Finite strain extension of a gradient enhanced microplane damage model for concrete at static and dynamic loading

The microplane model is a constitutive formulation, which provides a straightforward approach to model quasi-brittle materials such as concrete. The material model has been developed in various formulations in the small strain framework up to now, and it has been utilized successfully to predict crack patterns by combining with nonlocal damage. However, at high pressure, strain in concrete material or structures can become very large while in the absence of high pressure, finite deformations can be indicated by concrete that forms into rubble and has no stiffness anymore. Due to these challenges, the generalization of the microplane model from small strain to finite strain is needed in order to represent largely deformed structures. The generalization to finite strains can be performed using the Green-Lagrange strain tensor instead of strain components that are obtained by small strain analysis. The volumetric-deviatoric (V-D) decomposition is simply applied similar to the existing models. In order to construct a more stable damage approach, an implicit gradient enhancement is adopted. Furthermore, rate dependency of concrete is included in this extended model to accommodate dynamic loading. Finally, numerical examples in static and dynamic cases are discussed to verify and examine the capabilities of the proposed formulation.