An efficient return mapping algorithm for general isotropic elastoplasticity in principal space
An efficient return mapping algorithm for general isotropic elastoplasticity in principal space
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DOI：
10.1016/j.compstruc.2011.11.006
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发表时间：
2012-02
影响因子：
4.7
通讯作者：
Q. Peng;M. X. Chen
中科院分区：
文献类型：
--
作者：
Q. Peng;M. X. Chen
本文发展了一种求解一般各向同性弹塑性本构方程隐式积分的高效返回映射算法。一组三个相互正交的单位基张量结合一组新的三个不变量的表示任意各向同性张量值和标量值函数的应力张量。基张量由应力张量通过表示定理构造而成，三个不变量由应力在基张量上的投影定义。在几何上，基张量由三个相互正交的单位向量表征，三个不变量被视为主空间中向量的分量。利用它们，弹性本构方程和塑性流动法则都可以表示为主空间中向量之间的简单关系。返回映射算法与表示制定在主空间和维度的问题从六个减少到三个。省略了主方向的显式计算和从主坐标系到全局坐标系的坐标变换。所提出的算法的一致切线算子的表达式推导出一个有效的和封闭的形式。它由两部分组成：一个与固定主应力方向上的返回映射一致，另一个反映主应力方向的变化。最后，一个数值例子证明了所提出的实现的性能。
This paper develops an efficient return mapping algorithm for implicit integration of general isotropic elastoplastic constitutive equations. A set of three mutually orthogonal unit base tensors in conjunction with a new set of three invariants are employed for the representation of arbitrary isotropic tensor valued and scalar valued functions of the stress tensor involved. The base tensors are constructed from the stress tensor by using the representation theorem and the three invariants are defined by the projection of the stress onto the base tensors. Geometrically, the base tensors are characterized by three mutually orthogonal unit vector and the three invariants are regarded as the components of a vector in principal space. With them, both the elastic constitutive equations and the flow rule of plasticity are represented as simple relationship among vectors in principal space. The return mapping algorithm associated with the representation is formulated in principal space and dimensions of the problem are reduced from six down to three. The explicit computation of the principal directions and the coordinate transformation from the principal reference frame to the global reference frame are omitted. The expressions for the consistent tangent operator for the proposed algorithm are derived in an efficient and closed-form manner. It consists of two parts: one is consistent with the return mapping in the fixed principal stress directions and another reflects the changes in the principal stress directions. Finally, a numerical example demonstrates the performances of the proposed implementation.