We show that propagating transitions fronts observed recently in multistable structural networks are analogous to solid–solid phase transformations in crystals and can therefore be described quantitatively as propagating shock fronts. We demonstrate that the well-established sharp-interface theory from shock physics agrees well with the exact and approximate wave solutions obtained from treating the multistable metamaterial as a discrete chain and as a homogenized continuum, respectively. We further discuss the energy transport that governs the underlying dynamic transition phenomenon. Through numerical examples we showcase the diverse nature of the achievable transition effects depending on the interplay between inertia and dissipation in the multistable network, which enables wave tailoring and guidance. We further confirm applicability of the theory by comparison to experimental data. Though focusing on one-dimensional transition front propagation as the most fundamental problem, our results and conclusions admit extension to higher dimensions.

我们表明，最近在多稳态结构网络中观察到的传播过渡前沿类似于晶体中的固-固相变，因此可以定量地描述为传播冲击前沿。我们证明，由冲击物理学建立的完善的锐界面理论与将多稳态超材料分别视为离散链和均质连续体所获得的精确和近似波解非常吻合。我们将进一步讨论控制潜在动态过渡现象的能量传输。通过数值示例，我们根据多稳态网络中惯性与耗散之间的相互作用展示了可实现的过渡效应的多样性，从而实现了波的剪裁和引导。通过与实验数据进行比较，我们进一步证实了该理论的适用性。尽管将一维过渡前沿传播作为最基本的问题，但我们的结果和结论承认可以扩展到更高的维度。