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Pure Plastic Behavior and the Assumption of Zero Elasticity at the Limit Load


 The authors have introduced an analysis based on a modification of the Mooney Rivlin material to obtain an estimate of the plastic behavior of a structure near its failure point. In this paper we generalize the concept of zero elasticity and pure plastic behavior at the limit loads and beyond [1–2]. The theorems of limit analysis assume rigid plastic behavior that is equivalent to zero elasticity. We are concerned with the regions just beyond the limit load, so it is not unreasonable to again assume zero elasticity in this region.
 The neglect of elastic behavior allows us to concentrate on large plastic strains that take place at or beyond the limit loads as defined by Limit Analysis [3–4]. We can focus on tearing, Plastic Fracture Mechanics and low-cycle fatigue respectively. In such situations the practice has been adopted to label such state points as ‘Ultimate’ behavior. Here we adopt the same label to refer to behavior at or beyond the limit load, where the full large displacement and work hardening effects can be accounted for by the modified Mooney Rivlin material.
 The mechanics of fracture has also been applied to the tearing of Vulcanized rubber by Rivlin and Thomas[5]. This study concerned large nonlinear incompressible strains that were modeled by Mooney Rivlin Materials, Mooney[6]. The Fracture is modeled by the balance of internal and external work caused by the advancing crack surface area [7–8]. One final benefit of the assumption of zero elasticity is its simplification of dynamic analysis.