Related papers: A continuum and computational framework for viscoe…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
This paper deals with the rigorous study of the diffusive stress relaxation in the multidimensional system arising in the mathematical modeling of viscoelastic materials. The control of an appropriate high order energy shall lead to the…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
We report a method for describing plasticity in a broad class of amorphous materials. The method is based on nonlinear (geometric) deformation theory allowing the separation of the plastic deformation from the general deformation tensor.…
We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
A macro-constitutive model for the deformation response of periodic rotating bistable auxetic surfaces is developed. Focus is placed on isotropic surfaces made of bistable hexagonal cells composed of six triangular units with two stable…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the…
This work presents a unified viscoelastic-viscoplastic continuum framework for modeling rate-dependent granular flows across regimes. The formulation incorporates two distinct rate-dependent mechanisms, namely micro-inertia and viscoelastic…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…
In the spirit of the "Principle of Equipresence" introduced by Truesdell & Toupin, The Classical Field Theories (1960), we use the full version of the viscous stress tensor which was originally derived for compressible flows, instead of the…
A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the `natural…
A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano- and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…