Shear banding as an optimal dissipative structure

  • Nicot, Francois (Univ Savoie Mont Blanc)
  • Wang, Xiaoxiao (USTB / USMB)
  • Wautier, Antoine (INRAE)
  • Wan, Richard (Univ Calgary)
  • Darve, Felix (Univ Grenoble Alpes)

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Granular materials are now known to be an illustration of complex materials as they display emergent macroscopic properties when loaded. An initially homogenous response can bifurcate into a heterogeneous one with the appearance of a rich variety of structured kinematical patterns. The shear banding that ensues illustrates a symmetry-breaking transition with multiple choices of macroscopic behaviours, a common feature of dynamical complex systems. Even though the phenomenon has been studied for decades, this regime transition remains mostly mysterious in geomaterials, with no convincing arguments that could link it to the underlying microscopic mechanisms. This contribution revisits this issue by invoking fundamental extremal entropy production principles to seek any connection with the second-order work theory in the mechanics of failure. Our findings are verified through discrete element simulations that highlight the fundamental role played by the elastic energy stored within a granular material before a bifurcation occurs, which also corresponds to a minimization of the entropy production. The analysis suggests a new interpretation of the intriguing shear banding phenomenon as a bifurcation with the emergence of optimal dissipative structures germane to nonequilibrium thermodynamics of open systems. Deng, N., Wautier, A., Tordesillas, A., Thiery, Y., Yin, Z. Y., Hicher, P. Y., & Nicot, F. (2022). Lifespan dynamics of cluster conformations in stationary regimes in granular materials. Physical Review E, 105(1), 014902. Parisi, G., Procaccia, I., Rainone, C., Singh, M. (2017): Shear bands as manifestation of a criticality in yielding amorphous solids. Proc. Natl. Acad. Sci. U. S. A., Vol. 114, pp. Prigogine, I., and Lefever, R. (1968): Symmetry Breaking Instabilites in Dissipative Systems. The Journal of Chemical Physics, vol. 48, no 4, pp. 1695–1700. Prigogine, I., and Lefever, R. (1975): Stability and Self-Organization in Open Systems. Advances in Chemical Physics, Vol. 29, pp. 1–28. Wan, R., Nicot, F., and Darve, F. (2017): Failure in geomaterials, a contemporary treatise. Wiley. Ziegler, H., and Wehrli, C. (1987). On a principle of maximal rate of entropy production. J. Non-Equilib. Thermodyn., Vol. 12 (3), pp. 229–243.