当动力学支配力学时：有限弹性力学模型简化的局部保体积基元
When Kinematics Dominates Mechanics: Locally Volume-Preserving Primitives for Model Reduction in Finite Elasticity
摘要：
一个新的，非常快的，计算建模范例在这里介绍了特定的有限弹性问题，出现在软机器人的背景下。而连续介质力学是一个非常经典的研究领域，和显着的努力已经投入到发展复杂的本构模型有限弹性，我们表明，在软机器人中出现的大应变力学问题的种类，本构模型中的许多参数是无关紧要的。在大多数情况下，等容（局部体积保持）约束主导行为，这可以建立到封闭形式的运动变形场之前，甚至考虑本构建模的其他方面。因此，我们专注于开发和应用基本变形，每个观察这个约束。它表明，通过组成足够广泛的各种变形，观察到的最常见的行为，在软体机器人可以复制。案例研究包括一个充气橡胶室，一个细长的橡胶杆，橡胶块受到不同的边界条件。我们表明，这种方法是至少50倍的速度比有限元法（FEM）的ABAQUS实现。物理实验和测量表明，我们的方法和ABAQUS有大约10%的误差相对于实验测量的位移，以及彼此。我们的方法提供了一个实时的替代FEM，并捕获必要的自由度用于反馈控制系统。
英文摘要：
A new, and extremely fast, computational modeling paradigm is introduced here for specific finite elasticity problems that arise in the context of soft robotics. Whereas continuum mechanics is a very classical area of study, and significant effort has been devoted to the development of intricate constitutive models for finite elasticity, we show that in the kinds of large-strain mechanics problems arising in soft robotics, many of the parameters in constitutive models are irrelevant. For the most part, the isochoric (locally volume-preserving) constraint dominates behavior, and this can be built into closed-form kinematic deformation fields before even considering other aspects of constitutive modeling. We therefore focus on developing and applying primitive deformations that each observe this constraint. It is shown that by composing a wide enough variety of such deformations that the most common behaviors observed in soft robots can be replicated. Case studies include an inflatable rubber chamber, a slender rubber rod, and a rubber block subjected to different boundary conditions. We show that this method is at least 50 times faster than the ABAQUS implementation of the finite element method (FEM). Physical experiments and measurements show that both our method and ABAQUS have approximately 10% error relative to experimentally measured displacements, as well as to each other. Our method provides a real-time alternative to FEM, and captures essential degrees of freedom for use in feedback control systems.
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