Related papers: Minimum energy paths for dislocation nucleation in…
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…
Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the…
We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle…
We discuss an M-dimensional phantom elastic manifold of linear size L crushed into a small sphere of radius R << L in N-dimensional space. We investigate the low elastic energy states of 2-sheets (M=2) and 3-sheets (M=3) using analytic…
We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice…
We study an energy minimization problem $\sum_{i \neq j} W(z_i - z_j)$ for $N$ points $\left\{z_1, \dots, z_N\right\}$ with applications in dislocation theory. The $N$ points lie in the two-dimensional domain $\mathbb{R} \times [-\pi,…
Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective…
The paper investigates two-phase microstructures of optimal 3D composites that store minimal elastic energy in a given strain field. The composite is made of two linear isotropic materials which differ in elastic moduli and self-strains. We…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
Understanding the mechanism of martensitic transformation is of great importance in developing advanced high strength steels, especially TRansformation-Induced Plasticity (TRIP) steels. The TRIP effect leads to enhanced work-hardening rate,…
Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…
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…
Plastic response due to dislocation activity under intense electric fields is proposed as a source of breakdown. A model is formulated based on stochastic multiplication and arrest under the stress generated by the field. A critical…
The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…
We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on…
A quantitative mathematical model for the critical thickness of strained epitaxial metal films is presented, at which the magnetic moment experiences a reorientation from in-plane to perpendicular magnetic anisotropy. The model is based on…
We prove the existence of minimisers for a family of models related to the single-slip-to-single-plane relaxation of single-crystal, strain-gradient elastoplasticity with $L^p$-hardening penalty. In these relaxed models, where only one…
In classical elasticity theory the stress-field of a dislocation is characterized by a $1/r$-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this…
To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For…
Transition states and minimum energy paths are essential to understand and predict chemical reactivity. Double-ended methods represent a standard approach for their determination. We introduce a new double-ended method that optimizes…