Phase field method with strain orthogonal decompositions for modelling of damage in heterogeneous materials obtained by X-ray computed tomography images

Abstract

The phase-field method has become a robust tool to describe the complex crack nucleation and propagation in heterogeneous materials. In these materials, an interaction between bulk brittle damage and interfacial damage through the splitting the strain tensor into a bulk strain part and a jump strain part at the interfaces. Moreover, the material response of the heterogeneous materials in tension and compression, the bulk strain part needs to be decomposed into a positive part and a negative part. However, most of the previous works, these decompositions do not verify the negative part be orthogonal the positive part, which lead to the inaccuracy in the material mechanical behavior. To solve the shortcomings, the strain orthogonal decompositions problem that is applied to decompose the bulk strain in our work. In the present work, author combined the phase-field modeling taking into account interfacial damage with the problem of the bulk strain orthogonal decompositions by two proposed solutions. The successful prediction of the crack propagation for the inclusion-matrix structures and the multi-phases materials of X-ray computed tomography (XR-CT) images by two proposed solutions will be demonstrated in several numerical examples.