Related papers: Existence and regularity of solutions for an evolu…
This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…
We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in…
We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mechanism in the model prevents us from establishing even a…
We consider a thermodynamically consistent model for thermoviscoplasticity. For the related PDE system, coupling the heat equation for the absolute temperature, the momentum balance with viscosity and inertia for the displacement variable,…
This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable…
In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic…
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition…
We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…
The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the…
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
We discuss a finite-plasticity model based on the symmetric tensor $P^T P$ instead of the classical plastic strain $P$. Such a model structure arises from assuming that the material behavior is invariant with respect to frame…
We consider the two dimensional unsteady Prandtl system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative of the tangential velocity along the transversal axis solves a…
We present a continuum model for the propagation of cracks and fractures in brittle materials. The components of the strain tensor $\epsilon$ are the fundamental variables. The evolution equations are based on a free energy that reduces to…
We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending…
We derive a F\"{o}ppl-von K\'{a}rm\'{a}n-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we…
We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In…