Harnessing the rich nonlinear dynamics of highly deformable materials has the potential to unlock the next generation of functional smart materials and devices. However, unlocking such potential requires effective strategies to spatially engineer material architectures within the nonlinear dynamic regime. Here we introduce an inverse-design framework to discover flexible mechanical metamaterials with a target nonlinear dynamic response. The desired dynamic task is encoded via optimal tuning of the full-scale metamaterial geometry through an inverse-design approach powered by a fully differentiable simulation environment. By deploying such a strategy, mechanical metamaterials are tailored for energy focusing, energy splitting, dynamic protection and nonlinear motion conversion. Furthermore, our design framework can be expanded to automatically discover reprogrammable architectures capable of switching between different dynamic tasks. For instance, we encode two strongly competing tasks—energy focusing and dynamic protection—within a single architecture, using static precompression to switch between these behaviours. The discovered designs are physically realized and experimentally tested, demonstrating the robustness of the engineered tasks. Our approach opens an untapped avenue towards designer materials with tailored robotic-like reprogrammable functionalities.

利用高度可变形材料的丰富非线性动力学有可能解锁下一代功能性智能材料和设备。然而，要释放这种潜力，需要有效的策略在非线性动力学范围内对材料架构进行空间工程设计。在这里，我们介绍了一个逆向设计框架，以发现具有目标非线性动态响应的柔性机械超材料。通过由完全可微分仿真环境提供支持的逆向设计方法，通过对全尺寸超材料几何结构进行最佳调整，对所需的动态任务进行编码。通过部署这样的策略，机械超材料被定制用于能量聚焦、能量分配、动态保护和非线性运动转换。此外，我们的设计框架可以扩展为自动发现能够在不同动态任务之间切换的可重新编程架构。例如，我们在单个架构中编码了两个相互竞争的任务——能量聚焦和动态保护——使用静态预压缩在这些行为之间切换。发现的设计经过物理实现和实验测试，证明了工程任务的稳健性。我们的方法为具有类似机器人的定制可重新编程功能的设计师材料开辟了一条尚未开发的途径。