Constitutive structural response of Concrete Damaged Plasticity model under Willam’s test

The present work aims at analysing and calibrating the mechanical description of plastic strain-induced anisotropy and damage coupling by the so-called Concrete Damaged Plasticity (CDP) constitutive model, which is rather well known also since it comes to be available within popular FEM platforms, such as ABAQUS, and shall be able to reproduce typical features of failure processes in quasi-brittle materials, like concrete. This is achieved by combining an effective stress-based non-associative hardening/softening plasticity model with an isotropic damage model based on plastic strains, at a smeared continuum scale. In the paper, focusing on the mere elastoplastic coupling for tensile-dominated responses, and introducing an enhanced tuning by setting tensile exponential softening and damage evolutions through a convenient plastic to inelastic strain ratio parameter, by means of an external user implementation, an exhaustive numerical parametrization analysis is performed, starting at a constitutive-driver level, to experiment the outcomes of the constitutive description and to quantify the amount of material anisotropy induced by plastic deformation, under biaxial elongation/shearing Willam’s test, which prescribes/involves the rotation of the principal axes of strains/stresses. It is shown that the constitutive response is effectively regularized, allowing to fulfill the requirements of Willam’s test, independently from the amount of inherent plastic dilatancy, showing a rather mild presence of plastic-induced anisotropy, at the pure constitutive-driver scale. Furthermore, first extrapolating implications and outcomes at the small (specimen) structural scale are also investigated, with clear appearance of strain localization and related much pronounced plastic-induced anisotropy, in the (imperfection-triggered) macroscopic response, with features that are similar to those coming e.g. from more sophisticated anisotropic damage models, while significant practical applications may subsequently follow, within different structural engineering contexts, as that of large-scale concrete structures under static and dynamic loading scenarios, toward informed safety assessment and evaluation.