Related papers: A dynamic model for viscoelastic materials with pr…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in…
In this paper we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is…
In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
We investigate crack propagation in a simple two-dimensional visco-elastic model and find a scaling regime in the relation between the propagation velocity and energy release rate or fracture energy, together with lower and upper bounds of…
Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward…
A non-linear history-dependent cohesive zone model of crack propagation in linear elastic and visco-elastic materials is presented. The viscoelasticity is described by a linear Volterra integral operator in time. The normal stress on the…
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…
Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent,…
One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…
Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article, we have presented comprehensive new results for the critical behavior of the dynamic susceptibility of disordered…
Materials with properties that are modulated in time are known to display wave phenomena showing energy increasing with time, with the rate mediated by the modulation. Until now there has been no accounting for material dissipation, which…
This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to…
Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…