AN ENERGY-BASED CONSTITUTIVE MODEL FOR ANISOTROPIC SOLIDS SUBJECT TO DAMAGE

This paper presents an energy-based constitutive model for anisotropic solids. The model attempts to characterize initial anisotropic elastic response, elastic degradation due to anisotropic damage microcracking, yield and subsequent plastic flow, and material failure. The theory treats three-dimensional anisotropic materials subject to small strains. The treatment of anisotropic damage microcracking is approached from a macroscopic perspective. The generalized Hooke's law can be written in tensorial form in six-dimensional space. The six eigenvalues of the compliance tenser are then constants of proportionality between the stress and strain eigenvectors. Further, the strain energy stored in an anisotropic solid can be additively decomposed into six independent, non-interacting energy modes. Damage, characterized by a symmetrical second rank tenser, is postulated to grow when the energy level in any such mode reaches a critical value. The rate of damage growth is formulated in terms of the energy modes. The yield conditions are formulated in terms of the second invariants of the eigenstresses. An associated flow rule is developed. Material failure is assumed to occur when any one of the energy modes reaches a critical threshold. A numerical algorithm is used to solve the rate constitutive equations. The proposed constitutive model is compared to uniaxial stress-strain data and biaxial failure data for orthotropic paperboard. The model predicts the stress-strain response of this nonlinear material with reasonable accuracy. In the case of biaxial loading, the failure predictions are fairly consistent with the failure data in three of the four quadrants of the stress space.