Related papers: A variational principle for hardening elastoplasti…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front…
We consider a variational approximation scheme for the 3D elastodynamics problem. Our approach uses a new class of admissible mappings that are closed with respect to the space of mappings with finite distortion.
We present a novel theory of the adhesive contact of linear viscoelastic materials against rigid substrates moving at constant velocity. Despite the non-conservative behavior of the system, the closure equation of the contact problem can be…
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
A rate-independent model for the quasistatic evolution of a magnetoelastic thin film is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary $\Gamma$-convergence argument in order to pass to the…
We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing…
Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient…
We determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified medium comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to…
We propose a generalized finite element method for linear elasticity equations with highly varying and oscillating coefficients. The method is formulated in the framework of localized orthogonal decomposition techniques introduced by…