389/fmats.2023.1128954, Vol.10, No.1128954, pp.112, 2023 Streszczenie: Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with realworld complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly nonlinear deformations of solid bodies. The first two architectures are based on the recently proposed CNN UNET and MAgNET (graph UNET) frameworks which have shown promising performance for learning on meshbased data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attentionbased neural networks–a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the nonlinear mechanical responses of soft bodies. Słowa kluczowe: surrogate modeling, deep learningartificial neural network, CNN UNET, graph Unet, perceiver IO, finite element method Afiliacje autorów:
 70p.  
4.  Deshpande S.^{♦}, Lengiewicz J., Bordas S.P.A.^{♦}, Probabilistic deep learning for realtime large deformation simulations, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2022.115307, Vol.398, pp.115307111530726, 2022 Streszczenie: For many novel applications, such as patientspecific computeraided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deeplearning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in realtime. The surrogate model has a convolutional neural network architecture, called UNet, which is trained with force–displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deeplearning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations. Słowa kluczowe: convolutional neural network, Bayesian inference, Bayesian deep learning, large deformations, finite element method, realtime simulations Afiliacje autorów:
 200p.  
5.  Lavigne T.^{♦}, Mazier A.^{♦}, Perney A.^{♦}, Bordas S.P.A.^{♦}, Hild F.^{♦}, Lengiewicz J., Digital Volume Correlation for large deformations of soft tissues: Pipeline and proof of concept for the application to breast ex vivo deformations, Journal of the Mechanical Behavior of Biomedical Materials, ISSN: 17516161, DOI: 10.1016/j.jmbbm.2022.105490, Vol.136, No.105490, pp.113, 2022 Streszczenie: Being able to reposition tumors from prone imaging to supine surgery stances is key for bypassing current invasive marking used for conservative breast surgery. This study aims to demonstrate the feasibility of using Digital Volume Correlation (DVC) to measure the deformation of a female quarter thorax between two different body positioning when subjected to gravity. A segmented multipart mesh (bones, cartilage and tissue) was constructed and a threestep FEbased DVC procedure with heterogeneous elastic regularization was implemented. With the proposed framework, the large displacement field of a hard/soft breast sample was recovered with low registration residuals and small error between the measured and manually determined deformations of phase interfaces. The present study showed the capacity of FEbased DVC to faithfully capture large deformations of hard/soft tissues. Słowa kluczowe: Digital Volume Correlation, Elastic regularization, Hard/soft tissues, Large displacements, Kinematic fields, Xray tomography Afiliacje autorów:
 100p.  
6.  Magliulo M.^{♦}, Lengiewicz J., Zilian A.^{♦}, Beex L.A.A.^{♦}, Frictional interactions for non‐localised beam‐to‐beam and beam‐inside‐beam contact, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.6596, Vol.122, No.7, pp.17061731, 2021 Streszczenie: This contribution presents the extensions of beam‐to‐beam and beam‐inside‐beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams' true surfaces (instead of surfaces implicitly deduced from the beams' centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams' axial directions, but also in the circumferential directions. Both the frictional beam‐to‐beam approach as well as the frictional beam‐inside‐beam approach are applicable to shear‐deformable and shear‐undeformable beams, as well as to beams with both circular and elliptical cross‐sections (although the cross‐sections must be rigid). A penalty formulation is used to treat unilateral and frictional contact constraints. FE implementation details are discussed, where automatic differentiation techniques are used to derive the implementations. Simulations involving large sliding displacements and large deformations are presented for both beam‐to‐beam and beam‐inside‐beam schemes. All simulation results are compared to those of the frictionless schemes. Słowa kluczowe: beam contact, beamtobeam contact, beaminsidebeam contact, friction, Coulomb's law Afiliacje autorów:
 200p.  
7.  Piranda B.^{♦}, Chodkiewicz P.^{♦}, Hołobut P., Bordas S.P.A.^{♦}, Bourgeois J.^{♦}, Lengiewicz J., Distributed prediction of unsafe reconfiguration scenarios of modular robotic programmable matter, IEEE TRANSACTIONS ON ROBOTICS, ISSN: 15523098, DOI: 10.1109/TRO.2021.3074085, Vol.37, No.6, pp.22262233, 2021 Streszczenie: We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is executed by the modular robot itself and based on a distributed iterative solution of mechanical equilibrium equations derived from a simplified model of the robot. The model treats intermodular connections as beams and assumes nosliding contact between the modules and the ground. We also provide a procedure for simplified instability detection. The algorithm is verified in the Programmable Matter simulator VisibleSim, and in reallife experiments on the modular robotic system Blinky Blocks. Słowa kluczowe: distributed algorithms, modular robots, mechanical constraints, programmable matter, selfreconfiguration Afiliacje autorów:
 200p.  
