Phase field modeling of anisotropic silicon crystalline cracking in 3D thin-walled photovoltaic laminates

Abstract

A novel computational framework integrating the phase field approach with the solid shell formulation at finite deformation is proposed to model the anisotropic fracture of silicon solar cells in the thin-walled photovoltaic laminates. To alleviate the locking effects, both the enhanced assumed strain and assumed natural strain methods are incorporated in the solid shell element formulation. Aiming at tackling the poor convergence performance of standard Newton schemes, the efficient and robust quasi-Newton scheme is adopted for the solution of phase field modeling with enhanced shell formulation in a monolithic manner. Due to fracture anisotropy of the brittle silicon solar cells, the second-order structural tensor that is defined by the normal of preferential crack plane is introduced into the crack energy density function in the phase field modeling. On the other hand, to efficiently predict the crack growth of silicon solar cells, a global–local approach in the 3D setting proposed in the previous work is adopted here for the fracture modeling. In this approach, both mechanical deformation and phase field fracture are accounted for at the local model, while only mechanical deformation is addressed at the global level. At each time step, the solution of the global model is used to drive the local model, which corresponds to the one-way coupling in line with experimental evidence that the silicon cell cracking has negligible influence on the stiffness of photovoltaic modules. The capability of the modeling framework is demonstrated through numerical simulation of silicon solar cell cracking in the photovoltaic modules when subjected to different loading cases.