Appears in collection : Statistical Modeling for Shapes and Imaging

Additive manufacturing makes it possible to physically realize objects embedding complex, small scale structures, on a scale of a few tens of microns. These microstructures modify the large-scale behaviour of an object, making it flexible or porous, and allowing parts to be lightened while maintaining their structural integrity. Modeling these microstructures is difficult: it is necessary to represent a large quantity of details, to respect the angle and thickness constraints of additive manufacturing processes, while predicting the final behaviour induced by the microstructures, for example in terms of elasticity. For these reasons, most existing techniques are studying periodic structures. The periodicity, by repeating the same base structure in a regular grid simplifies analysis and processing. Unfortunately, it also prevents free variation of structures in space, for example orienting them along directions of maximal stresses. In the past few years we have focused on synthesizing microstructures using stochastic processes, which are inspired from procedural texturing techniques in Computer Graphics. The microstructures we synthesize resemble foams. By controlling the statistics of the generation process, we show that it is possible to control the final average elastic behavior. These techniques can be used in two-scale topology optimization problems, where a shape is globally optimized at a coarse scale, while the random process quickly generates a fine scale foam having the desired homogeneous behavior.