Numerical aspects of microplane constitutive models for concrete

This paper presents a comprehensive study on the numerical aspects of a class of microplane constitutive models for concrete, with emphasis on the most popular one, i.e., the model M4 developed by Bažant and co-workers. The effect of the computational procedures for the microplane shear stress components, the strain increment magnitude, the integration scheme and the loading direction on the model responses are investigated in detail. Several problems in the responses of the model, from the computational point of view, are detected and discussed. Some procedures to enhance the numerical performance of the model are then proposed. These include a removal of the tensile volumetric stress boundary in the original formulation, the introduction of a novel semi-explicit numerical algorithm for the microplane volumetric and deviatoric stresses, and a method to minimise the sensitivity of the model responses to the loading direction through a simple meshing-based integration scheme. Finally, some practical considerations for the choice of numerical integration scheme in the finite element calculations of large-scale concrete structures with the microplane model M4 are presented.