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针对第一部分发展的、能够合理描述循环稳定材料棘轮行为的粘塑性本构模型,详细讨论该模型的数值计算方法和有限元实现。在径向回退(RadialReturn)和向后欧拉积分方法的基础上,结合连续迭代(SuccessiveSubstitution)方法,推导并建立了针对循环粘塑性本构模型的、新的隐式应力积分算法。为了本构模型在大型有限元分析程序(如ABAQUS等)中的实现,针对有限元的整体节点迭代计算,推导和确立了一个新的、考虑率相关塑性的一致切线刚度矩阵(ConsistentTangentModulus)表达式。通过对一些算例的有限元分析,讨论了建立的隐式应力积分算法的优越性,同时对特定构件的棘轮行为进行了数值模拟,进而检验了有限元实现的合理性和必要性。
Aiming at the visco-plastic constitutive model developed in the first part, which can reasonably describe the ratcheting behavior of the cyclic stable material, the numerical calculation method and the finite element realization of the model are discussed in detail. Based on RadialReturn and backward Euler integral methods, a new implicit stress integration algorithm for cyclic visco-plastic constitutive model is derived and established in conjunction with Successive Subversion method. For the realization of constitutive model in large-scale finite element analysis program (such as ABAQUS), a new iterative computation of integral nodes of finite element method is deduced and established. ConsistentTangentModulus expression . Through the finite element analysis of some examples, the superiority of the established implicit stress integration algorithm is discussed. At the same time, the numerical simulation of the ratchet behavior of a specific component is carried out, and the rationality and necessity of the finite element realization are verified.