The 15th U.S. National Congress on Computational Mechanics was held in downtown Austin from July 28 - Augest 1, 2019. I gave an oral presentation, A Homogenization-based Phase Field Approach to Fracture. Also I joined the poster competition.
Pictures
Abstract
- Title: A Homogenization-based Phase Field Approach to Fracture
- Abstract: The regularized variational theory of fracture (Bourdin et al., 2000), or so-called phase field approach to fracture, has gained popularity due to its ability to predict crack nucleation, propagation, and branching without extra criteria. This approach works by minimizing a total energy functional with the displacement field and phase field (0=intact material, 1=crack) as arguments, and eliminates the cumbersome geometric tracking compared with traditional discrete crack methods such as the extended finite element method. However, each of the prevailing models (Amor et al., 2009; Miehe et al. 2010) predicts a different crack path even under certain simple loadings. In order to get a model with proper tension-compression decomposition, we apply the homogenization theory to construct a phase field model, which predicts reasonable crack paths for the three-point bending test and through-crack shear test, among others. We will compare the prediction of our model with similar ones proposed by Stobl and Seelig (2015) and Steinke and Kaliske (2018).
- Reference:
- Bourdin, B., Francfort, G. A., Marigo, J.-J., 2000. Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids 48 (4) 797–826.
- Steinke, C., Kaliske, M., 2018. A phase-field crack model based on directional stress decomposition. Computational Mechanics. https://doi.org/10.1007/s00466-018-1635-0.
- Strobl, M., Seelig, T., 2015. A novel treatment of crack boundary conditions in phase field models of fracture. Proceedings in Applied Mathematics and Mechanics 15 (1) 155–156.