An adaptive Ritz formulation for progressive damage modelling in variable angle tow composite plates

In this work, an adaptive Ritz model for the analysis of variable angle tow composite plates featuring damage initiation and evolution under progressive loading is proposed, developed, implemented and tested. The plate kinematics is represented employing a first-order shear deformation theory, while the plate equilibrium equations at a given load step are obtained by minimizing the structure potential energy. The constitutive behaviour is modelled within the framework of continuum damage mechanics. In particular the initiation and evolution of damage, up to failure, are tracked by defining irreversible damage indices related to both fibres and matrix, both in tensile or compression loading. The discrete equations are then obtained by assuming a polynomial Ritz approximation of the primary kinematic variables in the energy minimization. Preliminary tests show how the application of the method as a single-domain approach induces the emergence of problematic spurious effects, related to Gibbs artefacts due to the inability of the selected polynomial basis to represent damage localization. An adaptive multi-domain technique is thus proposed to circumvent such issues, which has been successfully validated by benchmark tests. Eventually, original results about variable angle tow plates featuring damage evolution under progressive loading are presented.