Worst-case stress relief for microstructures

Julian Panetta, Abtin Rahimian, Denis Zorin

Research output: Contribution to journalConference articlepeer-review


Additive fabrication technologies are limited by the types of material they can print: while the technologies are continuously improving, still only a relatively small discrete set of materials can be used in each printed object. At the same time, the low cost of introducing geometric complexity suggests the alternative of controlling the elastic material properties by producing microstructures, which can achieve behaviors significantly differing from the solid printing material. While promising results have been obtained in this direction, fragility is a significant problem blocking practical applications, especially for achieving soft material properties: due to stress concentrations at thin joints, deformations and repeated loadings are likely to cause fracture. We present a set of methods to minimize stress concentrations in microstructures by evolving their shapes. First, we demonstrate that the worstcase stress analysis problem (maximizing a stress measure over all possible unit loads) has an exact solution for periodic microstructures. We develop a new, accurate discretization of the shape derivative for stress objectives and introduce a low-dimensional parametric shape model for microstructures. This model supports robust minimization of maximal stress (approximated by an Lp norm with high p) and an eficient implementation of printability constraints. In addition to significantly reducing stresses (by a typical factor of 5×), the new method substantially expands the range of effective material properties covered by the collection of structures.

Original languageEnglish (US)
Article number122
JournalACM Transactions on Graphics
Issue number4
StatePublished - 2017
EventACM SIGGRAPH 2017 - Los Angeles, United States
Duration: Jul 30 2017Aug 3 2017


  • Additive fabrication
  • Deformable objects
  • Goal-based material design
  • Homogenization
  • Microstructures
  • Shape optimization
  • Stress minimization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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