The role of non-normality in soil mechanics and some of its mathematical consequences

✍ Scribed by R. Nova

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 268 KB
• Volume: 31
• Category: Article
• ISSN: 0266-352X
• DOI: 10.1016/j.compgeo.2004.01.006

✦ Synopsis

Experimental data suggest that the normality rule concept, widely used in metal plasticity, is not applicable to geomaterials. The concept of plastic potential can be retained, however, provided it is assumed that this is different from the loading function (nonassociate flow rule). The elastic-plastic stiffness matrix becomes non-symmetric and the stiffness matrix looses its positive definiteness in the hardening regime. From that point onwards, some of its principal minors can become zero. It is proven that, each time this occurs, it is possible to find a particular loading programme for which an infinity of solutions exist under a given load increment (homogeneous bifurcation). It is shown that various types of instability can be described this way, all occurring in the hardening regime. For example, the onset of instability in undrained tests on loose sand, the occurrence of drained and undrained shear bands in plane strain conditions, the possibility of unlimited pore water pressure generation in undrained conditions can be described.