Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions-Reference-Cited by-同舟云学术

Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions

Published:2014-10-16 Issue:14 Volume:24 Page:2929-2942
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Conti Sergio¹,Dolzmann Georg²

Affiliation:

1. Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

2. Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Abstract

We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density is given by the squared distance from two potential wells. We obtain the quasiconvex envelope of the energy density and therefore the relaxation of the variational problem. Our result includes the constraint of positive determinant.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202514500419

Reference29 articles.

1. Infinite-order laminates in a model in crystal plasticity

2. Fine phase mixtures as minimizers of energy

3. Proposed experimental tests of a theory of fine microstructure and the two-well problem

4. Self-accommodation in martensite

5. Numerical solution of the scalar double-well problem allowing microstructure

Cited by 11 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Analytical and numerical relaxation results for models in soil mechanics;Continuum Mechanics and Thermodynamics;2023-05-15

2. A study of energies in pressure dependent plasticity – mathematical model and mechanical analogies;PAMM;2023-03

3. Optimal laminates in single-slip elastoplasticity;Discrete & Continuous Dynamical Systems - S;2021

4. Numerical Study of Microstructures in Multiwell Problems in Linear Elasticity;Advances in Mechanics and Mathematics;2021

5. Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers;ESAIM: Control, Optimisation and Calculus of Variations;2019