An adaptive phase-field model based on bilinear elements for tensile-compressive-shear fracture

An efficient adaptive phase-field method based on bilinear elements for tensile-compressive-shear fracture is developed. On the one hand, refined meshes are needed near the crack path to obtain accurate results, and the computational efficiency is very low if a prior mesh refinement is applied, especially when the crack paths are unknown. On the other hand, conventional phase-field models are not applicable to tensile-compressive shear fracture under complex stress states at present. In this paper, an adaptive scheme is proposed to improve the computational efficiency, in which a bilinear multi-node element is adopted to avoid using high order quadrature and shape functions when new nodes are inserted in elements, and a new multi-node triangular element is outlined to expand the scope of application of the proposed adaptive method. Another important aspect of the contribution is the development of the phase-field model for tensile-compressive-shear fracture under complex stress states, in which a universal fracture criterion is embedded. To determine the optimal parameters in the adaptive scheme and demonstrate the advantages of the proposed bilinear adaptive method, a series of numerical examples are performed for sensitivity analysis. Comparison with experimental results is also conducted to validate the proposed phase-field model for tensile-compressive-shear fracture under complex stress states.

Automated summary

An efficient adaptive phase-field method based on bilinear elements is developed for tensile-compressive-shear fracture. The method improves computational efficiency by using a bilinear multi-node element and expands the scope of application through a new multi-node triangular element. The contribution also includes the development of a phase-field model for tensile-compressive-shear fracture under complex stress states, which is validated through numerical examples and comparison with experimental results.