This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting. A first focus lies on the derivation of a consistent constitutive law on basis of a Voigt-type spatial homogenization procedure across the relevant phases, powder, melt and solid. The proposed constitutive law accounts for the irreversibility of phase change and consistently represents thermally induced residual stresses. In particular, the incorporation of a reference strain term, formulated in rate form, allows to consistently enforce a stress-free configuration for newly solidifying material at melt temperature. Application to elementary test cases demonstrates the validity of the proposed constitutive law and allows for a comparison with analytical and reference solutions. Moreover, these elementary solidification scenarios give detailed insights and foster understanding of basic mechanisms of residual stress generation in melting and solidification problems with localized, moving heat sources. As a second methodological aspect, dual mortar mesh tying strategies are proposed for the coupling of successively applied powder layers. This approach allows for very flexible mesh generation for complex geometries. As compared to collocation-type coupling schemes, e.g., based on hanging nodes, these mortar methods enforce the coupling conditions between non-matching meshes in an $$L^2$$ -optimal manner. The combination of the proposed constitutive law and mortar mesh tying approach is validated on realistic three-dimensional examples, representing a first step towards part-scale predictions.

中文翻译：

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一种简单而一致的本构定律和基于砂浆的层耦合方案，用于金属增材制造过程的热机械宏观模拟

本文提出了一种耦合热机械有限元模型，该模型适用于金属增材制造过程（如选择性激光熔化）的宏观模拟。第一个重点是基于 Voigt 型空间均匀化程序在相关相、粉末、熔体和固体的基础上推导出一致的本构定律。拟议的本构定律解释了相变的不可逆性，并始终代表热致残余应力。特别是，结合以速率形式制定的参考应变项，允许在熔融温度下为新固化的材料始终实施无应力配置。对基本测试用例的应用证明了所提议的本构法的有效性，并允许与分析和参考解决方案进行比较。此外，这些基本的凝固场景提供了详细的见解，并促进了对局部移动热源的熔化和凝固问题中残余应力产生的基本机制的理解。作为第二个方法论方面，提出了双砂浆网格捆绑策略，用于耦合连续施加的粉末层。这种方法允许为复杂的几何图形生成非常灵活的网格。与搭配型耦合方案（例如，基于悬挂节点）相比，这些砂浆方法以 $$L^2$$ 最佳方式强制执行非匹配网格之间的耦合条件。