Limit analysis theorems for implicit standard materials: application to the unilateral contact with dry friction and the non-associated flow rules in soils and rocks

摘要

A new class of materials called Implicit Standard Materials was proposed in a previous work. It allows one to generalize Fenchel's inequality and then to recover flow rule normality for non-standard behaviours, in particular for soils andunilateral contact with dry friction. In this work an extension of the limit analysis theorems to this news class of materials is presented. Some relevant features are pointed out. such as non-uniqueness of the limit load and coupling of the lower andupper bound problems. Some analytical and numerical solutions are presented to illustrate the theory.