An open-source LS-DYNA implementation of the variational damage model

The variational damage model (VDM), formulated within a variational framework, provides an effective and computationally efficient approach to fracture modeling. However, existing implementations primarily rely on custom-developed codes, which limits their accessibility and broader adoption in engineering applications. To address this limitation, this study integrates newly developed variational damage models into the commercial finite element software LS-DYNA, enabling their practical use in large-scale simulations. Building upon the VDM and the novel variational damage model (NVDM) proposed by Ren et al. (2024), this work develops user-defined material subroutines (UMATs) for LS-DYNA: (i) UMAT-VDM: A variational damage model. (ii) UMAT-NVDM: An enhanced variational damage model incorporating a threshold parameter. The effectiveness of these implementations is assessed through a series of quasi-static and dynamic fracture simulations. The results demonstrate that both UMAT-VDM and UMAT-NVDM accurately capture sharp crack interfaces while maintaining computational efficiency due to the absence of gradient terms. Additionally, UMAT-NVDM produces finer crack patterns and exhibits improved capability in modeling complex fracture processes compared to UMAT-VDM. To facilitate further research and application, the open-source implementation of these subroutines, written in free-format FORTRAN90 syntax, is publicly available on GitHub at https://github.com/yaduann/vdm-and-nvdm.