Instytut Podstawowych Problemów Techniki

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Estimation of macroscopic properties of heterogeneous materials has always posed significant problems. Procedures based on numerical homogenization, although very flexible, consume a lot of time and computing power. Thus, many attempts have been made to develop analytical models that could provide robust and computationally efficient tools for this purpose. The goal of this paper is to develop a reliable analytical approach to finding the effective elastic–plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: “hard-in-soft” (MMC) and “soft-in-hard” (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%.

Słowa kluczowe:

Periodic composite , Micro-mechanics , Effective properties, Elasto-plasticity, Particle interactions

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The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori–Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approach to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an inhomogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

Słowa kluczowe:

composite material, micromechanics, computational modelling, packing effect, shape effect

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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 no-sliding 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 real-life experiments on the modular robotic system Blinky Blocks.

Słowa kluczowe:

distributed algorithms, modular robots, mechanical constraints, programmable matter, self-reconfiguration

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The issue of applicability of the Morphologically Representative Pattern (MRP) approach to elastic-plastic composites is addressed. The extension to the regime of non-linear material behaviour is performed by employing the concept of incremental linearization of the material response in two basic variants: tangent and secant. The obtained predictions are evaluated through comparison with the outcomes of numerical analyses. Finite Element simulations are carried out using periodic unit cells with cubic arrangements of spherical particles and representative volume elements (RVE) with 50 randomly placed inclusions. In addition to the analysis of the packing effect in two-phase composites, the size effect is also studied by assuming an interphase between the matrix and inclusions. It is concluded that the MRP approach can be used as an effective predictive alternative to computational homogenization, not only in the case of linear elasticity but also in the case of elastic-plastic composites.

Słowa kluczowe:

particulate composites, elastoplasticity, micromechanics, size effect, packing effect, morphologically representative pattern

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We propose a methodology of planning effective shape shifting and locomotion of large-ensemble 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 surface-flow 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 cubic-lattice-based.

Słowa kluczowe:

modular robots, self-reconfiguration, maximum flow search, programmable matter, distributed algorithms

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Effects of particle packing and size on the overall elastic properties of particulate random composites are analyzed. In order to account for the two effects the mean-field Morphologically Representative Pattern (MRP) approach is employed and an additional interphase surrounding inclusions (coating) is introduced. The analytical mean-field estimates are compared with the results of computational homogenization performed using the finite element (FE) method. Periodic unit cells with cubic crystal-type arrangements and representative volume elements with random distributions of particles are used for verification purposes. The validity of the MRP estimates with respect to the FE results is assessed.

Słowa kluczowe:

Composite materials, Elasticity, Micro-mechanics, Packing and size effects

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The purpose of this work is the development of an efficient and high-sensitive damage localization technique for truss structures, based on the rank-revealing QR decomposition (RRQR) of the difference-of-flexibility matrix. The method is an enhancement of the existing techniques of damage detection, which rely on the set of so-called damage locating vector (DLV). The advantages of the RRQR decomposition-based DLV (RRQR-DLV) method are its less computational effort and high sensitivity to damage. Compared with the frequently used stochastic DLV (SDLV) method, RRQR-DLV offers higher sensitivity to damage, which has been validated based on the presented numerical simulation. The effectiveness of the proposed RRQR-DLV method is also illustrated with the experimental validation based on a laboratory-scale Bailey truss bridge model. The proposed method works under ambient excitation such as traffic excitation and wind excitation; therefore, it is promising for real-time damage monitoring of truss structures.

Słowa kluczowe:

damage localization, rank-revealing QR decomposition, damage sensitivity, truss structure, structural health monitoring

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We propose a new class of modular-robotic 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 collective-actuator 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, self-reconfiguration, programmable matter, actuators, mechanical strength

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In the paper we show how some basic informational quality measures (e.g. the Shannon entropy and the relative entropy/Kullback-Leibler divergence) defined for stochastic dynamical systems change in time and how they depend on the system properties and intensity of random disturbances. First, the Liouvillian systems (when randomness is present in the initial states only) are discussed and then various (linear and nonlinear) systems with random external excitations are treated in detail. Both, general and specific systems are considered, including numerical and graphical illustrations.

Słowa kluczowe:

stochastic dynamics, information, entropy, relative entropy, information gain, non-Gaussian prediction, maximum entropy approximation

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A stochastic analysis of hydrogen-assisted fatigue crack growth in steel plates is presented. First, a simplified deterministic model of the process is proposed. It captures the basic empirical property that the influence of hydrogen diminishes, as the crack growth rate increases. However, it only applies to cases, when diffusion is rate-limiting. Next, the model parameters are randomized to reflect the uncertainty inherent in the physical situation. On the basis of the obtained stochastic equation, probabilistic moments of the time, in which the crack reaches a critical length, are computed. Theoretical results are illustrated by a numerical example.

Słowa kluczowe:

random fatigue, crack growth model, hydrogen embrittlement, hydrogen diffusion, probabilistic moment, time to failure

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A method of predicting fatigue crack growth in hydrogen-charged thin steel plates is proposed. It consists in computing modified stress intensity factors which reflect the presence of hydrogen, and using them in a fatigue crack growth equation for an uncharged plate. The modification accounts for both, hydrogen embrittlement of crack tips and hydrogen-induced residual stresses in the plate. The new stress intensity factors are derived for two special cases - uniform and stationary hydrogen distribution in the plate. With their use bounds are established on the rate of hydrogen-assisted fatigue crack growth. Theoretical results are illustrated by numerical calculations.

