Homotopy Shear Band Solutions in Gradient Plasticity
Homotopy Shear Band Solutions in Gradient Plasticity
复制标题
梯度塑性中的同伦剪切带解
DOI：
10.1515/zna-2016-0475
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
E. Aifantis
中科院分区：
文献类型：
--
作者：
A. Raees;Hang Xu;E. Aifantis
摘要在梯度塑性理论的框架下，利用同伦分析方法导出了有限域的解析剪切带型解。这种类型的解决方案在文献中仅适用于非线性材料软化状态和稳态条件下的无限域，以及材料硬化状态下的有限域。HAM允许获得硬化和软化材料模型的解，以及非定常条件下的周期解。数值模拟验证了仿真结果的正确性。并给出了误差分析，保证了级数解的收敛性。
Abstract Analytical shear band type solutions for finite domains are derived within the framework of gradient plasticity theory by employing the homotopy analysis method (HAM). Such types of solutions were available in the literature only for infinite domains in the nonlinear material softening regime and steady-state conditions, as well as for finite domains in the material hardening regime. HAM allows for solutions to be obtained for both hardening and softening material models, as well as for unsteady conditions periodic solutions are also derived. The HAM results are verified with numerical simulations, which show excellent agreement. Moreover, an error analysis is provided which guarantees the convergence of our series solution.