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Related papers: On 2D Viscoelasticity with Small Strain

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In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a…

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

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…

Analysis of PDEs · Mathematics 2020-07-14 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli

The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and…

Analysis of PDEs · Mathematics 2020-03-03 Xiaoping Zhai , Zhi-Min Chen

A model of saturated hyperelastic porous solids at large strains is formulated and analysed. The material response is assumed to be of a viscoelastic Kelvin-Voigt type and inertial effects are considered, too. The flow of the diffusant is…

Analysis of PDEs · Mathematics 2022-10-13 Tomas Roubicek , Ulisse Stefanelli

We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…

Analysis of PDEs · Mathematics 2025-10-01 Fan Cheng , Robert Lasarzik , Marita Thomas

The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a…

Dynamical Systems · Mathematics 2015-10-20 George Haller

A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…

Analysis of PDEs · Mathematics 2024-08-28 Willem J. M. van Oosterhout

We are interested in the multi-dimentional compressible viscoelastic flows of Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to capture the damping effect of the additional deformation tensor,…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu , Yi Zhu

By revisiting a model proposed in [45], we address the accretive growth of a viscoelastic solid at large strains. The accreted material is assumed to accumulate at the boundary of the body in an unstressed state. The growth process is…

Analysis of PDEs · Mathematics 2025-08-28 Andrea Chiesa , Ulisse Stefanelli

This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu

In this paper, we consider a two-phase flow model consisting of the compressible Navier-Stokes systems with degenerate viscosity coupled with the compressible Navier-Stokes systems with constant viscosities via a drag force, which can be…

Analysis of PDEs · Mathematics 2022-03-11 Ya-Ting Wang , Ling-Yun Shou

We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an…

In a continuum description of materials, the stress tensor field $\bar{% \bar{\sigma}}$ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that…

Soft Condensed Matter · Physics 2007-05-23 Marius Asipauskas , Miguel Aubouy , James A. Glazier , François Graner , Yi Jiang

The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity…

Materials Science · Physics 2020-01-15 Péter Dusán Ispánovity , Stefanos Papanikolaou , István Groma

We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…

Analysis of PDEs · Mathematics 2019-10-23 Martin Kalousek

Traditionally, the deformation of continuum is divided into elastic, plastic, and flow. For a large deformation with cracking, they are combined together. So, for complicated deformation, a formulation to express the evolution of…

Classical Physics · Physics 2007-05-23 Jianhua Xiao

We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is…

Analysis of PDEs · Mathematics 2020-10-23 Dan Crisan , Oana Lang

The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts…

Analysis of PDEs · Mathematics 2023-11-08 Franz Achleitner , Anton Arnold , Volker Mehrmann

Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional…

Materials Science · Physics 2010-10-15 Thomas Hochrainer , Michael Zaiser , Peter Gumbsch

We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…

Analysis of PDEs · Mathematics 2015-09-11 Sergio Frigeri , Ciprian G. Gal , Maurizio Grasselli