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Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

# International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i1.40
pages 29-46

## Multiscale Total Lagrangian Formulation for Modeling Dislocation-Induced Plastic Deformation in Polycrystalline Materials

Xinwei Zhang
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Shafigh Mehraeen
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Jiun-Shyan Chen
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Nasr M. Ghoniem
Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095, USA

### ABSTRACT

Multiscale mathematical and computational formulation for coupling mesoscale dislocation mechanics and macroscale continuum mechanics for prediction of plastic deformation in polycrystalline materials is presented. In this development a total Lagrangian multiscale variational formulation for materials subjected to geometric and material nonlinearities is first introduced. By performing scale decomposition of kinematic variables and the corresponding dislocation kinematic variables, several leading-order equations, including a scale-coupling equation, a mesoscale dislocation evolution equation, and a homogenized macroscale equilibrium equation, are obtained. By further employing the Orowan relation, a mesoscopic plastic strain is obtained from dislocation velocity and its distribution, and a homogenized elastoplastic stress-strain relation for macroscale is constructed. The macroscale, mesoscale, and scale-coupling equations are solved interactively at each macroscopic load increment, and information on the two scales is passed through the macroscale integration points. In this multiscale approach the phenomenological hardening rule and flow rule in the classical plasticity theory are avoided, and they are replaced by a homogenized mesoscale material response characterized by dislocation evolution and their interactions.