Sensitivity of the thermomechanical response of elastic structures to microstructural changes

This paper is focused on the analysis of the sensitivity of the thermomechanical response of a macroscopic elastic body to changes that occur at the microstructure. This problem is a key issue in material design. The sensitivity analysis relies on an accurate determination of the effective properties of the heterogeneous material. These effective properties are determined by computational homogenization. And their sensitivities, with respect to the parameters defining the microstructure, are then computed. For an efficient evaluation of the thermomechanical response, we propose to build response surfaces for the effective material properties. The surfaces are generated in an offline stage, by solving a series of homogenization problems at the microscale. In such a way, the fully online multiscale response analysis reduces to a standard problem at the macroscale. Thus, an important reduction in computational time is achieved, which is a crucial advantage for material design. The capability of the proposed methodology is shown in light of its application to the design of a thermally-loaded structure with variable microstructure. Considerable improvements in the structural response are achieved.