8.  Lengiewicz J., Souza M.^{♦}, Lahmar M.A.^{♦}, Courbon C.^{♦}, Dalmas D.^{♦}, Stupkiewicz S., Scheibert J.^{♦}, Finite deformations govern the anisotropic shearinduced area reduction of soft elastic contacts, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 00225096, DOI: 10.1016/j.jmps.2020.104056, Vol.143, pp.104056119, 2020 Streszczenie: Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent highload experiments can be obtained, with no adjustable parameter, using a nonadhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying anisotropic shearinduced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shearinduced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials. Słowa kluczowe: contact mechanics, friction, contact area, elastomer, fullfield measurement Afiliacje autorów:
 140p.  
9.  Magliulo M.^{♦}, Lengiewicz J., Zilian A.^{♦}, Beex L.A.A.^{♦}, Nonlocalised contact between beams with circular and elliptical crosssections, COMPUTATIONAL MECHANICS, ISSN: 01787675, DOI: 10.1007/s00466020018171, Vol.65, No.5, pp.12471266, 2020 Streszczenie: The key novelty of this contribution is a dedicated technique to efficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical crosssections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams' crosssections. Two contact integration schemes are considered: the conventional slavemaster approach (which is biased as the contact virtual work is only integrated over the slave surface) and the socalled twohalfpass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation, which is suitably implemented using Automatic Differentiation techniques, are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants. Słowa kluczowe: beams, contact, circular and elliptical crosssections, rigid crosssections, singlepass algorithm, twohalfpass algorithm Afiliacje autorów:
 100p.  
10.  Magliulo M.^{♦}, Lengiewicz J., Zilian A.^{♦}, Beex L.A.A.^{♦}, Beaminsidebeam contact: mechanical simulations of slender medical instruments inside the human body, Computer Methods and Programs in Biomedicine, ISSN: 01692607, DOI: 10.1016/j.cmpb.2020.105527, Vol.196, pp.105527114, 2020 Streszczenie: This contribution presents a rapid computational framework to mechanically simulate the insertion of a slender medical instrument in a tubular structure such as an artery, the cochlea or another slender instrument. Słowa kluczowe: surgical simulation, contact mechanics, beaminsidebeam, artery, cochlea Afiliacje autorów:
 100p.  
11.  Lengiewicz J., Hołobut P., Efficient collective shape shifting and locomotion of massivelymodular robotic structures, Autonomous Robots, ISSN: 09295593, DOI: 10.1007/s1051401897096, Vol.43, No.1, pp.97122, 2019 Streszczenie: We propose a methodology of planning effective shape shifting and locomotion of largeensemble modular robots based on a cubic lattice. The modules are divided into two groups: fixed ones, that build a rigid porous frame, and mobile ones, that flow through the frame. Mobile modules which flow out of the structure attach to the frame, advancing its boundary. Conversely, a deficiency of mobile modules in other parts of the boundary is corrected by decomposition of the frame. Inside the structure, appropriate module flow is arranged to transport the modules in a desired direction, which is planned by a special distributed version of a maximum flow search algorithm. The method engages a volume of modules during reconfiguration, which is more efficient than common surfaceflow approaches. Also, the proposed interpretation as a flow in porous media with moving boundaries seems particularly suitable for further development of more advanced global reconfiguration scenarios. The theoretical efficiency of the method is assessed, and then partially verified by a series of simulations. The method can be possibly also applied to a wider class of modular robots, not necessarily cubiclatticebased. Słowa kluczowe: modular robots, selfreconfiguration, maximum flow search, programmable matter, distributed algorithms Afiliacje autorów:
 100p.  
12.  Vakis A.I.^{♦}, Yastrebov V.A.^{♦}, Scheibert J.^{♦}, Nicola L.^{♦}, Dini D.^{♦}, Minfray C.^{♦}, Almqvist A.^{♦}, Paggi M.^{♦}, Lee S.^{♦}, Limbert G.^{♦}, Molinari J.F.^{♦}, Anciaux G.^{♦}, Aghababaei R.^{♦}, Echeverri Restrepo S.^{♦}, Papangelo A.^{♦}, Cammarata A.^{♦}, Nicolini P.^{♦}, Putignano C.^{♦}, Carbone G.^{♦}, Stupkiewicz S., Lengiewicz J., Costagliola G.^{♦}, Bosia F.^{♦}, Guarino R.^{♦}, Pugno N.M.^{♦}, Müser M.H.^{♦}, Ciavarella M.^{♦}, Modeling and simulation in tribology across scales: An overview, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2018.02.005, Vol.125, pp.169199, 2018 Streszczenie: This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions. Słowa kluczowe: Tribology, Multiscale modeling, Multiphysics modeling, Roughness, Contact, Friction, Adhesion, Wear, Lubrication, Tribochemistry Afiliacje autorów:
 35p.  
