Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

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 capacit...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2021-11, Vol.122 (21), p.6234-6252
Main Authors: Cier, Roberto J., Poulet, Thomas, Rojas, Sergio, Veveakis, Manolis, Calo, Victor M.
Format: Article
Language:English
Subjects:
automatic adaptivity
Cnoidal waves
Cold flow
compaction banding
Creep (materials)
discontinuous Galerkin
Finite element method
Geomaterials
Loading rate
Mass transfer
Nonlinearity
numerical continuation
Parameter identification
Parameter sensitivity
Perturbation
Process parameters
Regularization
stabilized finite element method
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Summary: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. Finally, we show the evolution of the spacing between peaks for all solutions as a function of that parameter.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6790