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In this paper we construct, by means of a variational formulation, the solutions of a problem of elastodynamics which includes the effect of damage for the elastic material. The result is a wave equation with time dependent operators which…

Analysis of PDEs · Mathematics 2020-09-21 Adriana Garroni , Christopher J. Larsen , David Sarrocco

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for…

Analysis of PDEs · Mathematics 2021-09-27 Helmut Abels , Tobias Ameismeier

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…

Analysis of PDEs · Mathematics 2018-06-13 Manuel Friedrich , Martin Kruzik

In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We do not assume the "initial state" assumption and the "div-curl" structure inspired by the works [59,61]. It is…

Analysis of PDEs · Mathematics 2024-03-04 Chengfei Ai , Yong Wang

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out of plane damage. Current models neglect the influence of a finite dissipation…

Materials Science · Physics 2022-06-10 Thibault Roch , Mathias Lebihain , Jean-François Molinari

We propose a phase-field model of dynamic fracture based on the Ambrosio--Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in…

Analysis of PDEs · Mathematics 2025-10-06 Maicol Caponi

A model is derived for the viscoelastic response of glasses at isothermal uniaxial deformation with small strains. A glass is treated as an ensemble of relaxing units with various activation energies for rearrangement. With reference to the…

Materials Science · Physics 2007-05-23 A. D. Drozdov , J. deC. Christiansen

We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued…

Analysis of PDEs · Mathematics 2025-05-08 Ulisse Stefanelli , Andreas Vikelis

In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Chiara Zanini

While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…

Computational Engineering, Finance, and Science · Computer Science 2020-08-13 Hyoung Suk Suh , WaiChing Sun , Devin O'Connor

The work analyzes a one-dimensional viscoelastic model of blood vessel growth under nonlinear friction with surroundings, and provides numerical simulations for various growing cases. For the nonlinear differential equations, two sufficient…

Analysis of PDEs · Mathematics 2010-10-18 Chunjing Xie , Xiaoming Zheng

We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation…

Statistical Mechanics · Physics 2008-09-23 Daniel Bonamy , Stéphane Santucci , Laurent Ponson

We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…

Dynamical Systems · Mathematics 2007-05-23 Eduard Feireisl

We continue our study of the exact solutions for steady-state cracks in ideally brittle viscoelastic lattice models by focusing on mode I in a triangular system. The issues we address include the crack velocity versus driving curve as well…

Materials Science · Physics 2007-05-23 Leonid Pechenik , Herbert Levine , David A. Kessler

A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…

Computational Engineering, Finance, and Science · Computer Science 2026-02-20 Sarah Dinkelacker-Steinhoff , Klaus Hackl

We investigate a model for the accretive growth of an elastic solid. The reference configuration of the body is accreted in its normal direction, with space- and deformation-dependent accretion rate. The time-dependent reference…

Analysis of PDEs · Mathematics 2024-03-14 Elisa Davoli , Katerina Nik , Ulisse Stefanelli , Giuseppe Tomassetti

Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviours have previously been investigated typically using purely elastic substrates. For a…

Biological Physics · Physics 2019-07-31 Partho Sakha De , Rumi De

Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is…

Analysis of PDEs · Mathematics 2024-03-27 Miroslav Bulíček , Tomáš Los , Josef Málek

We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical…

Soft Condensed Matter · Physics 2023-06-09 Yann-Edwin Keta , Rituparno Mandal , Peter Sollich , Robert L. Jack , Ludovic Berthier

In this paper we address a model coupling viscoplasticity with damage in thermoviscoelasticity. The associated PDE system consists of the momentum balance with viscosity and inertia for the displacement variable, at small strains, of the…

Analysis of PDEs · Mathematics 2017-01-03 Riccarda Rossi