Related papers: A variational principle for hardening elastoplasti…
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…
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
In this paper we consider an optimal control problem governed by a time-dependent variational inequality arising in quasistatic plasticity with linear kinematic hardening. We address certain continuity properties of the forward operator,…
We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the…
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
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…
We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…
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…
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement fields and their associated crack sets converge to a solution…
In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…
We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…
In this work we study a quasi-static evolution of thermo-visco-elastic model with homogeneous thermal expansion. We assume that material is subject to two kinds of mechanical deformations: elastic and inelastic. Inelastic deformation is…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…