Rate-Dependent Augmented Finite Element Method for Arbitrary Crack Growth Under Cyclic and Impact Loading
摘要
Experimental observations indicate that the loading rate, such as frequency in cyclic loading or velocity in impact loading, can significantly influence crack propagation. To accurately capture this phenomenon in numerical simulations, this study introduces a rate-dependent augmented finite element method (AFEM), which enables the analysis of crack propagation along arbitrary paths under repetitive loading. The method employs the maximum principal stress criterion to determine whether a crack will propagate and to predict its growth path. The crack propagation path splits the existing elements into two sub-elements, which are then reassembled with cohesive elements inserted between them to create augmented finite elements. The cohesive elements are based on a rate-dependent cohesive zone model (CZM) and account for the accumulation of damage, reflecting the rate dependence of material damage and cracking during repeated loading. The internal nodal degrees of freedom (DoFs) of the augmented finite elements are condensed, retaining only the external nodal DoFs. Based on the proposed methodology, this study develops a numerical algorithm implemented through a user-defined element (UEL) subroutine in the commercial finite element software ABAQUS. The proposed approach is validated through case studies involving both cyclic and impact loading scenarios. Results demonstrate that the method can predict arbitrary crack propagation paths under different loading frequencies and velocities, providing an effective tool for analyzing rate-dependent fracture processes in engineering structures.