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Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into…

Numerical Analysis · Mathematics 2021-10-27 Patrick Dondl , Martin Jesenko , Martin Kružík , Jan Valdman

We derive an effective one-dimensional limit from a three-dimensional Kelvin-Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comply with a frame-indifference principle. The limiting system…

Analysis of PDEs · Mathematics 2023-12-13 Manuel Friedrich , Lennart Machill

An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…

Analysis of PDEs · Mathematics 2025-06-13 S. N. Antontsev , H. B. de Oliveira , I. V. Kuznetsov , D. A. Prokudin , Kh. Khompysh

This work presents a new constitutive and computational framework based on strain-like internal variables belonging to Sym(3) and two representative rheological configurations. The generalized Maxwell and generalized Kelvin-Voigt models are…

Soft Condensed Matter · Physics 2025-08-21 Chongran Zhao , Hongyan Yuan , Ju Liu

We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…

Analysis of PDEs · Mathematics 2026-03-02 Yoshiho Akagawa , Kazunori Matsui

The semi-implicit (partly decoupled, also called staggered or fraction-step) time discretization is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e.\ in the actual deforming…

Numerical Analysis · Mathematics 2025-10-14 Tomáš Roubíček

In this paper we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a…

Analysis of PDEs · Mathematics 2025-10-06 Maicol Caponi , Alessandro Carbotti , Francesco Sapio

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…

Analysis of PDEs · Mathematics 2024-10-10 Gennaro Ciampa , Giulio G. Giusteri , Alessio G. Soggiu

The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions…

Analysis of PDEs · Mathematics 2025-02-05 Tomáš Roubíček

This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for…

Analysis of PDEs · Mathematics 2014-02-06 Dorothee Knees , Riccarda Rossi , Chiara Zanini

We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…

Numerical Analysis · Mathematics 2023-06-27 Salim Meddahi , Ricardo Ruiz-Baier

A simple, yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced.…

Numerical Analysis · Mathematics 2014-02-27 C. G. Panagiotopoulos , V. Mantic , T. Roubicek

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The…

Analysis of PDEs · Mathematics 2023-02-23 Tomáš Roubíček

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Antonio DeSimone , Maria Giovanna Mora , Massimiliano Morini

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…

Numerical Analysis · Mathematics 2015-05-13 A. V. Shutov , R. Kreissig

We analyze the finite-strain Poynting-Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin-Voigt viscoelastic element. In the finite-strain case,…

Analysis of PDEs · Mathematics 2023-12-20 A. Chiesa , M. Kružík , U. Stefanelli

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

Analysis of PDEs · Mathematics 2022-02-23 Lorena Bociu , Boris Muha , Justin T. Webster

We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…

Analysis of PDEs · Mathematics 2023-12-22 Thomas Eiter , Katharina Hopf , Robert Lasarzik

The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of thermo-viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration, formulated…

Numerical Analysis · Mathematics 2025-12-09 Tomáš Roubíček

We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the…

Analysis of PDEs · Mathematics 2020-09-24 Roberto Alessi , Vito Crismale , Gianluca Orlando