Related papers: A unified model for stress-driven rearrangement in…
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…
Some variational micro-macro models are briefly reviewed: it is shown how, starting from the Taylor model and passing through the relaxed Taylor model, a consistent intermediate between Taylor's upper bound and the lower bound (Sachs or…
We consider flow along a finite-length collapsible channel driven by a fixed upstream flux, where a section of one wall of a planar rigid channel is replaced by a plane-strain elastic beam subject to uniform external pressure. A modified…
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
Voids can limit the life of engineering components. This motivates us to understand local plasticity around voids in a nickel base superalloy combining experiments and simulations. Single crystal samples were deformed in tension with…
Some variational problems for a Foppl-von Karman plate subject to general equilibrated loads are studied. The existence of global minimizers is proved under the assumption that the out-of-plane displacement fulfils homogeneous Dirichlet…
Understanding thermal fluctuations yields insights into a wide range of behaviors in many-body systems. In this work, we analyze the dynamical adaptation of two-dimensional crystalline lattice system under harmonic interaction in response…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
We study the interior and exterior contact problems for hemitropic elastic solids. We treat the cases when the friction effects, described by Tresca friction (given friction model), are taken into consideration either on some part of the…
We examine the dynamics of a compressible active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model…
This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and…
In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…
The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
A unified classification framework for models of extended plasticity is presented. The models include well known micromorphic and strain gradient plasticity formulations. A unified treatment is possible due to the representation of strain…