Fundamental Mathematical Modeling of Additive Manufacturing

This book elucidates the fundamental thermomechanical behaviour inherent in the 3D printing process within a laser-based powder bed fusion (L-PBF) system. It presents foundational concepts and provides in-depth derivations of the governing equations. The analysis encompasses arbitrary anisotropic linear viscoelastic materials, accounting for thermal effects. The authors leverage the theory of axially moving materials, a framework previously employed in the analysis of production processes within the process industry. They introduce a coordinate frame that moves in tandem with the printing laser, adopting an Eulerian perspective towards the in-motion solid. Designed for graduate students and researchers, this book is poised to foster a profound comprehension and spur innovative technological advancements in the realm of additive manufacturing.

Introduction.- Kinematics of industrial processes.- Fundamental balance laws for a moving continuum.- Constitutive equations.- Fluids versus solids.- Process model for L-PBF 3D printing of metals.- Analytical solution in one dimension.- Temperature-dependent 1D models, with analytical techniques and their limitations.- Numerical solution in two dimensions.