CALCULATION FOR PATH-DOMAIN INDEPENDENT J INTEGRAL WITH ELASTO-VISCOPLASTIC CONSISTENT TANGENT OPERATOR CONCEPT-BASED BOUNDARY ELEMENT METHODS

This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.

Elasto-viscoplastic consistent tangent operator concept-based implicit boundary element methods

An elasto-viscoplastic consistent tangent operator (CTO) concept-based implicit algorithm for nonlinear boundary element methods is presented. Both kinematic and isotropic strain hardening are considered. The elasto-viscoplastic radial return algorithm (RRA) and the elasto-viscoplastic CTO and its related scheme are developed. In addition, the limit cases (e.g. elastoplastic problem) of vis-coplastic RRA and CTO are discussed. Finally, numerical examples, which are compared with the latest FEM results of Ibrahimbegovic et al. and ABAQUS results, are provided.

黏弹-双曲线Drucker-Prager塑性模型应力更新隐式算法

黏弹-塑性模型是由黏弹性模型与塑性元件串联而成,可视为黏弹-黏塑性模型中黏塑性黏度参数趋于0的一种极限情况,为黏弹性材料的结构破坏分析提供了一个途径。把黏弹-塑性模型的应变增量分解为黏弹和塑性增量两部分,考虑黏弹性应变历史,把黏弹性积分型本构关系在一个时步内线性化,定义与时间增量相关的剪切模量和体积模量,导出应力递推公式,把黏弹-塑性本构积分转化为与弹塑性相似的形式。针对由黏弹性和双曲线Drucker-Prager塑性、各向同性硬化的黏弹-塑性模型,通过黏弹性预估和塑性校正"二步"算法实现对应力的更新,给出完全隐式算法和最终的计算公式。算例比较分析表明,由于迭代过程中仅需要简单的函数计算,该算法具有很好的收敛性。一般经过2次迭代运算后,屈服函数值已达到10-10的量级,应力点便返回到屈服面上。

黏弹-Perzyna黏塑性有限元法应力更新隐式算法

黏弹-黏塑性耦合模型的黏弹性部分由弹簧、黏壶和Kelvin链串联而成,黏塑性部分为双曲线型DruckerPrager屈服函数、各向同性硬化和Perzyna黏塑性流动模型。基于黏弹性蠕变柔度,通过定义与弹性问题相对应的与时间增量相关的黏弹性剪切模量和体积模量,导出增量递推形式的本构方程。为保证算法的收敛和稳定性,把Perzyna黏塑性流动方程转化为与弹塑性相似的一致性条件,建立黏塑性增量因子单侧逼近其收敛值的N-R迭代算法。最后,给出应力更新完全隐式算法和最终计算公式。分别采用黏弹性、黏弹-塑性和黏弹-黏塑性本构关系对一地基蠕变模型进行三维有限元分析和比较,结果表明,本文算法具有较高的计算效率和稳定性。

用于设计灵敏度分析的弹粘塑性边界元法

基于一致切线算子概念的弹粘塑性隐式边界元方法,进行了弹粘塑性设计灵敏度分析.采用了Perzyna经典粘塑性本构模型,针对包含各向同性硬化和运动硬化的混合硬化模型,导出了弹粘塑性灵敏度分析的径向返回算法和一致切线算子.利用直接微分的方法,建立了设计灵敏度分析的弹粘塑性边界元增量方程,导出了弹粘塑性径向返回的灵敏度公式.给出了在不同粘塑性流动参数下的三个典型算例的结果,与ANSYS结果相吻合,证明了方法是正确的.

有限元实现含应变非强化区的双面循环塑性模型

在有限单元方法的框架下,由广义径向返回法来实现含有应变非强化区的循双面环塑性本构模型。在小变形的假设下,本文详细描述了有限元方法实现率无关的双面循环塑性本构模型的完整算法。采用向后Euler隐式算法进行离散积分,其最终可化简为一个非线性方程,并且由Peg-asus方法来求解。对径向返回法进行线性化,可以得到切向刚度算子。最后,文中通过两个算例表征了离散积分的精确性和材料模型的正确性。