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

翻译：条纹图案在自然界和日常生活中无处不在。虽然这些图案的合成已在文献中得到深入研究，但它们控制结构化材料力学性能的潜力仍未得到充分探索。在这项工作中，我们提出可微条纹图案——一种用于自动化设计具有条纹状双材料分布的结构化表面的计算方法。我们的方法基于Knoppel及其同事生成全局连续且等间距条纹图案的研究。为充分释放该设计空间的潜力，我们提出一种基于梯度的优化工具，以自动计算最能逼近宏观力学性能目标的条纹图案。具体而言，我们提出一种结合实体壳有限元与XFEM的计算模型，用于精确且完全可微的弹性双材料表面建模。为解决原始方法中的非唯一性问题，我们进一步提出一种鲁棒公式，能够生成唯一且可微的条纹图案。我们将这些组件与平衡态导数相结合，构建了一个端到端的可微流水线，从而实现力学条纹图案的逆向设计。我们通过一系列多样化示例展示了该方法，揭示了条纹图案作为结构化材料设计空间的潜力。仿真结果通过物理原型实验得到了验证。