  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.
