Microplane model for brittle-plastic material: I. Theory

A generalized microplane model for brittle-plastic heterogeneous materials such as concrete, which describes not only tensile cracking but also nonlinear triaxial response in compression and shear, is presented. The constitutive properties are characterized separately on planes of various orientations within the material, called the microplanes, on which there are only few stress and strain components and no tensorial requirements need to be observed. These requirements are satisfied automatically by integration over all spatial directions. The state of each microplane is characterized by normal deviatoric and volumetric strains and shear strain, which makes it possible to match any Poisson ratio. The microplane strains are assumed to be the resolved components of the macroscopic strain tensor. The central assumption is that on the microplane level the stress-strain diagrams for monotonic loading are path-independent and that all the path dependence on the macrolevel is due to unloading, which happens selectively on microplanes of some orientations. The response on the microplane is assumed to depend on the lateral normal strain, which does no work. In consequence, the incremental elastic moduli tensor is nonsymmetric, which is necessary to model friction and dilatancy. This tensor is also generally anisotropic and fully populated (i.e., none of its elements can be prescribed as zero). The model involves many fewer free material parameters than the existing comprehensive macroscopic phenomenologic constitutive models for concrete.