  In additive manufacturing, the fabrication sequence has a large influence on
the quality of manufactured components. While planning of the fabrication
sequence is typically performed after the component has been designed, recent
developments have demonstrated the possibility and benefits of simultaneous
optimization of both the structural layout and the corresponding fabrication
sequence. The simultaneous optimization approach, called space-time topology
optimization, introduces a pseudo-time field to encode the manufacturing
process order, alongside a pseudo-density field representing the structural
layout. To comply with manufacturing principles, the pseudo-time field needs to
be monotonic, i.e., free of local minima. However, explicitly formulated
constraints are not always effective, particularly for complex structural
layouts.
  In this paper, we introduce a novel method to regularize the pseudo-time
field in space-time topology optimization. We conceptualize the monotonic
additive manufacturing process as a virtual heat conduction process starting
from the surface upon which a component is constructed layer by layer. The
virtual temperature field, which shall not be confused with the actual
temperature field during manufacturing, serves as an analogy for encoding the
fabrication sequence. In this new formulation, we use local virtual heat
conductivity coefficients as optimization variables to steer the temperature
field and, consequently, the fabrication sequence. The virtual temperature
field is inherently free of local minima due to the physics it resembles. We
numerically validate the effectiveness of this regularization in space-time
topology optimization under process-dependent loads, including gravity and
thermomechanical loads.
