An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metmaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. hese effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

中文翻译：

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一种基于优化的方法，用于定制经历速率相关不稳定性的软超材料的机械响应


提出了一种基于优化的设计框架来调整涉及几何不稳定性和非线性粘弹性材料行为的软超材料的响应。设计软金属材料对利用不稳定性并进行大规模、量身定制的配置更改的响应，将使软机器人、冲击和振动缓解以及柔性电子技术取得进步。根据超材料概念，这些材料的响应在很大程度上受其小尺度特征的几何和拓扑构成的控制。然而，对于软超材料来说，结构和响应之间的联系不太直观，因为它们依赖于由几何不稳定性触发的高度非线性响应。粘弹性弛豫的影响使情况进一步复杂化，最近的研究表明，粘弹性弛豫会以非直观的方式改变不稳定性的出现。在我们的框架中考虑了这些效应，以实现各种设计目标，包括定制的力-位移响应以及从几何和材料效应中最大限度地吸收能量。为了实现这一过程的完全自动化，必须有一个完全健壮的方程求解器来处理涉及不稳定性和粘弹性松弛的正向问题。我们通过将寻找稳定的机械平衡（即正向问题）作为最小化问题来实现这一目标，并利用信任域算法来稳健地处理不稳定性，并通过临界点遵循能量有利的平衡路径。