Słowa kluczowe:

hydrogen fatigue, crack growth model, hydrogen embrittlement, residual stresses

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The paper presents a method for quantitative characterization of random hydrogen-induced stresses. The method is based on randomized diffusion-elasticity equations. Also a stochastic parametric model, suitable for representing relevant empirical data, is outlined. The general considerations are illustrated by two particular examples. The first one concerns the effect of random hydrogen concentration on material failure time in a half-space, whereas the second one shows its effect on the Mode-I stress intensity factor for a crack in a circular cylinder.

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A method of optimization intended to speed up motions of non-redundant hydraulic manipulators along prescribed paths of their end-effectors is presented. A parametric path of the end-effector of a non-redundant manipulator determines the corresponding path in the manipulator joint-space. The optimization problem therefore reduces to finding the optimum distribution of the parameter of the path in time. The proposed optimization scheme is based on discretization of the distribution of the parameter into a fixed number of points, and finding their optimum locations by methods of constrained nonlinear programming. Incompressibility of the hydraulic fluid is assumed throughout for greater effectiveness of the procedure. Results of sample optimizations performed on a three-link hydraulic excavator are presented.

Słowa kluczowe:

hydraulic manipulators, time-optimal control, trajectory optimization

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Large-scale 3D autonomous self-reconfigurable 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 inter-modular connections), which are irreversible and need to be detected in advance. In the present contribution, we further develop the idea of performing model-based 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.

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This paper presents the measurement and model updating of a pedestrian's center of mass trajectory. A mathematical model proposed by the authors is updated using the actual trajectory of a pedestrian. The mathematical model is based on the principle that a human's control capability tries to maintain balance with respect to the pedestrian's center of mass (CoM), independently of the surface type. In this research, the human is considered as a mass point concentrated at CoM. The parameters of the models are updated using experimental identification of the human walking trajectory on a rigid surface. The proposed measurement technique uses a depth sensor, which enable skeletal tracking of the pedestrian walking on rigid or flexible structures. Experiments were performed using a mobile platform with the time-of-flight commercial camera Microsoft Kinect for Windows 2.0. The velocity of the mobile platform is set to maintain a 1 m separation from the pedestrian in order to provide high resolution. The results of the measurement technique allowed the identification of the human's CoM trajectory. The results of the model updating process present the probability density function of the parameters which could be used for modeling the CoM's trajectory of the pedestrian.

Słowa kluczowe:

Human-structure interaction, Pedestrian's trajectory, Human-induced vibrations, MS Kinect sensor

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We discuss selected mechanical aspects of self-reconfiguration of densely-packed 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 one-node-per-module 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

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Module localization is an important aspect of the operation of self-reconfigurable 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 locally-consistent assignment of coordinates to all modules then it is found.

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We present a new human-structure interaction (HSI) model of walking on a flexible surface. A human is considered as a mass point, located at the body’s center of mass (COM). The mass moves along a predefined trajectory, which deforms together with the surface on which the human walks. The forces of motion, equal to the sum of inertial and gravitational forces acting on the mass, are transfered to the surface at prescribed foot positions. The motion of the surface is described using a few selected mode shapes, corresponding damping ratios, and natural frequencies. The equations of motion of the system are time-dependent and discontinuous. They can be written in the form of the second order differential equations of structural dynamics, but with the right-hand forcing dependent on the deformation of the surface. We present a numerical example of a human walking on a long beam structure. The motion of the beam is described by three mode shapes, representing its vertical, lateral, and torsional deflections.

Słowa kluczowe:

Human induced vibrations, Dynamics of bridges, Human walking model

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A collective actuator is a self-reconfigurable modular-robotic structure which produces useful mechanical work through simultaneous reconfiguration of its constituent units. An actuator is additionally called scalable if its force-to-weight 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 force-to-weight ratio. We present a number of designs of high strength, whose force capacities significantly exceed those of similar actuators reported previously.

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The term Programmable Matter (PM) describes the class of future meta-materials 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 micro-robots (modules), acting at a very fine length-scale 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 linear-actuator microstructure are presented and studied in more detail. A rotary-actuator microstructure is also introduced.

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Słowa kluczowe:

NiAl crystal, cubic anisotropy, Deformable Discrete Element Method, numerical modeling, mechanical properties

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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, inter-modular connections are represented as beams and the contact between modules and external supports is accounted for by a predictor-corrector scheme. The algorithm is verified through simulations in the Programmable Matter simulator VisibleSim and real-life experiments on the modular robotic system Blinky Blocks.

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Słowa kluczowe:

Representative Volume Element, Effective Properties, Random Microstructure

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Słowa kluczowe:

mean-field modelling, numerical homogenization, elasto-plasticity

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Different approaches to model packing and size effects are studied to model overall properties of particulate composites of different morphological features of phase distribution. The micromechanical schemes originating in the composite sphere model and its extension by morphologically-based pattern approach are taken as a basis. Analytical predictions are compared with results of computational homogenization performed on the generated representative volume elements of prescribed statistical characteristics.

Słowa kluczowe:

micromechanics, morphologically representative pattern, computational homogenization, size and scale effect

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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

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