Intrinsic Incremental Mechanics

Abstract

We produce a coordinate free presentation of some concepts usually involved in incremental mechanics (tangent linear stiffness matrix, stability, loading paths for example) but not always well founded. Thanks to the geometric language of vector bundles, a well defined geometrical object may be associated to each of these tools that allows us to understand some latent difficulties linked with these tools due to the absence of a natural connection and also to extend some of our recent results of linear stability to a non linear framework.