A discrete model for layered growth

TL;DR

This paper introduces a simple discrete model for layered additive manufacturing that explains residual stresses, allows inverse problem formulation for stress control, and highlights the impact of interlayer bonding on final stress states.

Contribution

It presents a minimal, analytically tractable discrete model capturing key mechanical behaviors of additive manufacturing, including residual stress origin and control strategies.

Findings

Residual stresses arise from incompatible layer deformations.

The model enables inverse design of deposition protocols for desired stress states.

Interlayer bonding significantly influences the final stress distribution.

Abstract

In this work we present a discrete model that captures the fundamental properties of additively manufactured solids in a minimal setting. The model is based on simplified kinematics and allows for the onset of incompatible deformations between discrete layers of an additively manufactured stack. Thanks to the discrete nature of the model, we obtain an averaged formulation of mechanical equilibrium for the growing stack, leading to closed-form solutions that are both analytically simple and physically transparent. In particular, we are able to explain the origin of residual stresses by the accumulation of incompatible deformations between adjacent layers. At the same time, we are able to formulate the technologically relevant inverse problem that provides the deposition protocol required to produce a desired state of internal stress in the manufactured stack. Another important aspect analyzed in the work is the role played by an ideal ``glue'' between the layers, whose presence is fundamental to prevent their sliding and whose mechanical behavior can quantitatively influence the final stress distribution in the stack. Although the model is an elementary approximation of additive manufacturing, its simplicity makes it possible to highlight how the controls exerted during deposition will have qualitative or quantitative effects on the final stress state of the stack. This understanding is crucial in shedding light on the complex mechanical behavior of additive manufactured solids.