Formulation based on combined loading function strategy to improve the description of the bi-modularity of quasi-brittle material degradation with multiple damage evolution laws.

This paper proposes a method to describe the bi-modular behavior of quasi-brittle materials. The approach is based on using multiple loading functions that are associated with the stress state of the material point. The model also includes degradation laws that control the evolution of the internal variables under tension and compression, which allows the representation of the material response with fidelity. The following approach outlines an objective methodology for improving classical models and provides a theoretical framework for developing new constitutive models. This work also presents an updated version of the Mazars damage model, with improved material parametrization through multiple damage laws. Similarly, the modified von Mises model has been extended to include different functions for damage evolution, combining exponential and continuum polynomial laws for tension and compression. A third model was developed to showcase the full potential of the proposed formulation. This model formulates the Lemaitre and Chaboche criterion, typically used for ductile materials, to describe quasi-brittle materials. The model provides a comprehensive characterization of the tension and compression behavior by utilizing various loading functions and multiple damage laws. Numerical simulations of experimental benchmarks are presented to show the performance of the proposal, including a nonlocal approach to avoid strain localization and mesh dependency problems. • A formulation to represent simply the bi-modularity of quasi-brittle materials by isotropic damage models is presented. • The proposal provides versatility to prescribe any damage law, especially with fill constitutive parameters. • The strategy is applied to classical models present in literature providing an enhancement of the model behavior. • The approach can be extended and applied to other models presented in the literature. [ABSTRACT FROM AUTHOR]