A higher gradient formulation and meshfree-based computations for elastic rock

Abstract

In this work a non-classical continuum is derived from a unified formulation based on the generalized deformation field. This approach involves new strain measures which allow for the formulation of a generalized variational principle. It is demonstrated how to model micro-structure related material behaviour by a continuum mechanical approach in a very straight forward way. As an illustration excavations in dry rock conglomerate with two different geometrical configuration are modelled with a meshfree method based on moving least squares (Lancaster and Salkauskas, 1981). Thereby, the resulting displacement and stress field using a classical Green strain tensor based formulation (Skatulla and Sansour, 2005) is compared with the solution of the non-classical formulation. The use of meshfree methods in particular, proves to be advantageous, because it makes it possible to approximate the displacement field, and also its first derivatives.