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Enhanced Assumed Strain Methods for Implicit Gradient‐Enhanced Damage‐Plasticity

The combination of plasticity theory and continuum damage mechanics facilitates the description of hardening and softening material behavior, accumulation of inelastic strains, and stiffness degradation due to damage. For regularizing softening material behavior in finite element simulations, the enrichment of the constitutive relations by means of a nonlocal counterpart of an internal strain‐like thermodynamic state variable, implicitly defined as the solution of a higher order PDE, is a suitable approach in order to obtain mesh‐insensitive results [1]. However, for plasticity models assuming dilatant plastic flow, such as commonly employed for cohesive‐frictional materials like concrete or rock, spurious locking phenomena due to kinematic constraints can arise in conjunction with low order finite elements. This issue was observed and discussed in [2] for simple (local) linear‐elastic perfectly plastic material models. As a remedy, specific enhanced assumed strain (EAS) methods to enrich the normal strain rate field were proposed and assessed. The present contribution demonstrates the formulation of these EAS methods combined with the fully coupled displacement‐nonlocal damage framework, and shows an application to mode II failure employing a gradient‐enhanced damage‐plasticity model for concrete. The insensitivity of the presented approach with respect to the finite element mesh is discussed.