An implicit gradient formulation for microplane Drucker-Prager plasticity

A microplane plasticity model is regularized by an implicit gradient enhancement. The plasticity model is defined by a Drucker-Prager yield criterion and within the thermodynamically consistent framework of the microplane theory. Thus, the advantages of both the microplane approach and the pressure sensitive Drucker-Prager yield criterion are combined within a nonlocal implicit gradient type method. The microplane approach allows for the description of induced anisotropy which is observed in the failure of quasi-brittle materials. Based on the volumetric-deviatoric split, a microplane version of the Drucker-Prager yield function is defined. The implicit gradient enhancement is employed to remedy the pathological mesh sensitivity. It yields the advantage of being strongly nonlocal and equivalent to the integral-type models, while it preserves the mathematical locality of the equations and keeps the implementation straightforward within the classical finite element method. The proposed formulation is implemented in a 3D finite element code. The stress return mapping algorithm and the consistent tangent are derived. Numerical examples are simulated to demonstrate the capability of the proposed method to regularize the model and eliminate the pathological mesh dependency.