Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials - Part I: Formulations

Innovative strain energy based coupled elastoplastic hybrid isotropic and anisotropic damage and healing formulations for geomaterials are developed and implemented for numerical 2D earth-moving processes and cyclic loading simulations. A class of elastoplastic constitutive damage-healing models, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy based formulation. In particular, the governing incremental damage and healing evolutions are coupled and characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence. The plastic flow is introduced by means of an additive split of the stress tensor. In this innovative formulation, we introduce two characteristic energy norms of the tensile and compressive strain tensors, respectively, for the damage and healing mechanisms. By incorporating a micromechanics-motivated brittle (tensile) damage characterization (P+) and a ductile (mixed tension-compression) damage-healing characterization (P-mix(+)), the proposed hybrid isotropic and anisotropic models for soils are derived. Completely new computational algorithms are systematically developed in Part II of this sequel, based on the two-step operator splitting methodology. The elastic damage-healing predictor and the effective plastic return mapping corrector are implemented within the reproducing kernel particle method meshfree codes.