The Modified Maximum Shear Stress Failure Theory of Ductile Material

Abstract

In this study, the maximum and smallest vertical principle stresses σ1 and σ3 as well as maximum shear stress τmax distributions, obtained from Mohr circle in each quadrant, are used to investigate the applicability of various ductile material failure theories. Based on the yield tensile stress σyt equals to yield compressive stress σyc (σyt=σyc=σy) and the known practical yield shear stress and yield stress ratio τy/σy=0.42~0.75 of ductile materials, we prove that the maximum vertical stress failure theory cannot be applied to the first quadrant (σ1>σ3≧0) as well as the third quadrant (σ3<σ1≦0) while τy/σy< 0.5, and it does also not applicable to the second or fourth quadrant (σ1>0 and σ3<0). In this study, the modified maximum shear stress failure line can be fit all ductile material depending on τy/σy=0.42~0.75 in all quadrants, thus the more reasonable results can be obtained.

An Optimized Model for the Local Compression Deformation of Soft Tissue

“…To reduce the computational overhead, we divide the soft tissue compression deformation into the local deformation region and non-deformation region. Meanwhile, the vertical stress component plays a major role in material failure [38], we only consider the role of vertical stress component in soft tissue compression. Assuming that an indenter acts on the soft tissue with uniform pressure, the vertical stress F ⊥ is expressed as:…”