Micropolar elastoplasticity using a fast Fourier transform-based solver

TL;DR

This paper introduces a spectral method using Fourier transforms for efficiently modeling the full-field and homogenized responses of elastoplastic micropolar composites, capturing size effects and micro-plasticity.

Contribution

It develops a novel spectral formulation with a closed-form radial-return mapping for micropolar elastoplasticity, enabling fast and accurate simulations of size-dependent behaviors.

Findings

Efficient simulation of size-dependent material responses.

Verification of the algorithm with manufactured solutions.

Capability to generate large datasets rapidly.

Abstract

This work presents a micromechanical spectral formulation for obtaining the full-field and homogenized response of elastoplastic micropolar composites. A closed-form radial-return mapping is derived from thermodynamics-based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size-dependent material response and micro-plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.