Active mechanical metamaterials are artificially engineered microstructures that can be externally controlled to exhibit novel and switchable mechanical behavior on the macroscopic scale. Pneumatically actuated variants of these metamaterials can then change their mechanical, acoustic, or other types of effective behavior in response to applied pressure with possible applications ranging from soft robotic actuators to phononic crystals. Such materials often undergo large deformations, leading to self-contact, which makes their modeling and generative design challenging. We propose to use the third medium method to simulate both pneumatic actuation and contact behavior. In contrast to existing formulations, we (i) combine together contact with pneumatic actuation in a single material model for the third medium, (ii) include more permissive regularization scheme for our model, penalizing gradient of pseudo-rotation and gradient of volume change only, and (iii) introduce pneumatic actuation as an exact value of Cauchy stress. Our formulation is energetically consistent and admits advanced finite element solvers, such as the modified Cholesky decomposition to detect instabilities. We demonstrate the behavior of the proposed formulation on several examples of traditional contact benchmarks, including a standard patch test, and validate it with experimental measurement.

中文翻译：

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气动系统的第三种介质有限元接触公式


活性机械超材料是人工设计的微观结构，可以通过外部控制在宏观尺度上表现出新颖且可切换的机械行为。这些超材料的气动变体可以改变其机械、声学或其他类型的有效行为，以响应施加的压力，其可能的应用范围从软机器人执行器到声子晶体。此类材料通常会发生较大变形，导致自接触，这使得它们的建模和生成设计具有挑战性。我们建议使用第三种介质方法来模拟气动驱动和接触行为。与现有的公式相反，我们（i）将接触与气动驱动结合在第三种介质的单一材料模型中，（ii）为我们的模型包含更宽松的正则化方案，仅惩罚伪旋转梯度和体积变化梯度，以及 (iii) 引入气动驱动作为柯西应力的精确值。我们的公式在能量上是一致的，并且允许先进的有限元求解器，例如用于检测不稳定性的改进的 Cholesky 分解。我们在传统接触基准的几个示例（包括标准补丁测试）上展示了所提出的公式的行为，并通过实验测量对其进行验证。