Related papers: A Gibbs-potential-based framework for ideal plasti…
We extend the results about existence of minimizers, relaxation, and approximation proven by Chambolle et al. in 2002 and 2007 for an energy related to epitaxially strained crystalline films, and by Braides, Chambolle, and Solci in 2007 for…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
Microstructural changes in solids, driven by energy flows, do not develop in a static continuous space, such as the space considered in conventional plasticity models. The applied forces create an evolving internal energy landscape, which…
We present a gradient-based theoretical framework for predicting hydrogen assisted fracture in elastic-plastic solids. The novelty of the model lies in the combination of: (i) stress-assisted diffusion of solute species, (ii) strain…
We study the interaction of small hydrophobic particles on the surface of an ultra-soft elastic gel, in which a small amount of elasticity of the medium balances the weights of the particles. The excess energy of the surface of the deformed…
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain…
Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are…
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…
We consider a simple lattice spring model in which every spring is elastoplastic and is capable to conduct current. The elasticity bounds of spring $i$ are taken as $[-c_i,c_i]$ and the resistance of spring $i$ is taken as $1/c_i$, which…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…
In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
The isothermal quasistatic (i.e.\ acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition of the total strain and the isochoric plastic distortion. The Eulerian…
A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field $\bi u$ and the lattice velocity ${\bi v}=\p {\bi u}/\p t$. Damping is…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
Impact of single particle onto a rigid substrate leads to its deformation and fragmentation. The flow associated with the particle spreading on a solid substrate after impact is extremely complicated. In this theoretical study a simplified…
A quasi 2-dimensional recursive lattice formed by planar elements have been designed to investigate the surface thermodynamics of Ising spin glass system with the aim to study the metastability of supercooled liquids and the ideal glass…
The propulsion of many eukaryotic cells is generated by flagella, flexible slender filaments that are actively oscillating in space and time. The dynamics of these biological appendages have inspired the design of many types of artificial…
In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the…
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale…