Mechanism-based strain gradient Drucker–Prager elastoplasticity for pressure-sensitive materials

Modeling strain gradient plasticity effects has achieved considerable success in recent years. However, incorporating the full mechanisms of the pressure-sensitive yielding and the size dependence of plastic deformation still remains an open challenge. In this work, a mechanism-based stain gradient (MSG) plasticity theory for pressure sensitive materials with a variable material length-scale parameter is presented. The flow theory of MSG plasticity based on the Drucker–Prager yield function is established following the same hierarchical framework of MSG plasticity proposed by Gao et al. (1999), Huang et al. (2000) and Qiu et al. (2003) in order to link the strain gradient plasticity theory on the mesoscale to the Taylor dislocation model on the micro-scale. The incremental constitutive relation based on the associated flow rule is derived for the Drucker–Prager yield function on the micro-scale, including the higher-order stress introduced as the thermodynamic conjugate of strain gradient at the mesoscale. The proposed theory successfully predicts the experimental results. The numerical results show that when the pressure-sensitivity index defined by the Drucker–Prager yield function takes different values, the material response curves are different and the material strength increases with the increase of pressure-sensitivity index. It proves that this procedure is able to represent the material behavior of pressure-sensitive materials such as geomaterials, polymeric materials, metallic foams and metallic glass.