Related papers: Optimal energy scaling for a shear experiment in s…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
We consider a single disclination in a thin elastic sheet of thickness $h$. We prove ansatz-free lower bounds for the free elastic energy in three different settings: First, for a geometrically fully non-linear plate model, second, for…
The theory of plastic bending of single crystal beam having two active slip systems is proposed. Applying the variational-asymptotic method we reduce the energy functional of the beam to the one-dimensional energy functional which admits…
A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
The Navier slip boundary condition is interpreted as an equilibrium of shear rate and slip rate. From the argument that the slip rate shall be proportional to the molecules' collision rate, the temperature dependence of the Navier slip…
For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the dependence of the pinning energy barrier on the misfit angle and contact area. The resulting data are used to investigate the distribution of…
How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop a rigorous method via $\Gamma$-convergence for answering this question to leading…
We analyze dissipative scale effects within a one-dimensional theory, developed in [L. Anand et al. (2005) J. Mech. Phys. Solids 53], which describes plastic flow in a thin strip undergoing simple shear. We give a variational…
A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…
Anti-plane shear deformations of a hexagonal quasi-crystal with multiple screw dislocations are considered. Using a variational formulation, the elastic equilibrium is characterized via limit of minimizers of a core-regularized energy…
Simple homogeneous shear flows of frictionless, deformable particles are studied by particle simulations at large shear rates and for differently soft, deformable particles. The particle stiffness sets a time-scale that can be used to scale…
Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a…
Based on the atomistic studies presented in Part I we develop analytical yield criteria for single crystals that capture the effect of shear stresses other than the Schmid stress (non-glide stresses) on the shear stress needed for…
We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved…
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern…
We present the results of numerical simulations of an atomistic system undergoing plastic shear flow in the athermal, quasistatic limit. The system is shown to undergo cascades of local rearrangements, associated with quadrupolar energy…