In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms — low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets’ unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community.

在这项工作中，我们为建筑板材构建了一个有效的连续体模型，这些板材由通过细长的弹性接头连接的大块瓷砖组成。由于它们的细观结构，这些片材具有准机制——低能局部运动模式，比其他变形更受青睐。在具有非均匀细观结构的片材中，相邻区域之间会出现运动学不相容性，从而导致面外屈曲。有效的连续体模型基于对片材单元格及其能量有利的变形模式的几何分析。它的主要特点是构建一种应变能，以惩罚偏离这些首选的变形模式。非周期性的影响完全是通过在模型中使用空间变化的几何参数来描述的。我们的模拟捕获了在非周期性试样中发生的平面外屈曲，并与实验表现出良好的一致性。虽然我们只考虑一类准机制，但我们的建模方法可以应用于力学界感兴趣的各种形状变形系统。