Explicit edge-based smoothed numerical manifold method for transient dynamic modeling of two-dimensional stationary cracks

Abstract

Abstract Modeling and prediction of dynamic behaviors of cracked bodies are vital to the safety evaluation of structures. The numerical manifold method (NMM) has achieved considerable success in crack analysis as it provides a powerful representation of complex discontinuities. Strain smoothing has been incorporated into enriched methods such as NMM to improve their accuracy, efficiency, and tolerance to mesh distortion. However, conventional strain smoothing cannot reproduce the large spatial variance in the strain surrounding crack tips. Consequently, the accuracy is reduced when it is applied to crack-tip enrichment bases. High-fidelity representation of crack-tip fields can be achieved by crack-tip enrichment. Therefore, it is desirable to combine compatible strain for the enriched areas with edge-based smoothed strain for the remaining areas. When explicit time integration is employed, it is beneficial to use a lumped mass matrix because it provides a larger critical time step and a straightforward solution of the linear algebraic equation. A local-approximation-based mass lumping strategy is used to obtain a block-diagonal mass matrix with small blocks. Finally, the proposed methodology is applied to various static and dynamic crack analyses, and highly accurate and stable results are obtained.