A new approach on constitutive modeling for quasi-brittle materials under multiaxial loading

Abstract This work introduces a new method for expanding unidimensional models to predict material behavior under multiaxial loading. The concept of six-dimensional mechanical space is adopted, and in each basis direction of the space, there is one fiber-bundle model (FBM), so these six FBMs are independent amongst one another but follow the same damage evolution rule. Under triaxial loading, these FBMs have different stress and strain states, so six corresponding damage variables have different values. The anisotropic damage is thus represented by the six damage variables. When it is under uniaxial loading, the six-dimensional space reduces to one-dimensional space, so the proposed model can be calibrated using uniaxial loading test data, and the calibrated model can predict the material behavior under multiaxial loading conditions. Biaxial loading and triaxial loading test data are used to verify the proposed model, and parametric analyses are performed to analyze model predictions under different loading conditions. It shows that model predictions agree well with the test data and are consistent with experimental observations.