13.  LeyvaMendivil M.F.^{♦}, Lengiewicz J., Limbert G.^{♦}, Skin friction under pressure. The role of micromechanics, Surface Topography: Metrology and Properties, ISSN: 2051672X, DOI: 10.1088/2051672X/aaa2d4, Vol.6, No.1, pp.114, 2018 Streszczenie: The role of contact pressure on skin friction has been documented in multiple experimental studies. Skin friction significantly raises in the lowpressure regime as load increases while, after a critical pressure value is reached, the coefficient of friction of skin against an external surface becomes mostly insensitive to contact pressure. However, up to now, no study has elucidated the qualitative and quantitative nature of the interplay between contact pressure, the material and microstructural properties of the skin, the size of an indenting slider and the resulting measured macroscopic coefficient of friction. A mechanistic understanding of these aspects is essential for guiding the rational design of products intended to interact with the skin through optimallytuned surface and/or microstructural properties. Here, an anatomicallyrealistic 2D multilayer finite element model of the skin was embedded within a computational contact homogenisation procedure. The main objective was to investigate the sensitivity of macroscopic skin friction to the parameters discussed above, in addition to the local (i.e. microscopic) coefficient of friction defined at skin asperity level. This was accomplished via the design of a largescale computational experiment featuring 312 analyses. Results confirmed the potentially major role of finite deformations of skin asperities on the resulting macroscopic friction. This effect was shown to be modulated by the level of contact pressure and relative size of skin surface asperities compared to those of a rigid slider. The numerical study also corroborated experimental observations concerning the existence of two contact pressure regimes where macroscopic friction steeply and nonlinearly increases up to a critical value, and then remains approximately constant as pressure increases further. The proposed computational modelling platform offers attractive features which are beyond the reach of current analytical models of skin friction, namely, the ability to accommodate arbitrary kinematics, nonlinear constitutive properties and the complex skin microstructure. Słowa kluczowe: skin friction, contact mechanics, pressure, microstructure, finite element, homogenisation, material properties Afiliacje autorów:
 
14.  Chodkiewicz P.^{♦}, Lengiewicz J., Zalewski R.^{♦}, Discrete element method approach to modelling VPP dampers, MATEC Web of Conferences, ISSN: 2261236X, DOI: 10.1051/matecconf/201815702014, Vol.157, No.02014, pp.18, 2018 Streszczenie: In this paper, we present a novel approach to modeling and analysis of Vacuum Packed Particle dampers (VPP dampers) with the use of Discrete Element Method (DEM). VPP dampers are composed of loose granular medium encapsulated in a hermetic envelope, with controlled pressure inside the envelope. By changing the level of underpressure inside the envelope, one can control mechanical properties of the system. The main novelty of the DEM model proposed in this paper is the method to treat special (pressure) boundary conditions at the envelope. The model has been implemented within the opensource Yade DEM software. Preliminary results are presented and discussed in the paper. The qualitative agreement with experimental results has been achieved. Słowa kluczowe: VPP, discrete element method, Yade DEM, modelling, smart structures, smart materials Afiliacje autorów:
 
15.  LeyvaMendivil M.F.^{♦}, Lengiewicz J., Page A.^{♦}, Bressloff N.W.^{♦}, Limbert G.^{♦}, Skin microstructure is a key contributor to its friction behaviour, TRIBOLOGY LETTERS, ISSN: 10238883, DOI: 10.1007/s1124901607944, Vol.65, No.1, pp.12117, 2017 Streszczenie: Due to its multifactorial nature, skin friction remains a multiphysics and multiscale phenomenon poorly understood despite its relevance for many biomedical and engineering applications (from superficial pressure ulcers, through shaving and cosmetics, to automotive safety and sports equipment). For example, it is unclear whether, and in which measure, the skin microscopic surface topography, internal microstructure and associated nonlinear mechanics can condition and modulate skin friction. This study addressed this question through the development of a parametric finite element contact homogenisation procedure which was used to study and quantify the effect of the skin microstructure on the macroscopic skin frictional response. An anatomically realistic twodimensional imagebased multilayer finite element model of human skin was used to simulate the sliding of rigid indenters of various sizes over the skin surface. A corresponding structurally idealised multilayer skin model was also built for comparison purposes. Microscopic friction specified at skin asperity or microrelief level was an input to the finite element computations. From the contact reaction force measured at the sliding indenter, a homogenised (or apparent) macroscopic friction was calculated. Results demonstrated that the naturally complex geometry of the skin microstructure and surface topography alone can play as significant role in modulating the deformation component of macroscopic friction and can significantly increase it. This effect is further amplified as the groundstate Young's modulus of the stratum corneum is increased (for example, as a result of a dryer environment). In these conditions, the skin microstructure is a dominant factor in the deformation component of macroscopic friction, regardless of indenter size or specified local friction properties. When the