## 1 Introduction  
In the past decade, metal additive manufacturing (AM) has evolved from rapid prototyping and low volume production to mass production of various metallic components [1]. This trend has triggered a need for manufacturing processes that have high deposition rates, such as metal big area AM (mBAAM) or laser metal deposition with wire (LMD-w) AM [1; 2; 3; 4; 5]. However, high deposition rates often result in undesired defects, an inhomogeneous microstructure, and poorer, anisotropic mechanical properties compared to their wrought counterparts. Therefore, process control and optimization is important for attaining defect-free parts that have performance-critical applications [2]. The laser metal deposition with wire (LMD-w) system consists of a laser heat source mounted on a robotic arm, a wire feeder, tables, and tools for process conditions (e.g., cameras and thermocouples). The motion of the laser and wire feeder is controlled via a robotic arm and computer program. The laser melts the wire as it is being fed by the wire feeder, repeating in a layer-by-layer fashion until the part is completed, with each layer being deposited on a substrate which is the previous layer. As a result of this layer-by-layer deposition, every deposited layer except for the last one undergoes multiple heating and cooling cycles, which typically produces non-uniform thermal stress and distortion in the final parts [6]. There are several remedies reported in the literature to address this problem. Since the interlayer cooling time, i.e., the dwell time between depositing subsequent layers along the build direction, changes the thermal history and heat build-up during deposition, [PERSON] et al. [7] investigated the effect of interlayer cooling time on distortion and residual stress using laser direct energy deposition with a blown powder of Ti-6 Al-4V. They reported that a shorter interlayer cooling time produces lower distortion and residual stresses. [PERSON] et al. [8] also presented that the residual stress can be reduced by controlling the interlayer cooling time. [PERSON] and [PERSON] [9] studied the effect of preheating on the residual stresses using a laser engineered net shaping (LENS) process. They reported that the uniform preheating alters temperature distributions and consequently reduces residual stress by up to 18%. Nevertheless, the interlayer cooling time and preheating temperature should be carefully controlled because shortening the cooling time and increasing preheating temperature can excessively increase the energy input into the system, particularly during continuous printing. Overheating can consequently lead to undesirable remelting, poor surface finish and poor dimensional tolerances in the final part. Tool path optimization is an alternative way to control part distortion, residual stress, and mechanical properties. Many types of tool path strategies have been developed in various AM processes such as raster, spot melting, zigzag, contour, spiral, fractal and modular path, etc. [5; 10; 11; 12]. These studies showed that the tool path strategies have a strong influence on spatial and temporal thermal signatures, which affects the solidification, solid-state transformation, distortion, and residual stress evolution. Particularly, distortion and residual stress seriously limit the wide application of large-scale metal AM [6]. Numerical simulations have been used to understand part distortion and residual stress evolution in various AM processes [13]. They have been limited to mostly experimental scale AM processes (i.e., powder bed fusion or direct energy deposition with blown powder), such that few large-scale simulations have been reported in the literature of wire-arc AM (WAAM), mBAAM and LMD-w. [PERSON] et al. [11] developed a computationally efficient finite element method (FEM) for a large-scale metal AM process and investigated the stress evolution during the thermal cycle of the AM process.