Multi-Scale Damage Model for Quasi-Brittle Composite Materials

Abstract

A multi-scale damage model of concrete is proposed based on the concept of energy equivalent strain for generic two- or three-dimensional applications. Continuum damage mechanics serves as the framework to describe the basic damage variables, namely the tensile and compressive damage. The homogenized Helmholtz free energy is introduced as the bridge to link the micro-cell and macroscopic material. The crack propagation in micro-cells is modeled, and the Helmholtz free energy in the cracked micro-structure is calculated and employed to extract the damage evolution functions in the macroscopic material. Based on the damage energy release rates and damage consistent condition, the energy equivalent strain is used to expand the uniaxial damage model to the multi-dimensional damage model. Agreements with existing experimental data that include uniaxial tensile and compressive tests, biaxial compression and biaxial peak stress envelop demonstrate the capacity of the multi-scale damage model in reproducing the typical nonlinear performances of concrete specimens. The simulation of precast laminated concrete slab further demonstrates its application to concrete structures.