An alternative approach to microplane theory

In this paper an alternative approach to the well-known microplane theory is developed. This approach mainly consists of two parts, i.e. the mathematical representation based on the improved representation theorem on stiffness and the equivalent thermodynamical description within the framework of irreversible thermodynamics. On one hand, the material stiffness is represented in the form of irreducible decomposition which can be sufficiently determined by the orientation distribution functions for the macroscopic bulk and shear moduli (or those for the corresponding macroscopic damages). The introduced macroscopic orientation distribution functions are then expanded into the converged Fourier series and approximated by the second- or fourth-order macroscopic damage variables which are defined as the fabric tensorial functions of the microscopic (microplane) damage variables. The combination of the improved representation theorem on stiffness with the proposed macroscopic and microscopic damage variables yields the general forms of the microplane models with bulk-shear split and with volumetric–deviatoric–tangential split. On the other hand, the macroscopic Helmholtz free energy potentials are defined by introducing the damage effect tensors in terms of the macroscopic damage variables. The integral relation between the microscopic and macroscopic Helmholtz free energy potentials as well as the kinematic constraint is derived. Within the framework of irreversible thermodynamics, the consistent microscopic and macroscopic damage evolution laws are established. Moreover, the other concepts of damage mechanics such as the conjugated damage forces, the damage dissipations and so on, are also investigated on both the microscopic and macroscopic levels.