Variational eigenerosion for rate-dependent plasticity in concrete modeling at small strain

In the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack-tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ-limit proof, thus the existence of (local) minimizers is guaranteed by the Γ-convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker-Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate-dependent three-surface smooth yield function that requires hardening and hardening-rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate-independent and rate-dependent plasticity. © 2019 John Wiley & Sons, Ltd.