  The accumulation of residual stress during welding and additive manufacturing
is an important effect that can significantly anticipate the workpiece failure.
In this work we exploit the physical and analytical transparency of a 1.5D
model to show that the deposition of thermally expanded material onto an
elastic substrate leads to the accumulation of strain incompatibility. This
field, which is the source of residual stress in the system, introduces memory
of the construction history even in the absence of plastic deformations. The
model is then applied to describe the onset and the progression of residual
stresses during deposition, their evolution upon cooling, and the fundamental
role played by the velocity of the moving heat source.
