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Stripe patterns are ubiquitous in nature and everyday life. While thesynthesis of these patterns has been thoroughly studied in the literature,their potential to control the mechanics of structured materials remainslargely unexplored. In this work, we introduce Differentiable Stripe Patterns-- a computational approach for automated design of physical surfacesstructured with stripe-shaped bi-material distributions. Our method builds onthe work by Knoppel and colleagues for generating globally-continuous andequally-spaced stripe patterns. To unlock the full potential of this designspace, we propose a gradient-based optimization tool to automatically computestripe patterns that best approximate macromechanical performance goals.Specifically, we propose a computational model that combines solid shell finiteelements with XFEM for accurate and fully-differentiable modeling of elasticbi-material surfaces. To resolve non-uniqueness problems in the originalmethod, we furthermore propose a robust formulation that yields unique anddifferentiable stripe patterns. %Finally, we introduce design spaceregularizers to avoid numerical singularities and improve stripe neatness Wecombine these components with equilibrium state derivatives into an end-to-enddifferentiable pipeline that enables inverse design of mechanical stripepatterns. We demonstrate our method on a diverse set of examples thatillustrate the potential of stripe patterns as a design space for structuredmaterials. Our simulation results are experimentally validated on physicalprototypes.

Differentiable Stripe Patterns for Inverse Design of Structured Surfaces