A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening
A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening
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DOI：
10.1016/j.ijsolstr.2005.06.042
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发表时间：
2006-05
影响因子：
3.6
通讯作者：
C. Bouby;G. Saxcé;Jean-Bernard Tritsch
中科院分区：
文献类型：
--
作者：
C. Bouby;G. Saxcé;Jean-Bernard Tritsch
广义标准材料的类别与非结合本构方程的建模无关。的bipotential的方法，根据可能的推广Fenchel的不等式，允许恢复的流动规则正常的一个弱形式的隐式关系。这定义了隐式标准材料的类别。对于这样的行为，这导致了一个弱扩展的经典的安定分析的界限定理。在本文中，我们回顾了这一理论的相关特征。考虑弹塑性材料的非线性随动硬化规则，我们将其应用到问题的一个样品在平面应变条件下的恒定牵引和交变扭转，以确定解析的相互作用曲线界定安定域。本文的目的是证明这个例子的解决方案的准确性，通过比较它的逐步计算的弹塑性响应的机构下重复循环载荷的增加水平。提出了一个可靠的停止计算的准则。将解析解和数值解进行了比较，发现两者是相互封闭的.此外，该方法允许揭示一个额外的“2周安定曲线”，可能是有用的结构的安定设计。
The class of generalized standard materials is not relevant to model the nonassociative constitutive equations. The bipotential approach, based on a possible generalization of Fenchel’s inequality, allows the recovery of the flow rule normality in a weak form of an implicit relation. This defines the class of implicit standard materials. For such behaviours, this leads to a weak extension of the classical bound theorems of the shakedown analysis. In the present paper, we recall the relevant features of this theory. Considering an elastoplastic material with nonlinear kinematic hardening rule, we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain. The aim of the paper is to prove the exactness of the solution for this example by comparing it to step-by-step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level. A reliable criterion to stop the computations is proposed. The analytical and numerical solutions are compared and found to be closed one of each other. Moreover, the method allows uncovering an additional ‘2 cycle shakedown curve’ that could be useful for the shakedown design of structure.