相关论文: Energy of a non-linear viscoelastic model compatib…

In the one-dimensional isothermal case, we introduce a simple model of nonlinear viscoelasticity within the Rational Extended Thermodynamics (RET) framework. The differential system is determined by the universal principles of RET,…

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution…

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, the…

We introduce a one-dimensional, hyperbolic model for non-Newtonian fluids with finite relaxation time, derived within the framework of Rational Extended Thermodynamics (RET). Unlike classical parabolic models, our formulation preserves…

We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a…

We study a variant of the well known Maxwell model for viscoelastic fluids, namely we consider the Maxwell fluid with viscosity and relaxation time depending on the pressure. Such a model is relevant for example in modelling behaviour of…

We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present…

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…

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…

We start from a variational model for nematic elastomers that involves two energies: mechanical and nematic. The first one consists of a nonlinear elastic energy which is influenced by the orientation of the molecules of the nematic…

This paper examines the oscillatory behaviour of complex viscoelastic systems with power law-like relaxation behaviour. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which…

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 principle of frame indifference under rotations.…

We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law…

We introduce a data-driven fractional modeling framework aimed at complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous…

We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…

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…

In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent…

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…

Large deformations play a central role in the shape transformations of slender active and biological structures. A classical example is the eversion of the Volvox embryo, which demonstrates the need for shell theories that can describe…