A bipotential approach for plastic limit loads of strip footings with non-associated materials. (April 2017)

• Record Type: Journal Article
• Authors: Hamlaoui, Madani; Oueslati, Abdelbacet; Saxcé, Géry De
• Is Part Of: International journal of non-linear mechanics. Volume 90(2017)
• Page Start: 1
• Page End: 10
• Publication Date: 2017-04
• Subjects: Non-associated plasticity -- Bipotential -- Mohr–Coulomb criterion -- Collapse load; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2016.12.001
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: This paper is concerned with a bipotential approach for estimating the plastic collapse loads of a half-space made with a non-associated Mohr–Coulomb material and indented by a rigid punch. In geotechnics, this problem is called the bearing capacity of shallow strip footing for which the analytical solution is derived by Prandtl (1920)[46] and Hill (1950)[35] in the context of associated plasticity. However, when the plastic model is not associated, no analytical methods have yet been developed. Here we explore this issue in a rigorous mathematical framework coupling the bipotential concept and limit analysis. First, the method proposed makes use of the method of characteristics to build a statically and plastically admissible stress field that enables a lower estimate of the plastic limit loads. Next, the extended kinematic theorem of limit analysis to non-standard plasticity is applied to derive an upper quasi-bound of the collapse loads. For this aim, the internal rate of plastic dissipation is obtained thanks to the bipotential functional depending on both a trial stress field and a Prandtl-like collapse mechanism. The analytic estimates are compared to the formulae and numerical results provided in literature.