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Shakedown with nonlinear strain-hardening including structural computation using finite element method. (English) Zbl 0766.73026

Summary: An overlay model intended to simulate the elastic, plastic strain- hardening material behaviour is presented. A static shakedown theorem is formulated. It is shown that the necessary shakedown conditions for a general nonlinear kinematic hardening material are the sufficient ones for the proposed material model. It is also shown that the result obtained by using the proposed model is a generalization of the result obtained by Melan [E. Melan, Ing.-Arch. 8, 116 ff (1938)] for materials with linear, unlimited, kinematic hardening. Based on a reduction technique, a numerical procedure for determination of shakedown loads of perfectly plastic materials is presented. Modification is also given, which is necessary for employing the developed algorithm to the proposed overlay model. The influence of strain-hardening on the shakedown loads is illustrated and discussed via different examples.

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74S05 Finite element methods applied to problems in solid mechanics
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