A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

Abstract

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.

Lattice Metamaterials with Mechanically Tunable Poisson’s Ratio for Vibration Control

“…We find that these structures exhibit J-shaped stress-strain curves, which are very similar to the mechanical response of bioinspired soft network composite materials and other stretchable electronics [56][57][58][59]. However, the stress-strain behavior is different from that of plates with rectangular auxetic perforations, which exhibit a softening phenomenon in the tensile stressstrain curve for an increasing magnitude of Poisson's ratio [44].…”

“…Recent numerical and experimental studies indicate that thin film materials with serpentine microstructures can have improved stretchability, owing to the introduced microstructure and small intrinsic strain in the materials [56][57][58][59]. A non-straight (corrugated) rib configuration for open cell polyurethane foams has also recently been considered as a likely explanation for the existence of an unusual blocked shape memory effect in auxetic open cell polyurethane foams [60].…”

“…A non-straight (corrugated) rib configuration for open cell polyurethane foams has also recently been considered as a likely explanation for the existence of an unusual blocked shape memory effect in auxetic open cell polyurethane foams [60]. Although it has been theoretically shown that the auxetic behavior can also be attained in hierarchically architected lattice metamaterials with triangular topology [57], a convincing experimental evidence of the auxetic behavior of these materials has not been reported yet. Moreover, little attention has been paid to the performance of engineered auxetic metamaterial lattices with sinusoidally curved (non-straight) ligaments in their microstructure, especially at the hierarchical level.…”

Reconfigurable systems for multifunctional electronics

“…In the application of bio-integrated electronics, it is desirable to match the effective modulus of devices to that of the skin even for various levels of stretching. In order to address this challenge, composite structures that embed serpentine fibers in a polymer matrix to mimic the living fabric in the biological tissues has also been explored in the substrate 28,29 ( Fig. 1f).…”

Engineering reversible elasticity in ductile and brittle thin films supported by a plastic foil

“…An alternative approach to produce stretchable devices and circuits out of non-elastic materials is the patterning of strain-relief motifs in the form of serpentines, to minimize local mechanical stress in the most fragile materials [5,6]. The advantage of such an approach is compatibility with standard microfabrication techniques and materials.…”