Numerical solution for plasticity models using consistency bisection and a transformed-space closest-point return: a nongradient solution method

A new approach is presented for computing the return in numerical solutions for computational plasticity models that ensures convergence through bisection of the plastic consistency parameter, while using a transformed-space closest-point return based on a geometric search that eliminates the need to compute gradients of the yield function or a consistent tangent operator. Numerical solution of the governing equations for computational plasticity is highly-nontrivial for complex constitutive laws. In particular for geomaterials, a predictive model may account for nonlinear elasticity, shear strength that depends nonlinearly on pressure and Lode angle, and nonlinear evolution models for internal variables such as porosity or pore pressure. Traditional gradient-based integration methods may perform poorly when the hardening laws are highly nonlinear or when the yield function has an ill-defined or cumbersome gradient because of high curvature, vertices, or complicated functional form. The application of this new approach to geomaterial modeling is described, along with verification benchmarks.