The Hot Optimal Transportation Meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions
The Hot Optimal Transportation Meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions
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DOI：
10.1016/j.cma.2020.112958
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发表时间：
2020-06
影响因子：
7.2
通讯作者：
Hao Wang;Huming Liao;Zongyue Fan;Jiang Fan;L. Stainier;XiaoBai Li;Bo Li
中科院分区：
文献类型：
--
作者：
Hao Wang;Huming Liao;Zongyue Fan;Jiang Fan;L. Stainier;XiaoBai Li;Bo Li
提出了一种基于无网格法的整体增量拉格朗日框架--热最优传输无网格法(HOTM)，用于求解材料在极端热机械条件下的动态响应，该条件可能涉及极大变形、相变和多相混合。HOTM方法结合了最优传输无网格(OTM)方法和变分热力本构修正。应用最优输运理论对具有一般内部耗散机制的动力系统的变分结构进行时间离散化，并引入物质点和节点进行空间离散化。建立了一个相敏本构模型来描述材料在熔融、汽化和凝固过程中各相的历史相关行为。用算子分裂算法同时求解完全离散的线性动量守恒方程和能量守恒方程，以预测计算域的变形、温度和内变量。通过与解析解的比较，研究了三维非定常热传导问题能量守恒方程无网格解的收敛性质。在不同的外部加热和冷却策略下，以锻造压缩比高达95%的金属方坯为例，对HOTM方法的准确性进行了评估。激光熔覆技术的应用证明了HOTM方法的适用范围和稳健性。
We present a monolithic incremental Lagrangian framework based on meshfree methods, the Hot Optimal Transportation Meshfree (HOTM) method, for a robust and efficient solution of the dynamic response of materials under extreme thermomechanical conditions, possibly involving extremely large deformation, phase transition and multiphase mixing. The HOTM method combines the Optimal Transportation Meshfree (OTM) method and the variational thermomechanical constitutive updates. The variational structure of a dynamic system with general internal dissipative mechanisms is discretized in time by applying the Optimal Transportation theory, while material points and nodes are introduced for the spatial discretization. A phase-aware constitutive model is developed to describe the history-dependent material behavior in various phases due to melting, vaporization and solidification. The fully discretized conservation equations of linear momentum and energy are solved simultaneously using an operator splitting algorithm to predict the deformation, temperature and internal variables of the computational domain. The convergence property of the meshfree solution of the energy conservation equation is studied in a three-dimensional transient heat conduction problem by comparing to the analytical solutions. Accuracy of the HOTM method is also assessed in the example of upsetting a metallic billet up to a compression ratio of 95% under various external heating and cooling strategies. The scope and robustness of the HOTM method are demonstrated in the application of the laser cladding technology.