skin is assumed to be an assembly of nominally flat layers, the resulting global coefficient of friction is reduced with respect to the local one. This seemingly counterintuitive effect had already been demonstrated in a recent computational study found in the literature. Results also suggest that care should be taken when assigning a coefficient of friction in computer simulations, as it might not reflect the conditions of microscopic and macroscopic friction one intends to represent. The modelling methodology and simulation tools developed in this study go beyond what current analytical models of skin friction can offer: the ability to accommodate arbitrary kinematics (i.e. finite deformations), nonlinear constitutive properties and the complex geometry of the skin microstructural constituents. It was demonstrated how this approach offered a new level of mechanistic insight into plausible friction mechanisms associated with purely structural effects operating at the microscopic scale; the methodology should be viewed as complementary to physical experimental protocols characterising skin friction as it may facilitate the interpretation of observations and measurements and/or could also assist in the design of new experimental quantitative assays. Słowa kluczowe: skin, friction mechanisms, contact mechanics, microstructure, finite element, imagebased modelling, material properties Afiliacje autorów:
 35p.  
16.  Lengiewicz J., Kursa M., Hołobut P., Modularrobotic structures for scalable collective actuation, ROBOTICA, ISSN: 02635747, DOI: 10.1017/S026357471500082X, Vol.35, No.4, pp.787808, 2017 Streszczenie: We propose a new class of modularrobotic structures, intended to produce forces which scale with the number of modules. We adopt the concept of a spherical catom and extend it by a new connection type which is relatively strong but static. We examine analytically and numerically the mechanical properties of two collectiveactuator designs. The simulations are based on the discrete element method (DEM), with friction and elastic deformations taken into account. One of the actuators is shown to generate forces proportional to its volume. This property seems necessary for building modular structures of useful strength and dimensions. Słowa kluczowe: modular robots, selfreconfiguration, programmable matter, actuators, mechanical strength Afiliacje autorów:
 25p.  
17.  LeyvaMendivil M.F.^{♦}, Lengiewicz J., Page A.^{♦}, Bressloff N.W.^{♦}, Limbert G.^{♦}, Implications of Multiasperity Contact for Shear Stress Distribution in the Viable Epidermis – An Imagebased Finite Element Study, BIOTRIBOLOGY, ISSN: 23525738, DOI: 10.1016/j.biotri.2017.04.001, Vol.11, pp.110123, 2017 Streszczenie: Understanding load transfer mechanisms from the surface of the skin to its deeper layers is crucial in gaining a fundamental insight into damage phenomena related to skin tears, blisters and superficial/deep tissue ulcers. It is unknown how shear stresses in the viable epidermis are conditioned by the skin surface topography and internal microstructure and to which extent their propagation is conditioned by the size of a contacting asperities. In this computational study, these questions were addressed by conducting a series of contact finite element analyses simulating normal indentation of an anatomicallybased twodimensional multilayer model of the skin by rigid indenters of various sizes and sliding of these indenters over the skin surface. Indentation depths, local (i.e. microscopic) coefficients of friction and Young's modulus of the stratum corneum were also varied. For comparison purpose and for isolating effects arising purely from the skin microstructure, a geometricallyidealised equivalent multilayer model of the skin was also considered. The multiasperity contact induced by the skin topographic features in combination with a nonidealised geometry of the skin layers lead to levels of shear stresses much higher than those produced in the geometricallyidealised case. These effects are also modulated by other system parameters (e.g. local coefficient of friction, indenter radius). These findings have major implications for the design and analyses of finite element studies aiming at modelling the tribology of skin, particularly if the focus is on how surface shear stress leads to damage initiation which is a process known to occur across several length scales. Słowa kluczowe: Skin, Microstructure, Contact mechanics, Indentation, Sliding contact, Finite element, Imagebased modelling, Material properties Afiliacje autorów:
 
18.  Stupkiewicz S., Lengiewicz J., Sadowski P., Kucharski S., Finite deformation effects in soft elastohydrodynamic lubrication problems, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2015.03.016, Vol.93, pp.511522, 2016 Streszczenie: Soft elastohydrodynamic lubrication regime is typical for many elastomeric and biological contacts. As one or both contacting bodies are then highly compliant, relatively low contact pressures may lead to large deformations which are neglected in the classical EHL theory. In the paper, the related finitedeformation effects are studied for two representative softEHL problems. To this end, a fullycoupled nonlinear formulation has been developed which combines finitestrain elasticity for the solid and the Reynolds equation for the fluid, both treated using the finite element method with full account of all elastohydrodynamic couplings. Results of friction measurements are also reported and compared to theoretical predictions for lubricated contact of a rubber ball sliding against a steel disc under high loads. Słowa kluczowe: SoftEHL problem, Finite deformation, Finite element method, Monolithic scheme Afiliacje autorów:
 35p.  
