Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress–strain curves of human skins. The underlying relations between the J-shaped stress–strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress–strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress–strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress–strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress–strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

可以模仿非矿化的软生物材料的机械性能的高级合成材料的开发对广泛的技术具有重要意义。具有马蹄形微结构的分层晶格材料属于此类生物启发的合成材料，在该类材料中，可以调整机械响应以匹配人体皮肤的非线性J形应力-应变曲线。J型应力-应变曲线及其微结构几何形状之间的潜在关系对于设计用于目标应用的系统至关重要。在此，通过组合构件的有限变形本构关系（即马蹄形微结构），开发了这种类型的分层晶格材料的理论模型，分析周期晶格中的平衡和变形相容性。该模型预测的非线性J形应力-应变曲线和泊松比与有限元分析（FEA）和实验结果非常吻合。基于该模型，获得了一些关键机械量的解析解，例如，弹性模量，泊松比，峰值模量和临界应变，正切模量围绕该临界应变迅速增加。在具有Kagome和蜂窝拓扑的分层格子中，在具有三角形拓扑的分层格子中显示出负的Poisson效应，与之相反。还发现晶格拓扑结构对应力-应变曲线有很大影响。对于三种各向同的晶格拓扑（三角形，Kagome和蜂窝），在相同的孔隙率和圆弧角的情况下，分层的三角形晶格材料在应力-应变曲线中具有最尖锐的过渡，并且具有相对较高的可拉伸性。此外，一个示例说明了开发的模型在快速优化分层晶格材料中的效用，以再现所需的人体皮肤应力-应变曲线。这项研究为具有分层晶格结构的软仿生材料的未来设计提供了理论指导。一个说明性的例子说明了所开发的模型在快速优化分层晶格材料中的效用，以再现人体皮肤所需的应力-应变曲线。这项研究为具有分层晶格结构的软仿生材料的未来设计提供了理论指导。一个说明性的例子说明了所开发的模型在快速优化分层晶格材料中的效用，以再现人体皮肤所需的应力-应变曲线。这项研究为具有分层晶格结构的软仿生材料的未来设计提供了理论指导。