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We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self- assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides. 

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle–particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system’s variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network’s resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid–liquid phase boundary using a single volume fraction of particles well beyond this phase boundary. 

Palpation utilizes the fact that solid breast tumours are stiffer than the surrounding tissue. However, cancer cells tend to soften, which may enhance their ability to squeeze through dense tissue. This apparent paradox proposes two contradicting hypotheses: either softness emerges from adaptation to the tumour’s microenvironment or soft cancer cells are already present inside a rigid primary tumour mass giving rise to cancer cell motility. We investigate primary tumour explants from patients with breast and cervix carcinomas on multiple length scales. We find that primary tumours are highly heterogeneous in their mechanical properties on all scales from the tissue level down to individual cells. This results in a broad rigidity distribution—from very stiff cells to cells softer than those found in healthy tissue—that is shifted towards a higher fraction of softer cells. Atomic-force-microscopy-based tissue rheology reveals that islands of rigid cells are surrounded by soft cells. The tracking of vital cells confirms the coexistence of jammed and unjammed areas in tumour explants. Despite the absence of a percolated backbone of stiff cells and a large fraction of unjammed, motile cells, cancer cell clusters show a heterogeneous solid behaviour with a finite elastic modulus providing mechanical stability.