19.  Stupkiewicz S., Lewandowski M.J., Lengiewicz J., Micromechanical analysis of friction anisotropy in rough elastic contacts, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 00207683, DOI: 10.1016/j.ijsolstr.2014.07.013, Vol.51, No.2324, pp.39313943, 2014 Streszczenie: Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a microtomacro scale transition scheme yields a macroscopic friction model with orientation and pressuredependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak nonassociativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials. Słowa kluczowe: Contact, Friction, Anisotropy, Roughness, Micromechanics Afiliacje autorów:
 35p.  
20.  Lengiewicz J., Wichrowski M.^{♦}, Stupkiewicz S., Mixed formulation and finite element treatment of the massconserving cavitation model, TRIBOLOGY INTERNATIONAL, ISSN: 0301679X, DOI: 10.1016/j.triboint.2013.12.012, Vol.72, pp.143155, 2014 Streszczenie: A mixed formulation of the massconserving cavitation model is developed. The cavitation problem is formulated in terms of the hydrodynamic pressure and a complementary variable representing the void fraction in the cavitation zone. Weak form of the massbalance equation is consistently derived, and it exhibits subtle differences with respect to the available formulations. Finite element treatment preserves the twofield formulation, and a semismooth Newton method is applied to solve the resulting discretized equations. A monolithic Newtonbased scheme is also applied to solve the fully coupled elastohydrodynamic lubrication problem in the softEHL regime. Numerical examples illustrate the performance of the computational scheme. Słowa kluczowe: Lubrication, Cavitation, Reynolds equation, SoftEHL problem Afiliacje autorów:
 35p.  
21.  Lengiewicz J., Stupkiewicz S., Efficient model of evolution of wear in quasisteadystate sliding contacts, WEAR, ISSN: 00431648, DOI: 10.1016/j.wear.2013.03.051, Vol.303, pp.611621, 2013 Streszczenie: A computationally efficient model of evolution of contact and wear is developed for a general periodic pinonflat problem with the focus on the pinondisc configuration and Archard wear model. The evolving contact state is assumed to be fully controlled by the wear process except during a short initial transient period controlled by both wear and elasticity. The contact pressure distribution is thus obtained by considering only the local wear model and the geometry of the conforming contact, without referring to the underlying elasticity problem. Evolution of the contact state is then obtained by time integration of the resulting rateproblem, and two computational schemes are developed for that purpose employing either the forward or the backwardEuler method. The model is successfully verified against a threedimensional finite element model. A dimensionless wearmode index specifying the relative magnitude of wear coefficients of the contact pair is introduced, and model predictions are presented as a function of this parameter. Słowa kluczowe: Contact mechanics, Wear, Simulation, Quasisteadystate process, Rigidwear model, Pinondisc Afiliacje autorów:
 35p.  
22.  Lengiewicz J., Stupkiewicz S., Continuum framework for finite element modelling of finite wear, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2010.12.020, Vol.205208, pp.178188, 2012 Streszczenie: A finite deformation contact problem with friction and wear is studied in which the shape changes due to wear are finite. Accordingly, in addition to the initial configuration and the current configuration, an intermediate timedependent configuration is introduced that corresponds to the undeformed body of the shape changed due to wear. Two time scales are also introduced in order to distinguish the fast time of the actual deformation (contact) problem from the slow time of the wear process (shape evolution problem). Separation of these time scales allows us to partially decouple the deformation problem and the shape evolution problem. Shape parameterization is introduced and the corresponding shape update scheme is formulated as a minimization problem. In particular, a secondorder scheme is developed which exploits shape sensitivities of the deformation problem. Numerical examples are provided to illustrate the performance and accuracy of the proposed numerical schemes. Słowa kluczowe: Frictional contact, Wear, Sensitivity analysis Afiliacje autorów:
 40p.  
