Integrated microplane model with the HFGMC micromechanics for nonlinear analysis of composite materials with evolving damage

A nonlinear formulation of the high fidelity generalized method of cells (HFGMC) is offered for the micromechanical analysis of two and three-dimensional (3D) multiphase periodic composites with evolving matrix damage. To that end, the microplane constitutive modeling theory is integrated within the HFGMC to represent the nonlinear and strain softening of the matrix subcells. The nonlinear micromechanical formulation of both the HFGMC and the microplane theories are both developed and integrated in a nested fashion. The formulation of the parametric HFGMC, with independent geometrical mapping, is expanded and shown to be well suited for efficient nonlinear computational micromechanics. A new average virtual work integral form is proposed for the HFGMC method which allows for the definition of a generalized internal resisting force vector along with its corresponding symmetric stiffness matrix. Unlike the nodal displacement-based finite element (FE), the proposed HFGMC and its weak form are cast in terms of the work-conjugate average displacement and traction vectors, defined on the surfaces (faces) of the subcells. This allows direct interface continuity relations between the hexahedral subcells. The microplane theory is formulated kinematically using its transformed strain with a double split, namely the volumetric (V) and a deviatoric-tangential (DT) splits. The microplane model is implemented with simple 1D continuum damage laws and strain softening, which are used in the two split parts. The stress-strain behavior in the volumetric part has independent nonlinear behaviors in tension and compression. Several applications for doubly and triply periodic 3D composites with evolving matrix damage are presented with refined micromechanical analysis. The use of the microplane theory is shown to be an effective approach for damage analysis in the constituents of the composite unit-cell. The HFGMC micromechanics is well suited for integrating the microplane response and predicting the fiber-matrix spatial local fields including damage effects. The proposed integrated microplane and micromechanics frameworks can be extended to other heterogeneous composites with different mechanical behaviors, such as visco-elasticity, visco-plasticity, among others.