循环稳定材料的棘轮行为:II.隐式应力积分算法和有限元实现

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。

RATCHETING OF CYCLICALLY STABLE MATERIALS: II. IMPLICIT STRESS INTEGRATION ALGORITHM AND FINITE ELEMENT IMPLEMENTATION

The numerical calculation method and finite element implementation of a new visco-plastic constitutive model developed in the first part of this work are discussed. The model describes the ratcheting of cyclically stable materials reasonably. Based on the radial return method and backward Euler integration, a new implicit stress integration algorithm is proposed for the developed visco-plastic constitutive model by combining the successive substitution method. Meanwhile, in order to implement the model into a commercial finite element code (such as ABAQUS), a new expression of consistent tangent modulus necessary for whole nodal iteration of finite element calculation is also derived for rate-dependent plasticity. Numerical examples are given to verify the advantage of the stress integration algorithm and the finite element implementation, as well as the capability of the model in simulating the ratcheting of specific structural components.