A failure criterion for homogeneous and isotropic materials distinguishing the different effects of hydrostatic tension and compression

A physically based failure criterion distinguishing the different effects of hydrostatic tensile and compressive stress is developed for homogeneous and isotropic materials. It is reasonably assumed that failure is related to the shape and volume change of isotropic materials at the macroscopic scale. Shape distortion and volume dilation (i.e., hydrostatic tension) are capable of producing material failure, while volume contraction (i.e., hydrostatic compression) has an impeding effect upon failure initiation. The different roles of hydrostatic tension and compression may lead to differences of the applied failure functions. In the present study, two failure formulas are proposed, considering the different effects of hydrostatic stress upon yielding/fracture of homogeneous and isotropic materials separately. The good agreement of the present theory with a large number of experimental data is observed, and the present theory shows a wide range of applicability.