Phase field numerical strategies for positive volumetric strain energy fractures

A reasonable crack driving force is the key to preventing compression cracks and eliminating unrealistic crack propagation in phase field fracture analysis. Thus, examining the roles of volumetric strain energy (VSE) and deviatoric strain energy (DSE) in influencing crack propagation is necessary. This paper presents a comprehensive analysis of the following four different approaches to energy decomposition-driven crack propagation: the positive volumetric strain energy method (VSEM), deviatoric strain energy method (DSEM), volumetric-deviatoric strain energy method (VDSEM), and no decomposition method (NM). All of the strain energy is involved in the development of the crack propagation. The following four examples are investigated: two benchmark single-side notched examples, a complex crack containing a hole example, and a crack coalescence in an asymmetric double notch example. The VSEM's numerical findings align with literature and experimental observations, confirming that positive VSE rather than DSE promotes crack propagation.