Peridynamic Modeling of Crystal Plasticity with an Adaptive Dynamic Relaxation Solver

Peridynamics;Dynamic method;Crystal plasticity;Zero-energy mode;Simulation;Microstructure;Mechanical Engineering;Engineering;Mechanical Engineering

Luo, JiangyiFan, Yue ;

University of Michigan

关键词: Peridynamics;    Dynamic method;    Crystal plasticity;    Zero-energy mode;    Simulation;    Microstructure;    Mechanical Engineering;    Engineering;    Mechanical Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/149913/jiangyi_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

A primary challenge in modeling polycrystalline materials under large deformation is capturing strong strain localizations, in the form of micro-scale sharp shear bands. Classical numerical approaches such as finite element methods are inefficient in handling discontinuities because continuum mechanics approximations become inaccurate. Peridynamics, introduced as an alternative integral formulation for continuum mechanics, has attracted significant attention in solid mechanics for its special treatment in the presence of high gradients and discontinuities. In addition, peridynamic models are powerful in predicting damage nucleation and propagation with an intrinsic characteristic length scale. Given this background, a peridynamic implementation of crystal plasticity with an adaptive dynamic relaxation method is presented in this thesis.Specifically, a parallelized code for non-ordinary state-based peridynamics via Newmark;;s dynamic method with artificial damping is developed in this work. Elasticity problems are tested first in order to understand numerical behavior of the algorithm comprehensively. A rate-independent crystal plasticity model is then introduced to conduct simulations of planar polycrystalline microstructures under plane strain pure shear and compression. The peridynamic solver is compared with the crystal plasticity finite element method for predicting the stress and strain fields, texture, and homogenized stress-strain response. Sharper and more numerous shear bands are observed in the peridynamic model. Emphasis is placed on the accuracy and efficiency of the peridynamics solver via development of new higher order approximation schemes for the deformation gradient and new boundary condition treatments.We have also proposed a new solution for achieving numerical stability based on the stress-point method. The thesis thus presents the first three-dimensional polycrystal plasticity simulations using peridynamics theory with strain fields and texture compared against experiments and published literature.