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Under compressive creep, visco-plastic solids experiencing internal masstransfer processes have been recently proposed to accommodate singular cnoidalwave solutions, as material instabilities at the stationary wave limit. Theseinstabilities appear when the loading rate is significantly faster than thecapability of the material to diffuse internal perturbations and lead tolocalized failure features (e.g., cracks and compaction bands). This type ofsolution, generally found in fluids, has strong nonlinearities and periodicpatterns. Due to the singular nature of the solutions, the applicability of thetheory is currently limited. Additionally, effective numerical tools requireproper regularization to overcome the challenges that singularity induces. Wefocus on the numerical treatment of the governing equation using a nonlinearapproach building on a recent adaptive stabilized finite element method. Thismethod provides a residual representation to drive adaptive mesh refinement, aparticularly useful feature for the problem at hand. We compare againstanalytical and standard finite element solutions to demonstrate the performanceof our approach. We then investigate the sensitivity of the diffusivity ratio,main parameter of the problem, and identify multiple possible solutions, withmultiple stress peaks. Finally, we show the evolution of the spacing betweenpeaks for all solutions as a function of that parameter.

Adaptive stabilized finite elements: Continuation analysis of compaction banding in geomaterials