A multi phase-field fracture model for long fiber reinforced composites based on the Puck theory of failure

Phase-Field (PF) methods of fracture have emerged as powerful modeling tools for triggering fracture events in solids. These numerical techniques efficiently alleviate mesh dependent pathologies and are very suitable for characterizing brittle as well as quasi-brittle fracture in a wide range of engineering materials and structures including fiber reinforced composites. In this work, a multi phase-field model relying on the Puck’s failure theory is proposed for triggering intra-laminar cracking in long fiber reinforced composites. The current formulation encompasses the differentiation of fiber and inter-fiber (matrix-dominated) failure phenomena via the consideration of two independent phase-field damage-like variables, and the corresponding evolution equations and length scales. Moreover, for matrix-dominated deformation states, the present formulations endow the incorporation of plastic effects via an invariant-based plasticity model. Special attention is also devoted to its finite element implementation, which is conducted using the user-defined capabilities UMAT and UEL of ABAQUS, in conjunction with the thorough assessment of its thermodynamic consistency. Several representative applications pinpoint the applicability of the proposed computational tool.