engleski

Length-scale insensitive phase-field model and dual-mesh FEM discretization for phase-field problems for reduced mesh requirements

The phase-field (P-F) method is the most promising diffusive approach for modelling fracture phenomena, but it is sensitive on the value of the length-scale parameter [1], and requires the use of high-density mesh as well as high computation costs. This paper presents a length-scale insensitive P-F model. In contrast to the model in [2], where the derivatives of a degradation function and the local part of a crack surface density function with respect to the phase-field at the undamaged state are utilized, we employ the scaling factor of the crack surface density function to obtain length-scale insensitivity. Following ideas from [3], a new family of crack surface density functions and a new softening law concept are introduced, which enable independent calibration of the P-F profile, the stress-strain response and the critical stress. In the conventional Finite Element Method (FEM) framework, a fully broken specimen contains one layer of fully broken elements. To develop this layer, additional spurious fracture energy needs to be dissipated, and the critical energy release rate and the critical force are seemingly increased. To reduce this additional parasitic fracture energy and reduce the mesh density requirements, a discretization by finite elements and finite volumes was utilized in [4]. In this work, a new dual-mesh discretization scheme is proposed, with the primary triangular mesh and the secondary polygonal or triangular mesh.

phase-field, fracture, length-scale sensitivity, dual mesh

nije evidentirano