Intrinsic incremental evolution of hypoelastic discrete mechanical systems

Abstract

AbstractThis 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.