Comprehensive Review of the Microplane Framework for Constitutive Modeling Focused on Homogenization Approaches

Over the past few decades, the microplane approach has emerged as a powerful framework for formulating nonlinear constitutive models that accurately represent the behavior of materials such as concrete, rock, and other brittle or quasi-brittle materials. Compared to traditional tensorial models, microplane models have demonstrated superior predictive abilities in capturing the complex behavior of these materials under a wide range of loading configurations. The paper provides a comprehensive review of the microplane framework for constitutive modeling of materials. The review includes a classification of existing microplane models based on the modeled material and the main captured phenomena. The paper also briefly discusses the thermodynamic and numerical aspects related to microplane models. Furthermore, it summarizes and discusses several regularization techniques for microplane models. In addition, the paper presents a comparison study between several homogenization approaches within the microplane theory. The first approach is based on the principle of virtual work (PVW), where the microplane stress is directly integrated into the macroscopic stress tensor. The second approach is an energy equivalence (EEQ) approach for damage-based microplane constitutive laws, where the damage quantities are integrated into a macroscopic damage tensor. Finally, the paper discusses a third approach that represents the material stiffness in the form of irreducible decomposition determined by the orientation distribution functions (ODFs) for the macroscopic stiffness components and the corresponding macroscopic damage. Based on the comparative studies, the suitability and limitations of the three compared approaches with respect to the constitutive hypothesis at the microplane level are highlighted. Furthermore, the presented review highlights the generality and efficacy of the microplane approach in providing a flexible framework for the formulation of realistic constitutive models for a wide range of materials subjected to a variety of loading conditions. In addition, the limitations of microplane models are also discussed and directions for future research and refinement are outlined.