Folding and Boudinage As the Same Fundamental Energy Bifurcation in Elasto-Visco-Plastic Rocks

Abstract:

Folding or boudinage are commonly thought to develop due to viscosity contrasts induced by either geometric interactions or material imperfections. However, there exists an additional localization phenomenon, i.e. strain localization out of steady state in homogeneous materials at a critical material parameter (set) or deformation rate. This study focuses on imperfections in terms of grain size variations, using the paleowattmeter relationship [Austin and Evans, 2007; 2009, Herwegh et al., 2014]. We identify the parameters for bifurcation, which is the critical amount of dissipation, expressed by the Gruntfest number [Gruntfest, 1963], incorporating flow stress, the Arrhenius number (Q/RT) and the layer dimensions. We verify the robustness of the solution through a method, developed to analyze such material instabilities [Rudnicki and Rice, 1975]. The second step is to identify the natural mode shapes and frequencies of the geometric structure and material parameters, including geometric imperfections. In a third step, the eigenmodes are perturbed and superposed to the initial conditions. We then subject the composite structure to natural deformation conditions. Grain sizes within the layer relatively quickly equilibrate to a homogeneous state, which is in response to energy optimization following the paleowattmeterrelationship. Upon continued loading, localization in terms of a necking or folding instability consequently arises out of this steady state. We obtain the criteria for the onset of localization from theory and numerical simulation, i.e. the critical Gruntfest number. Boudinage and folding instabilities occur when heat produced by dissipative work overcomes the diffusive capacity of the system. Both instabilities develop for the exact same Arrhenius and Gruntfestnumbers. Consequently, folding and boudinage instabilities can be seen as the same energy bifurcation triggered by dissipative work out of homogeneous state.

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Herwegh, M., Poulet, T., Karrech, A. and Regenauer-Lieb, K. (2014) Journal of Geophysical Research, 119

Rudnicki, J.W. and Rice, J.R. (1975) Journal of Mechanics and Physics of Solids, 23