Numerical evaluation of strain gradients in classical elasticity through the Boundary Element Method

Abstract Strain gradient fields seem to play an important role on the functionality of flexoelectric and functionally graded materials, bones, biomembranes, new sensing equipment and micro, nano and thin structures. A numerical method for evaluating strains and stresses with high accuracy is the Boundary Element Method (BEM). Despite to many BEM papers appearing so far in the literature, there is not a BEM reference dealing with the evaluation of strain gradients in classical elastic materials. The present work aims to fill this gap by presenting a BEM machinery for the evaluation of strain gradients in materials and structures under plane strain and plane stress conditions. Representative benchmark problems demonstrate the accuracy of the proposed method.