Extreme resilience and dissipation in heterogeneous disordered materials

TL;DR

The work addresses anisotropy limits in lattice-based heterogeneous materials and proposes a disordered two-phase design with randomly distributed subdomains that become nearly isotropic when connectivity is introduced. By combining micromechanical modeling, 3D printed prototypes, and numerical simulations, it demonstrates that near-complete elastic isotropy is achievable for $N\geq 7$ random points, with $A^U$ on the order of $10^{-2}$ and robust performance across loading directions. The study also shows that continuous hard networks dramatically reduce anisotropy and enable isotropic large-strain and cyclic behavior with high energy dissipation and good shape recovery, while dispersed-particle morphologies require connectivity to approach isotropy. The results establish a design principle for isotropic mechanical functionalities in disordered composites and point to applications in isotropic photonics, heat and mass transport, and reusable structures.

Abstract

Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a facile approach for designing heterogeneous disordered materials that exhibit nearly isotropic mechanical resilience and energy dissipation capabilities. We demonstrate, through experiments and numerical simulations on 3D-printed prototypes, that near-complete isotropy can be attained in the proposed heterogeneous materials with a small, finite number of random spatial points. We also show that adding connectivity between random subdomains leads to much enhanced elastic stiffness, plastic strength, energy dissipation, shape recovery, structural stability and reusability in our new heterogeneous materials. Overall, our study opens avenues for the rational design of a new class of heterogeneous materials with isotropic mechanical functionalities for which the engineered disorder throughout the subdomains plays a crucial role.

Figures (15)

• Figure 1: Constructing heterogeneous disordered materials with two distinct morphologies: (a) dispersed-particle morphology and (b) continuous morphology. (c) Representative volume elements (RVEs) with dispersed-particle and continuous morphologies with varying number of random spatial points (N = 4, 6, 7, 8, 9, 10, 15 and 20). Here, only hard domains are displayed in RVEs and note that v$_\mathrm{hard}$ = 50%.
• Figure 2: Elastic anisotropy in heterogeneous disordered materials with v$_\mathrm{hard}$ = 50% (v$_\mathrm{pack}$ = 50.75%)\ref{['note:packing']}. (a) Three-dimensional maps of the directional elastic modulus with $E_{\mathrm{soft}}/E_{\mathrm{hard}} = 1/30$ and (b) anisotropy indices in RVEs with dispersed hard domains with two different stiffness ratios ($E_{\mathrm{soft}}/E_{\mathrm{hard}}$) of 1/30 and 1/90. Here, $\mathrm{A}^{\mathrm{U}}$ is the universal anisotropy index and $\mathrm{A}^{\mathrm{eq}}$ is the equivalent Zener index (ranganathan2008universalnye1985physical). The blue and orange dashed lines indicate the anisotropy indices in the dispersed-particle RVEs constructed on a face-centered-cubic (fcc) lattice. (c) Three-dimensional maps of the directional elastic modulus with $E_{\mathrm{soft}}/E_{\mathrm{hard}} = 1/30$ and (d) anisotropy indices in the RVEs with continuous hard domains with $E_{\mathrm{soft}}/E_{\mathrm{hard}} = 1/30$ and $1/90$. The blue and orange dashed lines indicate the anisotropy indices in the continuous RVEs on a fcc lattice.
• Figure 3: Microstructural details in heterogeneous disordered materials with continuous morphology. (a) Average number of connectivities (or the coordination number, Z) as a function of the number of random spatial points; the dashed line indicates the coordination number in a fcc lattice (Z = 12). (b) Elastic anisotropy of the RVEs with continuous morphology with varying coordination number. Here, note that a RVE with the highest anisotropy was selected for analysis from the ten statistical realizations for each of N = 6, 7, 8 and 9. Rod length distributions in the continuous RVEs with (c) N = 6 and (d) N = 7, obtained from ten statistical realizations which are displayed in Figure \ref{['fig:design']}c; here, the red dashed line indicates the average rod length in each of N = 6 and N = 7. Note that v$_\mathrm{hard}$ = 50% (v$_\mathrm{pack}$ = 50.75%).
• Figure 4: Local bond-orientational order parameters ($Q_4$, $Q_6$) in ten statistical realizations with (a) N = 6, (b) N = 7, (c) N = 8, (d) N = 9, (e) N = 10 and (f) N = 20. Note that v$_\mathrm{hard}$ = 50% (v$_\mathrm{pack}$ = 50.75%).
• Figure 5: Local bond-orientational order parameters ($Q_4$, $Q_6$) in statistical realizations with N = 6 with varying packing fraction from v$_\mathrm{pack}$ = 10% to 50.75%