A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes

TL;DR

This paper introduces a consistent thermomechanical constitutive law and mortar-based layer coupling schemes for efficient, accurate macroscale simulations of metal additive manufacturing, capturing phase change and residual stresses.

Contribution

It presents a novel Voigt-type homogenized constitutive law and dual mortar mesh tying strategies, enabling flexible and precise simulation of complex metal additive manufacturing processes.

Findings

Validates the constitutive law with elementary test cases

Demonstrates the mortar coupling scheme on 3D examples

Provides insights into residual stress mechanisms

Abstract

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.