Elasticity-based microstructural optimization: An integrated multiscale framework

An integratedmultiscale computational framework is developed to identify material microstructures which minimize target field variables at the microstructural level aimed at enhancing structural performance. The computational framework is comprised of the Particle Swarm Optimization algorithm, a structural-level analytical solution to a technological problem, and the elasticity-based locally-exact homogenization theory at the microstructural level. The excellent stability and quick convergence of the homogenization theory with the concomitant rapid execution times enables repetitive solutions of the unit cell problem with variable geometric and material parameters within a multiscale framework. The unit cell solution provides accurate homogenized moduli for input into the structural-level analysis, as well as accurate local stress fields for the calculation of objective functions by the optimization algorithm. The integrated multiscale optimization capability is demonstrated in the context of the classical Kirsch problem with an underlying graded microstructure aimed at stress concentration reduction. The results reveal the limitations of stress field optimization in graded materials solely at the homogenized level, pointing to the need for repetitive micro-level stress field recovery from an accurate and efficient homogenization theory within multiscale optimization analysis. (C) 2017 Elsevier Ltd. All rights reserved.