NURBS plasticity: non-associated plastic flow
NURBS plasticity: non-associated plastic flow
复制标题
DOI：
10.1016/j.cma.2018.03.015
复制
发表时间：
2018-07
影响因子：
7.2
通讯作者：
W. Coombs;Y. G. Motlagh
中科院分区：
文献类型：
--
作者：
W. Coombs;Y. G. Motlagh
本文扩展了 Coombs 等人的非均匀有理基样条 (NURBS) 可塑性框架。 (2016) 和 Coombs 和 Ghaffari Motlagh (2017) 包括非相关塑性流动。 NURBS 塑性方法允许用 NURBS 曲面表示任何平滑的各向同性屈服包络，同时数值算法（和代码）保持不变。本文提供了非关联 NURBS 塑性方法的完整理论和算法基础，并展示了塑性框架使用小变形和大变形问题的预测能力。与本构公式相关的任何可能的错误都通过分析指定，如果没有数值分析则提供此信息。使用高效稳定的隐式应力更新算法对塑性框架内的速率方程进行积分，该算法允许推导算法一致的切线，从而确保在边界值模拟中使用时全局不平衡力残差的最佳收敛。本文提供的重要扩展是塑性应变的演化与屈服面法线解耦。这使得框架能够模拟更真实的材料行为，特别是在摩擦塑性模型的情况下，已知相关的流动规则会显着高估体积膨胀，从而导致虚假结果。因此，本文为 NURBS 塑性公式用于比目前更广泛的材料行为类别打开了大门。
This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. (2016) and Coombs and Ghaffari Motlagh (2017) to include non-associated plastic flow. The NURBS plasticity approach allows any smooth isotropic yield envelope to be represented by a NURBS surface whilst the numerical algorithm (and code) remains unchanged. This paper provides the full theoretical and algorithmic basis of the non-associated NURBS plasticity approach and demonstrates the predictive capability of the plasticity framework using both small and large deformation problems. Wherever possible errors associated with the constitutive formulation are specified analytically and if not numerical analyses provide this information. The rate equations within the plasticity framework are integrated using an efficient and stable implicit stress update algorithm which allows for the derivation of the algorithmic consistent tangent which ensures optimum convergence of the global out of balance force residual when used in boundary value simulations.The important extension provided by this paper is that the evolution of plastic strain is decoupled from the yield surface normal. This allows the framework to model more realistic material behaviour, particularly in the case of frictional plasticity models where an associated flow rule is known to significantly overestimate volumetric dilation leading to spurious results. This paper therefore opens the door for the NURBS plasticity formulation to be used for a far wider class of material behaviour than is currently possible.