Capturing size effects in effective field methods through the prism of strain gradient elasticity

Abstract

The majority of studies in the open literature use homogenization models that consider microstructural parameters such as shape, orientation, distribution, and volume fraction of inhomogeneities. However, size effects, that become important when small scales are considered, are not taken into account. This study presents a novel approach by combining property contribution tensors with strain gradient elasticity to offer a formulation of effective field methods (EFM) that captures size effects in a single step and improves the accuracy of predictions about effective elastic properties. Three commonly used EFM are considered, i.e., the Non-Interaction, the Mori–Tanaka, and the Maxwell. The effectiveness of the novel approach is validated through comparison with previous formulations in the open literature that do not consider property contribution tensors. The novel approach is further tested by applying it to a simple case of a material containing pores of different sizes and comparing the results with two-step homogenization approaches and finite element models from the open literature. The comparison demonstrates the ability of the novel formulation to capture size effects and to closely follow the predictions of the FE models.