Related papers: A continuum and computational framework for viscoe…
In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of…
A polymer-chain network is a collection of interconnected polymer-chains, made themselves of the repetition of a single pattern called a monomer. Our first main result establishes that, for a class of models for polymer-chain networks, the…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Recently, a widely applicable system of hyperbolic partial differential equations has been derived that enables the deterministic computation of a full heterogeneous stress field from a measured deformation field, for example, from a strain…
The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which…
We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of…
We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in $L^2$ norm. The proof is based on an error representation formula using a…
Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…
The classical Cauchy continuum theory is suitable to model highly homogeneous materials. However, many materials, such as porous media or metamaterials, exhibit a pronounced microstructure. As a result, the classical continuum theory cannot…
Constitutive equations are derived for the viscoelastic behavior of filled elastomers at isothermal loading with finite strains. A particle-reinforced rubber is thought of as a composite where regions with low concentrations of junctions…
We study theoretically the profile evolution of a thin viscoelastic film supported onto a no-slip flat substrate. Due to the nonconstant initial curvature at the free surface, there is a flow driven by Laplace pressure and mediated by…
Tangent stabilised large strain isotropic elasticity was recently proposed by Poya et al. [1] wherein by working directly with principal stretches the entire eigenstructure of constitutive and geometric/initial stiffness terms were found in…
Lubricant viscoelasticity arises due to a finite polymer relaxation time ($\lambda$) and can provide beneficial effects. In applications, such as bearings, gears, biological joints, etc., where the height-to-length ratio is small ($H_0 /…
We propose and analyze a generalized finite element method designed for linear quasistatic thermoelastic systems with spatial multiscale coefficients. The method is based on the local orthogonal decomposition technique introduced by…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…