23.  Lengiewicz J., Korelc J.^{♦}, Stupkiewicz S., Automation of finite element formulations for large deformation contact problems, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 00295981, DOI: 10.1002/nme.3009, Vol.85, pp.12521279, 2011 Streszczenie: The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automaticdifferentiationbased notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Słowa kluczowe: automatic differentiation, symbolic methods, automation, frictional contact, contact smoothing, augmented Lagrangian method Afiliacje autorów:
 40p.  
24.  Lengiewicz J., Turek K.^{♦}, Lewkowicz J.^{♦}, Models and measures to evaluate the effectiveness of funds utilization for scientific research and development of advanced technologies, Matematyka Stosowana, Vol.12, No.53, pp.111125, 2011 Streszczenie: The purpose of this report was to construct some alternative methods to estimate the effectiveness of investments in scientific research and development of advanced technologies, especially their longterm effects. Study Group decided to focus on the subproblem of finding the relation between the spending on science and the quality of science itself. As a result, we have developed two independent methodologies. The most promising one is based on the theory of timedelay systems, which allows capturing effects of the timelag between the use of funds and the results related to scientific work. Moreover, the methodology gives an opportunity to see kthe optimal spending scenario that would fulfill some prescribed constraints (e.g. it would minimize costs and at the same time remain above a desired level of quality of science). The second methodology is premised on Stochastic Frontier Analysis and it can be applied to determine the form of relation between the amount of financing and the results of scientific work. It offers considerable advantages for analyses of several forms of relation at once (production functions) and for a suitable choice of the best one. Both methods are promising, however, additional work is necessary to apply them successfully to some reallife problems Afiliacje autorów:
 
25.  Stupkiewicz S., Lengiewicz J., Korelc J.^{♦}, Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 00457825, DOI: 10.1016/j.cma.2010.03.021, Vol.199, No.3336, pp.21652176, 2010 Streszczenie: Direct differentiation method of sensitivity analysis is developed for frictional contact problems. As a result of the augmented Lagrangian treatment of contact constraints, the direct problem is solved simultaneously for the displacements and Lagrange multipliers using the Newton method. The main purpose of the paper is to show that this formulation of the augmented Lagrangian method is particularly suitable for sensitivity analysis because the direct differentiation method leads to a noniterative exact sensitivity problem to be solved at each time increment. The approach is applied to a general class of threedimensional frictional contact problems, and numerical examples are provided involving large deformations, multibody contact interactions, and contact smoothing techniques. Słowa kluczowe: Sensitivity analysis, Direct differentiation method, Frictional contact, Augmented Lagrangian method Afiliacje autorów:
 32p. 
Lista rozdziałów w ostatnich monografiach
1. 131  Korelc J.^{♦}, Lengiewicz J., Stupkiewicz S., Analysis and simulation of contact problems, Lecture notes in applied and computational mechanics, rozdział: A study of symbolic description, numerical efficiency and accuracy of 2D and 3D contact formulations, Springer, Wriggers P., Nackenhorst U. (Eds.), 27, pp.111118, 2006  
2. 132  Lengiewicz J., Stupkiewicz S., Korelc J.^{♦}, Rodic T.^{♦}, Analysis and simulation of contact problems, Lecture notes in applied and computational mechanics, rozdział: DDMbased sensitivity analysis and optimization for smooth contact formulations, Springer, Wriggers P., Nackenhorst U. (Eds.), 27, pp.7986, 2006 
Prace konferencyjne
1.  Hołobut P., Bordas S.P.A.^{♦}, Lengiewicz J., Autonomous modelbased assessment of mechanical failures of reconfigurable modular robots with a conjugate gradient solver, IROS, International Conference on Intelligent Robots and Systems, 20201025/1029, Las Vegas (US), pp.1169611702, 2020 Streszczenie: Largescale 3D autonomous selfreconfigurable modular robots are made of numerous interconnected robotic modules that operate in a close packing. The modules are assumed to have their own CPU and memory, and are only able to communicate with their direct neighbors. As such, the robots embody a special computing architecture: a distributed memory and distributed CPU system with a local messagepassing interface. The modules can move and rearrange themselves changing the robot's connection topology. This may potentially cause mechanical failures (e.g., overloading of some intermodular connections), which are irreversible and need to be detected in advance. In the present contribution, we further develop the idea of performing modelbased detection of mechanical failures, posed in the form of balance equations solved by the modular robot itself in a distributed manner. A special implementation of the Conjugate Gradient iterative solution method is proposed and shown to greatly reduce the required number of iterations compared with the weighted Jacobi method used previously. The algorithm is verified in a virtual test bed—the VisibleSim emulator of the modular robot. The assessments of time, CPU, communication and memory complexities of the proposed scheme are provided. Afiliacje autorów:
 
