Finite strain of cylindrical body rotating with acceleration

Рассмотрена задача деформирования цилиндрического тела вращающегося вокруг центральной оси с ускорением. Получены итоговая система уравнений, описывающая данный процесс в рамках математической модели теории больших деформаций при наличии необратимых деформаций. Рассмотрен частный случай упругого деформирования, для которого приведены выражения для расчёта напряжений и деформаций в среде, а также итоговые дифференциальные соотношения, решение которых необходимо искать. The problem of deformation of cylindrical body rotating with acceleration is considered. The system of equations describing this process in general case with non zero irreversible strains in frame of finite strain theory was obtained. A particular case of elastic deformation was considered and the resulting equations for this case was obtained.

Modeling the mechanobioelectricity of cell clusters

We propose a continuum finite strain theory for the interplay between the bioelectricity and the poromechanics of a cell cluster. Specifically, we refer to a cluster of closely packed cells, whose mechanics is governed by a polymer network of cytoskeletal filaments joined by anchoring junctions, modeled through compressible hyperelasticity. The cluster is saturated with a solution of water and ions. We account for water and ion transport in the intercellular spaces, between cells through gap junctions, and across cell membranes through aquaporins and ion channels. Water fluxes result from the contributions due to osmosis, electro-osmosis, and water pressure, while ion fluxes encompass electro-diffusive and convective terms. We consider both the cases of permeable and impermeable cluster boundary, the latter simulating the presence of sealing tight junctions. We solve the coupled governing equations for a one-dimensional axisymmetric benchmark through finite elements, thus determining the spatiotemporal evolution of the intracellular and extracellular ion concentrations, setting the membrane potential, and water concentrations, establishing the cluster deformation. When suitably complemented with genetic, biochemical, and growth dynamics, we expect this model to become a useful instrument for investigating specific aspects of developmental mechanobioelectricity.

Modified Green–Lindsay thermoelasticity wave propagation in elastic materials under thermal shocks

In this study, a nonlinear numerical method is presented to solve the governing equations of generalized thermoelasticity in a large deformation domain of an elastic medium subjected to thermal shock. The main focus of the study is on the modified Green–Lindsay thermoelasticity theory, solving strain and temperature rate-dependent model using finite strain theory. To warrant the continuity of the finding responses at the boundary after the applied shock, higher order elements are adopted. An analytical solution is provided to validate the numerical findings and an acceptable agreement between the two presented solutions is obtained. The findings revealed that stress and thermal waves have distinct interactions and a harmonic temperature variation may lead to a systematic uniform stress distribution. Besides, a notable difference in the results predicted by the modified Green–Lindsay model and classic theory is observed. It is also found that the modified Green–Lindsay theory is more efficient in determining the wave propagation phenomenon. Furthermore, the findings established that thermal shock induces tensile stresses in the structure immediately after the shock, and the perceived phenomenon mainly depends on the defined boundary conditions. The results show that the strain rate can have a significant influence on the displacement and stress wave propagation in a structure subjected to thermal shock and these impacts may be more considerable with mechanical loading.

Characterization of the Hot Anode Paste Compaction Process: A Computational and Experimental Study

The aim of this work is to model and characterize green anode paste compaction behavior. For this purpose, a nonlinear viscoplastic constitutive law for compressible materials, based on the finite strain theory and the thermodynamic framework, was used. An experimental study was carried out to characterize axial and radial behaviors of the anode paste. To this end, simple compaction tests using a thin steel instrumented mold were performed at a temperature of 150 °C. Results of these experiments brought out the nonlinear mechanical behavior of the anode paste. Furthermore, they showed the importance of its radial behavior. The constitutive law was implemented in Abaqus software through the user’s material subroutine VUMAT for explicit dynamic analysis. An inverse analysis procedure for material parameters identification showed that the model predicts compaction tests results with a good agreement. In order to assess the constitutive law predictive potential in situations involving density gradients, compaction tests using complex geometries such as slots and stub holes were carried out. Finite element simulation results showed the ability of the model to successfully predict density profiles measured by the X-ray tomography.