An elasto-plastic damage model for functionally graded plates with in-plane material properties variation: Material model and numerical implementation

The paper presents an elasto-plastic damage model based on irreversible thermodynamics for the analysis of functionally graded (FG) plates with in-plane material properties variations. The model considers a simple power law function to describe the FG plates as continua with smooth variation of material properties, such as Young's Modulus, yield stress, plastic material constants and damage parameters. By introducing two independent plastic and damage multipliers, the model is applicable to different types of materials. Employing the operator splitting methodology, a three-step predictor/multi-corrector algorithm is developed that includes an elastic predictor, a plastic corrector, and a damage corrector. Then, the damage finite element (FE) solutions are obtained using linear hexahedral solid elements with spatially graded property distribution (at different Gauss points), and subsequently implemented by a user material subroutine (UMAT) in the ABAQUS FE software. Good agreement is shown between the analytical damage models, the FE solutions and experimental results sourced from the literature. Several numerical examples establish that the present model is not only accurate, but provides a simple approach to predicting damage of different types of materials, including those that demonstrate both elastic-brittle damage and elasto-plastic damage behaviours. Moreover, the presented model effectively describes the continuum damage of FG plates, capturing variation of the damage variable throughout the plane of the plate.