On the elastic wedge problem within simplified and incomplete strain gradient elasticity theories

In this paper, we investigate the behavior of strain gradient elasticity solutions around sharp edges body loaded by concentrated loads. We consider general Mindlin–Toupin (SGET) and several simplified models, including dilatation theory (DGET) couple stress (CST). framework a plane problem for an elastic wedge with prescribed tip displacement obtain analytical assessments field state apex. Involving Papkovich–Neuber solution show that nonsingular can be obtained within SGET models provide regularization dilatational rotational parts both. incomplete theories such as DGET or CST singularity in displacements stresses at apex cannot avoided. This result is validated also based on full-field numerical wedge-type domains. It shown bounded complete theories, while mesh dependent are realized CST. Generally, results means boundary value problems edge-type loading should abandoned like it considered only under some additional assumptions (similarly to classical elasticity).