Mechanics of Stretchy Elastomer Lattices
Mechanics of Stretchy Elastomer Lattices
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DOI：
10.1016/j.jmps.2022.104782
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发表时间：
2022-01
影响因子：
5.3
通讯作者：
Yanchu Zhang;Kunhao Yu;Kyung Hoon Lee;Ketian Li;Haixu Du;Qiming Wang
中科院分区：
文献类型：
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作者：
Yanchu Zhang;Kunhao Yu;Kyung Hoon Lee;Ketian Li;Haixu Du;Qiming Wang
软物质和先进制造的最新进展使得弹性体晶格的设计和制造能够用于多种工程应用。与传统的工程结构相比，弹性体晶格表现出超高的可逆拉伸性，同时保持相对较低的密度。对弹性体晶格力学的机理理解对于其结构设计和优化非常重要。然而，该领域的现有研究仅限于经验模型或有限元方法，而理论建模在很大程度上仍未得到探索。这项工作报告了一类有限变形下弹性体晶格力学的理论模型。势能函数被构造为拉伸和弯曲模式的叠加，这分别与晶格梁的伸长和旋转相关。应力-拉伸行为是借助固定势能原理确定的。然后通过将每个层次顺序中的主拉伸引入为广义坐标，将该模型扩展为解释层次弹性体晶格的力学。编写了一组完整约束方程来定义分层晶格的运动相容性和单轴应力状态，并通过非线性优化算法进行数值求解。所提出的理论模型的结果与有限元模拟和实验非常吻合。对各种材料本构模型、体积分数、晶格结构和变形模式进行了案例研究，证明了所提出的理论模型的通用性和鲁棒性。
The recent advances in soft matter and advanced manufacturing have enabled the design and fabrication of elastomer lattices for versatile engineering applications. Compared with conventional engineering structures, elastomer lattices exhibit ultra-high reversible stretchability, while maintaining relatively low density. Mechanistic understanding of the mechanics of elastomer lattices is of great importance for their structural design and optimization. However, the existing studies in this field are limited to empirical models or finite element methods, while the theoretical modeling remains largely unexplored. This work reports a class of theoretical models for the mechanics of elastomer lattices over finite deformation. The potential energy function is constructed as a superposition of the stretching and bending modes, which are associated with the elongation and rotation of lattice beams, respectively. The stress-stretch behavior is determined with the aid of the principle of stationary potential energy. The model is then extended to explain the mechanics of hierarchical elastomer lattices by introducing the principal stretches in each hierarchical order as generalized coordinates. A set of holonomic constraint equations are written to define the kinematic compatibility and uniaxial stress state for hierarchical lattices, which are numerically solved via a nonlinear optimization algorithm. Results from the proposed theoretical models agree well with finite-element simulations and experiments. Case studies are performed for various material constitutive models, volume fractions, lattice architectures, and deformation modes, demonstrating the generality and robustness of the proposed theoretical models.