Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2023

Intrinsic incremental evolution of hypoelastic discrete mechanical systems

Résumé

This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete mechanics in the framework of potentially non integrable hypoelasticity. First, the general framework is developed in order to tackle hypoelasticity as an Ehresmann connection on the cotangent bundle . Two types of incremental evolutions may be distinguished, the weak or integrable incremental evolutions and the strong or non integrable incremental evolutions, according to the nature of the hypoelastic constitutive law. The geometric structure of the double tangent bundle is fully used in order to get the geometric counterpart κ of the so‐called tangent stiffness matrix. Subject to specific conditions in , the incremental evolution is then a well‐founded question. An hypoelastic four‐grains granular system illustrates in detail these general results.

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hal-04351304 , version 1 (06-04-2026)

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Jean Lerbet, Noël Challamel, Francois Nicot, Félix Darve. Intrinsic incremental evolution of hypoelastic discrete mechanical systems. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2023, 103 (11), ⟨10.1002/zamm.202300078⟩. ⟨hal-04351304⟩
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