Microstructure-based modeling of elastic functionally graded materials: One dimensional case

TL;DR

This paper introduces a microstructure-based modeling approach for one-dimensional elastic functionally graded materials, utilizing stochastic variational principles and finite element/boundary element discretizations to analyze their behavior.

Contribution

It develops a systematic microstructural modeling strategy for FGMs using stochastic variational principles and compares finite element and boundary element methods in a simplified 1D setting.

Findings

Finite element and boundary element methods provide comparable results.

The microstructure-based approach improves understanding of FGM behavior.

Discretization schemes effectively capture local field statistics.

Abstract

Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or a given smooth variation of material properties. Although these models are computationally efficient, their validity and accuracy remain questionable, since a link with the underlying microstructure (including its randomness) is not clear. In this paper, we propose a modeling strategy for the linear elastic analysis of FGMs systematically based on a realistic microstructural model. The overall response of FGMs is addressed in the framework of stochastic Hashin-Shtrikman variational principles. To allow for the analysis of finite bodies, recently introduced discretization schemes based on the Finite Element Method and the Boundary Element Method are employed to obtain statistics of local fields. Representative numerical examples are presented to compare the performance and accuracy of both schemes. To gain insight into similarities and differences between these methods and to minimize technicalities, the analysis is performed in the one-dimensional setting.