Granular micromechanics model for damage and plasticity of cementitious materials based upon thermomechanics*

The mechanical behavior of monolithic cementitious materials is known to be significantly affected by their granular nature. This paper describes an approach to incorporate the effects of granularity for cementitious material based upon the granular micromechanics paradigm and thermomechanics. As a result, macro-scale constitutive equations that utilize grain-scale force-displacement relationships have been derived. In this derivation, the connections between grain-scale free energy and dissipation and the macro-scale behavior are established based upon the thermomechanics framework. Expression for Cauchy stress tensor is obtained in terms of the free energy of grain-pair interactions. In addition, the free energy and dissipation potential of grain-pair interactions are used to find a grain-scale Clausius-Duhem type inequality. Thus, inter-granular constitutive equations are obtained in the usual manner with the exception that these are based upon simple physically motivated free energy and dissipation functions formulated in terms of grain-pair interactions. The derived model is used to simulate a wide variety of experimental tests that have been reported in the literature to evaluate material response under multi-axial conditions. The results are analyzed with the aim to reveal the connections between grain-scale mechanisms and the macro-scale behavior.