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Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e.\ networks with more degrees of freedom than…
By virtue of their open network structures and low densities, metal--organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a…
Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
Dielectric structures composed of many inclusions that manipulate light in ways the bulk materials cannot are commonly seen in the field of metamaterials. In these structures, each inclusion depends on a set of parameters such as location…
Replicating and surpassing the autonomy of natural organisms remains a long-standing goal in robotics. Yet most robotic systems have their structure, materials, and control designed separately, in sharp contrast to the co-evolution in…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial…
Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the…
Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…
The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials and their properties. In particular, controlling the…
Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the…
We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. While the influence of…
Metamaterials are engineered materials composed of specially designed unit cells that exhibit extraordinary properties beyond those of natural materials. Complex engineering tasks often require heterogeneous unit cells to accommodate…
Topological mechanical metamaterials have demonstrated exotic and robust mechanical properties which led to promising engineering applications. One of such properties is the focusing of stress at the interface connecting domains of…