A Continuum-mechanics solution of laminate free edges based on asymmetric stress and strain tensors. (15th November 2022) - Zhang, Boming; Kellermann, David; Webb, Lachlan; O'Shea, Daniel; Pearce, Garth
Highlights: Novel observation of the asymmetry of stress and strain tensors in the free-edge vicinity. An examination of the impact of releasing the stress and strain tensor symmetry. Reduction of mesh sensitivity contributes to the resolution of free-edge singularity. Addressment of the inconsistency between the existing FEM results and DIC experimental data. Integration of an asymmetric elasticity theory with commercial FEM software provides a better alternative to the classical elements. Abstract: A meaningful attempt is made to investigate the impact of using asymmetric stress and strain formulations in the prediction of free-edge response of laminated orthotropic materials. The paper contributes to the process of making the singular free-edge stresses and strains in the literature more proximate to the bounded (realistic) solutions. Related to the singularity issue, it was previously identified that the symmetry assumption for stress and strain tensors could lead to a contradiction with the predicted free-edge stress functions. It is, therefore, reasonable to assert that the classical continuum mechanics based on tensor symmetries is unfaithful for the modelling of free edges. The present study demonstrates that for the free-edge region, stress and strain tensors naturally become asymmetric when they are enabled to be, to reach the minimum strain energy. By comparing with strain predictions generated by Digital Image Correlation technique, the new framework is shown to be able to address the notable discrepancy between the classical theoretical result and experimental result, which suggested the higher fidelity of the new framework. Moreover, by resolving the contradiction, the model is also made less sensitive to mesh refinement which sets an important basis for reaching a bounded solution in the future.