Microplane Models for Elasticity and Inelasticity of Engineering Materials

Abstract

In the traditional approach to the modeling of mechanical behavior of engineering materials, the stress tensor is calculated directly from the prescribed strain tensor either by a closed form tensorial relation as in elasticity or by incremental analysis as in classical plasticity formulations in which the formulation is developed in terms of tensor invariants and their combinations. However, to model the general three-dimensional constitutive behavior of the so-called geomaterials at arbitrary nonproportional load paths that frequently arise in dynamic loadings, such direct approaches do not yield models with desired accuracy. Instead, microplane approach prescribes the constitutive behavior on planes of various orientations of the material microstructure independently, and the second-order stress tensor is obtained by imposing the equilibrium of second-order stress tensor with the microplane stress vectors. In this work, particular attention is devoted to the milestone microplane models for plain concrete, namely, the model M4 and the model M7. Furthermore, a novel autocalibrating version of the model M7 called the model M7Auto is presented as an alternative to both differential and integral type nonlocal formulations since the model M7Auto does not suffer from the shortcomings of these classical nonlocal approaches. Examples of the performance of the models M7 and M7Auto are shown by simulating well-known benchmark test data like three-point bending size effect test data of plain concrete beams using finite element meshes of the same element size and Nooru-Mohamed test data obtained at different load paths using finite element meshes having different element sizes, respectively.