Toward Elastically and Inelastically Isotropic Multiphase Interpenetrating Network

Heterogeneous or cellular materials architected on various crystal lattices have been extensively explored for a broad variety of engineering functionalities involving photonics, acoustics and mechanics with the recent advances in additive manufacturing and three-dimensional (3D) printing technologies. Long-range order in the heterogeneous materials architected on crystal lattices often culminates in undesirable, intrinsic anisotropy in elasticity and inelasticity in diverse mechanical loading scenarios. In this work, we propose a simple yet efficient design strategy to generate heterogeneous materials that exhibit nearly isotropic elasticity and inelasticity in extreme mechanical deformation events. Furthermore, we combine experiments and numerical simulations to explore how geometric connectivity (dispersed-particle vs. interpenetrating morphologies) throughout dissimilar domains influences shape recovery as well as energy dissipation in the disordered heterogeneous materials.<br/>We design two types of disordered morphologies: dispersed-particle morphology and its interpenetrating counterpart. Representative volume element (RVE) for dispersed-particle morphology is generated by distributing a finite number of spheres in the unit cube. The centers of the spheres are randomly placed inside the unit cube. When placing the spheres, newly inserted spheres does not overlap the existing spheres under three-dimensional periodic boundary conditions (PBC)^[1]. In order to generate an interpenetrating counterpart, we perform a Voronoi tessellation on the unit cube via the spatial random points seeded for the dispersed-particle morphology. We then perform rod-connecting the center point and the Voronoi neighbor points for each of the tessellated polyhedra in the RVE. Therefore, the RVE with interpenetrating morphology has randomly connected local microstructures throughout the tessellated polyhedral network.<br/>We then fabricated prototypes for the RVEs of both disordered morphologies using a high-resolution, multi-material 3D printer. A plastomeric material exhibiting large flow stresses and hysteresis under cyclic loading conditions was used for the hard domains (particles or rod-connected network) while a hyperelastic, elastomeric material was used for the soft domains. We then conducted large strain mechanical tests on the 3D-printed prototypes under diverse cyclic loading scenarios. Altering the connectivity throughout the disordered network was found to impact significantly on key elastic and inelastic features including initial stiffness, flow stresses, energy dissipation and elastic-inelastic shape recovery in the two morphologies upon cyclic loading and unloading conditions. Furthermore, the 3D-printed prototypes with interpenetrating morphology exhibited more robust performance in resilience and energy dissipation under repeated loading and unloading cycles. Last, we examined anisotropy in both morphologies in experiments and numerical simulations, by which the universal anisotropy index^[2] was calculated. Interestingly, though altering the connectivity from dispersed-particle to interpenetrating morphologies resulted in a slight increase in anisotropy, the universal anisotropy indices for both morphologies were found to be below 0.05 (nearly isotropic behavior). In addition to the elastic isotropy, our experimental data and numerical simulation results reveal that these disordered heterogeneous materials exhibit nearly isotropic behaviors in inelastic features involving energy dissipation and shape recovery in extreme deformation conditions.<br/>This work was funded by National Research Foundation of Korea (Grant No. 2021R1A4A103278312)<br/><br/>[1] M. Danielsson, D. M. Parks, and M. C. Boyce, J. Mech. Phys. Solids, vol. 55, no. 3, pp. 533-561, Mar. 2007.<br/>[2] S. I. Ranganathan and M. Ostoja-Starzewski, Phys. Rev. Lett., vol. 101, no. 5, p. 055504, Aug. 2008.