arXiv subjects

Petr Pelech

Publications and source records attributed to Petr Pelech.

4 recordsLinked to original sources

arXiv2021

On compatibility of the Natural configuration framework with GENERIC: Derivation of anisotropic rate-type models

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on~isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible).

cond-mat.stat-mech↗

arXiv2020

Separately Global Solutions to Rate-Independent Processes in Large-Strain Inelasticity

In this paper, we introduce the notion of separately global solutions for large-strain rate-independent systems, and we provide an existence result for a model describing bulk damage. Our analysis covers non-convex energies blowing up for extreme compressions, yields solutions excluding interpenetration of matter, and allows to handle nonlinear couplings of the deformation and the internal variable featuring both Eulerian and Lagrangian terms. In particular, motivated by the theory developed in [49] in the small strain setting, and for separately convex energies we provide a solution concept suitable for large strain inelasticity.

math-ph↗

arXiv2018

Shape memory alloys as gradient-polyconvex materials

We show existence of an energetic solution to a model of shape memory alloys in which the elastic energy is described by means of a gradient-polyconvex functional. This allows us to show existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Resulting deformations are orientation-preserving and injective everywhere in a domain representing the specimen.

math.AP↗

arXiv2018

The Peridynamic Stress Tensors and the Non-local to Local Passage

We re-examine the notion of stress in peridynamics. Based on the idea of traction we define two new peridynamic stress tensors $\mathbf{P}^{\mathbf{y}}$ and $\mathbf{P}$ which stand, respectively, for analogues of the Cauchy and 1st Piola-Kirchhoff stress tensors from classical elasticity. We show that the tensor $\mathbf{P}$ differs from the earlier defined peridynamic stress tensor $ν$; though their divergence is equal. We address the question of symmetry of the tensor $\mathbf{P}^{\mathbf{y}}$ which proves to be symmetric in case of bond-based peridynamics; as opposed to the inverse Piola transform of $ν$ (corresponding to the analogue of Cauchy stress tensor) which fails to be symmetric in general. We also derive a general formula of the force-flux in peridynamics and compute the limit of $\mathbf{P}$ for vanishing non-locality, denoted by $\mathbf{P}_0$. We show that this tensor $\mathbf{P}_0$ surprisingly coincides with the collapsed tensor $ν_0$, a limit of the original tensor $ν$. At the end, using this flux-formula, we suggest an explanation why the collapsed tensor $\mathbf{P}_0$ (and hence $ν_0$) can be indeed identified with the 1st Piola-Kirchhoff stress tensor.

physics.class-ph↗