Eliminating mesh sensitivities in microstructure design with an adjoint algorithm

Abstract

A microstructure design approach utilizing a discrete adjoint sensitivity analysis scheme is addressed. The microstructure is modeled with a one-point probability descriptor, known as Orientation Distribution Function (ODF). The ODF measures the volume densities of the unique orientations in a polycrystalline material. It can be discretized within an orientation space to describe the microstructure-sensitive features and calculate volume-averaged material properties. In this work, a finite element scheme is applied to discretize the ODF values in the Rodrigues orientation space to obtain the macro-scale properties. An adjoint sensitivity analysis is integrated into the solution framework to perform a design optimization for the microstructure to minimize/maximize a macro-scale property. Next, a gradient-based design optimization which utilizes the outputs of the sensitivity analysis is performed to enhance the material properties. The adjoint technique is shown to save a significant computational time compared to the existing design approaches. This is because the adjoint method is independent of the number of design variables. Thus, it eliminates the solution dependence to the finite element mesh that is used to model the problem.