Smoothed Constitutive Model for Concrete based on Micromechanical Solutions

New developments for simulating microcracking in cementitious composite materials – such as concrete – are presented. A micromechanical constitutive model for concrete is proposed which employs the classic Eshelby inclusion solution and a Mori-Tanaka homogenization scheme to simulate a two-phase composite comprising a matrix phase representing the mortar and spherical inclusions representing the coarse aggregate particles. Furthermore the material contains randomly distributed penny-shaped microcracks. The onset of cracking is addressed in a microcrack initiation criterion, governed by an exterior-point Eshelby solution, in which microcracks are assumed to initiate in the interfacial transition zone between aggregate particles and cement matrix [1]. The adopted solution captures tensile stress concentrations in the proximity of inclusion – matrix interfaces in directions lateral to a compressive loading path. An advantage of the two-phase formulation is that it is able to predict the build-up of tensile stresses within the matrix phase under uniaxial compression stresses thus allowing the model to naturally simulate compressive splitting cracks. The implementation of the microcrack initiation criterion into the constitutive model enables the use of realistic material properties in order to obtain a correct cross-cracking response. The model combines these solutions with a rough crack contact component which enables it to capture the dilatant behaviour of concrete subject to compression. A novel aspect of the present work deals with the development of a smoothed contact state function in order to remove spurious contact chatter behaviour at a constitutive level. It is shown, based on numerical predictions of uniaxial and biaxial behaviour that the model captures key characteristics of mechanical behaviour of concrete.