Analytical and numerical aspects of relaxation and regularization in models of crystal plasticity

我们的项目结合了分析和数值方法的变分模型的研究有限晶体塑性。一个范例是将松弛理论应用于塑性问题，也与收敛工具相结合。我们的项目涉及在选定的案例研究中的精确分析结果的推导，并与一个通用算法的开发和实施的有效的数值确定的松弛给定的能量密度。分析和数值松弛到有限元代码的集成允许验证和实验比较。在平行，我们调查的位错线张力能的作用。这包括在较小的尺度上从离散和/或连续模型导出这种类型的模型，通过收敛，以及研究几何上必要的位错能量与弛豫的相互作用。

Our project combines analytical and numerical approaches for the study of variational models for finite crystal plasticity. One paradigm is the application of the theory of relaxation to plasticity problems, also in combination with the tools of ¡-convergence. Our project deals both with the derivation of exact analytical results in selected case studies and with the development and implementation of a general algorithm for the efficient numerical determination of the relaxation of a given energy density. The integration of both analytical and numerical relaxation into a finite element code permits to validate and compare with experiment. In parallel, we investigate the role of dislocation line-tension energy. This includes both the derivation of this type of model from discrete and/or continuum models at a smaller scale, by means of ¡-convergence, and the study of the interplay of the energy of geometrically necessary dislocations with relaxation.