2.  Hołobut P., Lengiewicz J., Distributed computation of forces in modularrobotic ensembles as part of reconfiguration planning, ICRA 2017, IEEE International Conference on Robotics and Automation, 20170529/0603, Marina Bay Sands (SG), DOI: 10.1109/ICRA.2017.7989242, pp.798924221032109, 2017 Streszczenie: We discuss selected mechanical aspects of selfreconfiguration of denselypacked modular robots. The change of connection topology and transport of modules are fundamental mechanisms for these systems, which determine their desired emergent behavior, e.g., movement, shape change or interaction with their surroundings. At the same time, reconfiguration affects the forces between modules. We present a distributed procedure by which a robot can predict if the next planned reconfiguration step will overstress intermodular connections. We use a Finite Element model of a modular robot, with onenodepermodule discretization and beam elements representing intermodular connections. The analysis is restricted to static loads and linear elasticity. We present a distributed procedure of aggregation of the stiffness matrix and iterative solution of the resulting equations of elasticity. The procedure is illustrated with numerical examples and analyzed in terms of its efficiency. © 2017 IEEE. Słowa kluczowe: Finite element method, Modular robots, Stiffness matrix, Distributed computations, Iterative solutions, Reconfiguration planning Afiliacje autorów:
 
3.  Hołobut P., Chodkiewicz P.^{♦}, Macios A.^{♦}, Lengiewicz J., Internal localization algorithm based on relative positions for cubiclattice modularrobotic ensembles, IROS, IROS 2016  IEEE/RSJ International Conference on Intelligent Robots and Systems, 20161009/1014, Daejeon, South Korea (KP), DOI: 10.1109/IROS.2016.7759473, pp.30563062, 2016 Streszczenie: Module localization is an important aspect of the operation of selfreconfigurable robots. The knowledge of spatial positions of modules, or at least of the overall shape which the modules form, is the usual prerequisite for reconfiguration planning. We present a general, decentralized algorithm for determining the positions of modules placed on a cubic grid from local sensor information. The connection topology of the robot is arbitrary. We assume that a module can sense the presence of its immediate neighbors on the grid and determine their positions in its own local coordinate system, but cannot sense the orientations of the coordinate systems of its neighbors. Since orientation cannot be directly communicated between modules, the modules can only exchange information about the relative positions of their neighbors. The algorithm aggregates this information over the entire network of modules and narrows down the set of valid positions for each module as far as possible. If there exists a unique locallyconsistent assignment of coordinates to all modules then it is found. Afiliacje autorów:
 15p.  
4.  Hołobut P., Kursa M., Lengiewicz J., Efficient modularrobotic structures to increase the forcetoweight ratio of scalable collective actuators, IROS 2015, IEEE/RSJ International Conference on Intelligent Robots and Systems, 20150928/1002, Hamburg (DE), DOI: 10.1109/IROS.2015.7353836, pp.33023307, 2015 Streszczenie: A collective actuator is a selfreconfigurable modularrobotic structure which produces useful mechanical work through simultaneous reconfiguration of its constituent units. An actuator is additionally called scalable if its forcetoweight ratio does not depend on the number of its member modules. In this work, we consider scalable collective actuators built from spherical catoms with two connection types: strong but fixed and weak but mobile. We investigate how to construct these actuators in such a way, as to maximize their forcetoweight ratio. We present a number of designs of high strength, whose force capacities significantly exceed those of similar actuators reported previously. Afiliacje autorów:
 15p.  
5.  Hołobut P., Kursa M., Lengiewicz J., A class of microstructures for scalable collective actuation of Programmable Matter, IROS 2014, IEEE/RSJ International Conference on Intelligent Robots and Systems, 20140914/0918, Chicago (US), DOI: 10.1109/IROS.2014.6943113, pp.39193925, 2014 Streszczenie: The term Programmable Matter (PM) describes the class of future metamaterials of programmable and controllable properties and behavior, e.g., able to autonomously transform into an arbitrary shape. The robotic approaches towards PM are based on the concept of cooperation of millions of microrobots (modules), acting at a very fine lengthscale and collectively imitating deformation of a macroscopically continuous material. Recent ideas about reconfiguration of a collective of modules to obtain a desired overall mechanical response are promising. However, they are limited by the strength of individual connections between modules. In the present work, we propose a way of arranging spherical modules into microstructures, in which some connections are fixed and mechanically stronger, and the rest are active (reconfigurable) but weaker. If the fixed connections are sufficiently strong, the proposed microstructures perform the function of collective actuation by exerting forces proportional to their volumes. Two variants of a linearactuator microstructure are presented and studied in more detail. A rotaryactuator microstructure is also introduced. Afiliacje autorów:
 10p. 
