Differential evolution algorithm and artificial neural network surrogate model for functionally graded material homogenization and design

Abstract

In this paper, the differential evolution (DE) algorithm is employed to design functionally graded materials (FGMs). The design problem is formulated as a constrained optimization, where the objective function represents the global requirements of the macroscopic boundary value problem (BVP^m), and the constraints account for the feasibility (or manufacturability) of the generic microstructure. During optimization, the local constitutive behavior of the material, such as the components of the anisotropic effective stiffness tensor, is derived using homogenization theory, which involves solving the microscopic boundary value problem (BVP^µ). Both the macro and micro problems are solved using the finite element method. To accelerate computations, artificial neural networks (ANNs), trained with pre-computed homogenization data, are used as a surrogate homogenization model for the FGM optimization process. The examples presented demonstrate that using ANNs can reduce the optimization effort by several orders of magnitude, even when accounting for the computational cost of database preparation and ANN training. The proposed approach for designing FGMs has proven to be both efficient and reliable for the considered generic microstructure and example global problems. Moreover, the method is general enough to be applied to more complex microstructures and diverse global requirements.