相关论文: A numerical study of branching and stability of so…

In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…

We present, to the best of our knowledge, the first complete three-dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity. We have chosen for our work, Toupin's…

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…

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…

We study the mechanics of temperature-driven reconstructive martensitic transformations in crystalline materials, within the framework of nonlinear elasticity theory. We focus on the prototypical case of the square-hexagonal transition in…

In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context…

We propose a mesh-free method to solve nonconvex energy minimization problems for martensitic phase transitions and twinning in crystals, using the deep learning approach. These problems pose multiple challenges to both analysis and…

We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is $\lambda$-convex, which allows for solid phase transformations. We formulate this…

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the…

Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity…

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…

The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…

In the present article, we are interested in an initial boundary value problem for a coupled system of partial differential equations arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel.…

A thermodynamically consistent multiphase phase-field approach for stress and temperature-induced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are…

An original thermodynamically consistent large strains-based multiphase phase-field (PF) approach of Ginzburg-Landau type is developed for studying the grain boundary (GB)-induced martensitic transformations (MTs) in polycrystalline…

We explore the possibilities and limitations of using a coherent second phase to engineer the thermo-mechanical properties of a martensitic alloy by modifying the underlying free energy landscape that controls the transformation. We use…

Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…

How can a system in a macroscopically stable state explore energetically more favorable states, which are far away from the current equilibrium state? Based on continuum mechanical considerations we derive a Boussinesq-type equation which…

We study self-similar solutions of a multi-phase Stefan problem, first in the case of one space variable, and then in the radial multidimensional case. In both these cases we prove that a nonlinear algebraic system for determination of the…

We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…