相关论文: Asymptotic analysis of hierarchical martensitic mi…
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to…
We investigate low energy structures of a lattice with dislocations in the context of nonlinear elasticity. We show that these low energy configurations exhibit in the limit a Cosserat-like behavior. Moreover, we give bounds from above and…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
Martensitic materials show a complex, hierarchical microstructure containing structural domains separated by various types of twin boundaries. Several concepts exist to describe this microstructure on each length scale, however, there is no…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
The onset of plasticity in quenched martensitic microstructures is characterized by a low initial yield stress followed by an extremely strong initial hardening response, and then a sudden hardening saturation. Literature attributes this…
Understanding the evolution of dislocation structures during plastic deformation is critical for predicting the mechanical performance of metallic materials. In this work, we applied in situ scanning electron microscopy/electron backscatter…
We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic…
We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scaling regime where the total length of the dislocations is…
This work presents a detailed experimental-numerical analysis of a low-carbon dual-phase steel microstructure, revealing evidence of significant anisotropic plastic deformation in lath martensite. A careful determination of the habit plane…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
In this work we model the evolution of strain energy during different growth stages of heterostructure nanowires. We find that the minimum energy configuration changes abruptly from fully elastically strained to partially relaxed due to…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
We present a systematic approach to modeling the electrical and structural properties of charge-mismatched superlattices from first principles. Our strategy is based on bulk calculations of the parent compounds, which we perform as a…
The continuum theory of dislocations, as developed predominantly by Kr\"oner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy…
We present a practical algorithm for partially relaxing multiwell energy densities such as pertain to materials undergoing martensitic phase transitions. The algorithm is based on sequential lamination, but the evolution of the…
Battery interfaces critically influence lithium-metal battery performance through their role in ion diffusion and dendrite formation. However, structural characterization of these interfaces has remained challenging due to limitations in…
In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2\delta when \delta rightarrow 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…