Nonlinear viscoelasticity of strain rate type: an overview

Y Şengül - Proceedings of the Royal Society A, 2021 - royalsocietypublishing.org
There are some materials in nature that experience deformations that are not elastic.
Viscoelastic materials are some of them. We come across many such materials in our daily …

Thermoviscoelasticity in Kelvin–Voigt rheology at large strains

A Mielke, T Roubíček - Archive for Rational Mechanics and Analysis, 2020 - Springer
The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large
strain is formulated in the reference configuration by using the concept of the second-grade …

Nonlinear and linearized models in thermoviscoelasticity

R Badal, M Friedrich, M Kružík - Archive for Rational Mechanics and …, 2023 - Springer
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in
the Kelvin–Voigt rheology, where both the elastic and viscous stress tensors comply with the …

A variational approach to frame-indifferent quasistatic viscoelasticity of rate type

Y Şengül - Philosophical Transactions A, 2024 - royalsocietypublishing.org
The three-dimensional dynamical model for nonlinear viscoelasticity of strain-rate type is
investigated in a quasistatic setting under the assumption of higher-order regularity of the …

Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models

R Badal, M Friedrich, M Kružík, L Machill - arxiv preprint arxiv:2407.02035, 2024 - arxiv.org
According to the Nernst theorem or, equivalently, the third law of thermodynamics, the
absolute zero temperature is not attainable. Starting with an initial positive temperature, we …

Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture

S Almi, E Davoli, M Friedrich - Journal de Mathématiques Pures et …, 2023 - Elsevier
We characterize the passage from nonlinear to linearized Griffith-fracture theories under non-
interpenetration constraints. In particular, sequences of deformations satisfying a Ciarlet …

Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity

M Friedrich, M Kružík - Archive for Rational Mechanics and Analysis, 2020 - Springer
We apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain
setting in Kelvin's-Voigt's rheology to derive a viscoelastic plate model of von Kármán type …

Thermo-elastodynamics of nonlinearly viscous solids

S Almi, R Badal, M Friedrich… - arxiv preprint arxiv …, 2024 - arxiv.org
In this paper, we study the thermo-elastodynamics of nonlinearly viscous solids in the Kelvin-
Voigt rheology where both the elastic and the viscous stress tensors comply with the frame …

Nonlinear relations of viscous stress and strain rate in nonlinear Viscoelasticity

L Machill - Journal of Elasticity, 2025 - Springer
Abstract We consider a Kelvin–Voigt model for viscoelastic second-grade materials, where
the elastic and the viscous stress tensor both satisfy frame-indifference. Using a rigidity …

Derivation of a von K\'arm\'an plate theory for thermoviscoelastic solids

R Badal, M Friedrich, L Machill - arxiv preprint arxiv:2312.07196, 2023 - arxiv.org
We derive a von K\'arm\'an plate theory from a three-dimensional quasistatic nonlinear
model for nonsimple thermoviscoelastic materials in the Kelvin-Voigt rheology, in which the …