Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials
[1];
- Curtin University, Bentley, WA (Australia); Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington WA (Australia); OSTI
- Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington WA (Australia)
- Pontificia Universidad Católica de Valparaíso, Valparaíso (Chile)
- Duke University, Durham, NC (United States)
- Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington WA (Australia); Curtin University, Bentley, WA (Australia)
Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.
- Research Organization:
- Duke University, Durham, NC (United States)
- Sponsoring Organization:
- USDOE Office of Nuclear Energy (NE); Australian Research Council's Discovery Projects; Commonwealth Scientific and Industrial Research Organisation (CSIRO); European Union's Horizon 2020; National Fund for Scientific and Technological Development (FONDECYT)
- Grant/Contract Number:
- NE0008746
- OSTI ID:
- 1976366
- Journal Information:
- International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 21 Vol. 122; ISSN 0029-5981
- Publisher:
- WileyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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