Chen Yuzhen, Kuenstler Alexa S, Hayward Ryan C, Jin Lihua
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA.
Department of Chemical and Biological Engineering, University of Colorado Boulder, CO 80309, USA.
Soft Matter. 2022 Jun 1;18(21):4077-4089. doi: 10.1039/d1sm01830b.
Formation of desired three-dimensional (3D) shapes from flat thin sheets with programmed non-uniform deformation profiles is an effective strategy to create functional 3D structures. Liquid crystal elastomers (LCEs) are of particular use in programmable shape morphing due to their ability to undergo large, reversible, and anisotropic deformation in response to a stimulus. Here we consider a rectangular monodomain LCE thin sheet divided into one high- and one low-temperature strip, which we dub a 'bistrip'. Upon activation, a discontinuously patterned, anisotropic in-plane stretch profile is generated, and induces buckling of the bistrip into a rolled shape with a transitional bottle neck. Based on the non-Euclidean plate theory, we derive an analytical model to quantitatively capture the formation of the rolled shapes from a flat bistrip with finite thickness by minimizing the total elastic energy involving both stretching and bending energies. Using this analytical model, we identify the critical thickness at which the transition from the unbuckled to buckled configuration occurs. We further study the influence of the anisotropy of the stretch profile on the rolled shapes by first converting prescribed metric tensors with different anisotropy to a unified metric tensor embedded in a bistrip of modified geometry, and then investigating the effect of each parameter in this unified metric tensor on the rolled shapes. Our analysis sheds light on designing shape morphing of LCE thin sheets, and provides quantitative predictions on the 3D shapes that programmed LCE sheets can form upon activation for various applications.
通过具有可编程非均匀变形轮廓的扁平薄片形成所需的三维（3D）形状是创建功能性3D结构的有效策略。液晶弹性体（LCE）由于能够响应刺激而经历大的、可逆的和各向异性的变形，在可编程形状变形中具有特殊用途。在这里，我们考虑一个矩形单畴LCE薄片，它被分成一个高温带和一个低温带，我们将其称为“双条带”。激活后，会产生不连续图案化的、各向异性的面内拉伸轮廓，并导致双条带屈曲成具有过渡瓶颈的卷曲形状。基于非欧几里得板理论，我们推导了一个分析模型，通过最小化涉及拉伸和弯曲能量的总弹性能量，定量地捕捉具有有限厚度的扁平双条带卷曲形状的形成。使用这个分析模型，我们确定了从不屈曲构型到屈曲构型转变发生时的临界厚度。我们进一步研究了拉伸轮廓的各向异性对卷曲形状的影响，首先将具有不同各向异性的规定度量张量转换为嵌入在修改几何形状的双条带中的统一度量张量，然后研究这个统一度量张量中的每个参数对卷曲形状的影响。我们的分析为设计LCE薄片的形状变形提供了思路，并对编程的LCE薄片在激活后可形成的用于各种应用的3D形状提供了定量预测。
