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

• Published in: Geomechanics and geoengineering : an international journal Vol. 2; no. 1; pp. 3 - 15
• Main Authors: Sansour, C., Skatulla, S.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 20.03.2007
• Subjects: Generalized continua; Meshfree methods; Micro-continuum; Scale effects
• ISSN: 1748-6025; 1748-6033
• DOI: 10.1080/17486020601173185

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.