Abstrakty konferencyjne
1.  Piranda B.^{♦}, Chodkiewicz P.^{♦}, Hołobut P., Bordas S.^{♦}, Bourgeois J.^{♦}, Lengiewicz J., MODULAR ROBOTS AS DISTRIBUTED COMPUTERS OF THEIR OWN MECHANICAL STATE, CMMSolMech 2022, 24th International Conference on Computer Methods in Mechanics; 42nd Solid Mechanics Conference, 20220905/0908, Świnoujście (PL), No.134, pp.11, 2022  
2.  Piranda B.^{♦}, Chodkiewicz P.^{♦}, Hołobut P., Bordas S.^{♦}, Bourgeois J.^{♦}, Lengiewicz J., Distributed prediction of mechanically unsafe configurations by a system of robotic blocks, ICTAM2021, 25th International Congress of Theoretical and Applied Mechanics, 20210822/0827, Mediolan (virtual) (IT), No.0108761, pp.24132414, 2021 Streszczenie: Summary We present a computational scheme for predicting whether addition of new modules to an existing modular robotic structure will mechanically overload the system, causing it to break or lose stability. The algorithm is executed by the modular robot itself in a distributed way, and relies on the iterative solution of mechanical equilibrium equations derived from a simple Finite Element model of the robot. In the model, intermodular connections are represented as beams and the contact between modules and external supports is accounted for by a predictorcorrector scheme. The algorithm is verified through simulations in the Programmable Matter simulator VisibleSim and reallife experiments on the modular robotic system Blinky Blocks. Afiliacje autorów:
 
3.  Lengiewicz J., Multiscale frictional effects in rough soft contacts, CMIS, Contact Mechanics International Symposium, 20180516/0518, Sanctuary of Oropa, Biella (IT), pp.1011, 2018  
4.  Chodkiewicz P.^{♦}, Zalewski R.^{♦}, Lengiewicz J., Dem modeling of vacuum packed particles dampers, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 20180827/0831, Warszawa (PL), pp.208209, 2018  
5.  Lengiewicz J., LeyvaMendivil M.F.^{♦}, Limbert G.^{♦}, Stupkiewicz S., Macroscopic friction of microscopically rough soft contacts, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 20180827/0831, Warszawa (PL), pp.7475, 2018  
6.  Lengiewicz J., Kursa M., Hołobut P., Twodomain contact model of volumetric actuators, CMIS 2016, Contact Mechanics International Symposium, 20160511/0513, Warszawa (PL), No.P047, pp.9091, 2016  
7.  Lengiewicz J., Kursa M., Hołobut P., Twodomain model of volumetric actuators, ICTAM XXIV, 24th International Congress of Theoretical and Applied Mechanics, 20160821/0826, Montréal (CA), pp.26322633, 2016  
8.  Lengiewicz J., Kursa M., Hołobut P., Actuation by reconfiguration—modular active structures to create Programmable Matter, PCMCMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 20150908/0911, Gdańsk (PL), pp.799800, 2015 Streszczenie: We examine, analytically and numerically, forces produced by collective actuators–possible future building blocks of Programmable Matter. The actuators are composed of tiny spherical robotic modules which can strongly attach to their neighbors, and move by rolling over one another using electric or magnetic local propulsion mechanisms. An actuator works through collective reconfiguration–a coordinated motion of its constituent modules–which results in a global deformation of the structure. The simulations are performed using specially adapted discrete element method software, and account for friction and elastic deformations of modules. Słowa kluczowe: programmable matter, active materials, actuators, mechanical strength, modular robots Afiliacje autorów:
 
9.  Lengiewicz J., Sadowski P., Stupkiewicz S., Finite element modelling of elastohydrodynamic lubrication in the finite deformation regime, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.4344, 2014  
10.  Hołobut P., Kursa M., Macios A.^{♦}, Lengiewicz J., Evolving microstructures for scalable actuation in programmable matter, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.209210, 2014  
11.  Sadowski P., Kucharski S., Lengiewicz J., Stupkiewicz S., Soft elastohydrodynamic lubrication problems in the finite deformation regime: experimental testing and modelling, SolMech 2014, 39th Solid Mechanics Conference, 20140901/0905, Zakopane (PL), pp.323324, 2014 