Instytut Podstawowych Problemów Techniki

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When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this natural approach can prove cumbersome if the geometry is complex, in particular in 3D. In this work, we develop an efficient technique for a non-conforming finite-element treatment of weak discontinuities by using laminated microstructures. The approach is inspired by the so-called composite voxel technique that has been developed for FFT-based spectral solvers in computational homogenization. The idea behind the method is rather simple. Each finite element that is cut by an interface is treated as a simple laminate with the volume fraction of the phases and the lamination orientation determined in terms of the actual geometrical arrangement of the interface within the element. The approach is illustrated by several computational examples relevant to the micromechanics of heterogeneous materials. Elastic and elastic-plastic materials at small and finite strain are considered in the examples. The performance of the proposed method is compared to two alternative, simple methods showing that the new approach is in most cases superior to them while maintaining the simplicity.

Słowa kluczowe:

Finite element method,Interface,Weak discontinuity,Laminate,Homogenization,Elasticity,Plasticity

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Inspired by the high-speed camera experiments of YouTuber Destin Sandlin (SmarterEveryDay) [D. Sadlin, Dominoes – hardcore mode (2021), [Online; accessed 15-Jul-2021].] on the toppling speed of dominoes over different surfaces, we performed discrete-element simulations of this process, varying the spacing between adjacent and evenly spaced blocks (dominoes). We also varied the block-block and block-surface friction coefficients over a wide range of values to have a complete picture of the behavior of these cooperative, dissipative mechanical systems. We found that a steady wavefront speed v exists for a specific interval of spacings between dominoes and coefficients of friction. Surprisingly, while v is more affected by the domino-domino friction, the domino-surface friction determines whether or not toppling anomalies can appear and stop the wave. Finally, our observations led us to propose a scaling law that is able to predict v based on the domino configuration and friction coefficients, and to correctly reproduce experimental tests.

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Bactericidal properties of honey depend on botanical and geographical origin, where thermal treatment can have a significant affect. The aim of this study was to investigate the effect of temperature on minimum bactericidal concentration (MBC), vitamin C content, total polyphenols content and antioxidant capacity of ferric reducing antioxidant potential (FRAP) of several nectar honey varieties from northern Poland (lime, rapeseed, multifloral and buckwheat). The honeys were subjected to thermal treatment at 22 °C, 42 °C, 62 °C, 82 °C and 100 °C for two exposure times. The results showed a significant reduction of antimicrobial properties (MBC 50%) at 82 °C and 62 °C after 15 and 120 min exposure time for most samples. Short time exposure reduced vitamin C content (50 %) but increased total polyphenols content (27%) and FRAP value (106%).

Słowa kluczowe:

honey, vitamin C, polyphenols, antioxidant properties, antibacterial activity, temperature treatment

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This study deals with the secondary creep of a porous nuclear fuel. This material is composed of an isotropic matrix, weakened by randomly distributed clusters of pores. The viscous strain in the matrix is described by two power-law viscosities corresponding to two different creep mechanisms. The material microstructure is analyzed and appropriate descriptors of its morphology are identified. Representative Volume Elements (RVE's) are generated according to these descriptors. The local fields and overall response of these realizations RVE's are simulated within the framework of periodic homogenization using a full-field computational method based on Fast Fourier Transforms. An analytical model based on appropriate approximations of the effective potential governing the overall response of porous materials under creep is proposed. The accuracy of the model is assessed by comparing its predictions with full-field simulations and the agreement is found to be quite satisfactory.

Słowa kluczowe:

porous media, viscoplasticity, FFT method, homogenization, mathematical morphology, microstructures

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We present a numerical method for estimating the stiffness-to-porosity relationships for evolving microstructures of Fontainebleau sandstone. The proposed study is linked to geological storage of CO 2 and focuses on long-term and far field conditions, when the progressive degradation of the porous matrix can be assumed to be homogeneous at the sample scale. The method is based on microstructure sampling with respect to morphological descriptors extracted from microtomography. First, an efficient method of generation of accurate numerical media is proposed. The method is based on grain deposit, compaction and diagenesis and allows to reproduce user-defined morphological parameters. Second, two simple numerical models that mimic chemical degradation of porous aquifers are presented. Effective elastic properties are estimated within the framework of periodic homogenization and finite element approach. A fixed-point method on a self-consisted outer layer allows to consider non-periodic representative volume elements. Accurate predictions of elastic properties over a wide range of porosity are obtained. The overall evolutions of elastic behaviour due to the increase of porosity are in excellent agreement both, with experimental data and the results obtained by Arns et al. [1].

Słowa kluczowe:

Porous media, X-ray microtomography, Numerical dissolution, Fontainebleau sandstone, Self-consisted numerical method, Homogenization

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The paper is motivated by the long-term safety analysis of the CO2 geological storage. We present a methodology for the assessment of the geomechanical impact of progressive rock dissolution. The method is based on the use of X-ray tomography and the numerical dissolution technique. The influence of evolution of the microstructure on the macroscopic properties of the rock is analysed by using periodic homogenization method. The numerical computations show progressive degradation of all components of the stiffness (orthotropic) tensor. Moreover, the evolution of associated mass transfer properties (as tortuosity and conductivity tensors), by using the periodic homogenization method, is also calculated. The correlation between the mechanical parameters and the transfer properties during the dissolution process is presented. The results show that the highest increase of the hydraulic conductivity (in direction Y) is not associated with the highest decrease of Young modulus in this direction. Moreover, the highest decrease of Young modulus (in the direction X) is not associated with percolation in this direction. Finally, an incremental law to calculate settlement, in case of a rock with evolving microstructure, is proposed. The solution of the macroscopic settlement problem under constant stress and drained conditions showed that the geomechanical effects of the rock dissolution are rather limited.

Słowa kluczowe:

CO2 storage, homogenization, chemo-mechanical coupling, microstructure, X-ray tomography, numerical computations

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