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The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
Composite materials often exhibit mechanical anisotropy owing to the material properties or geometrical configurations of the microstructure. This makes their inverse design a two-fold problem. First, we must learn the type and orientation…
Materials either have a high hardness or excellent ductility, but rarely both at the same time. Mo$_2$BC is one of the only crystalline materials that simultaneously has a high Vickers hardness and is also relatively ductile. The origin of…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
Disordered hyperuniform many-body systems are distinguishable states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or…
Composite materials are used across engineering applications for their superior mechanical performance, a result of efficient load transfer between the structure and matrix phases. However, the inherently two-dimensional structure of…
Amorphous solids are mechanically rigid while possessing a disordered structure similar to that of dense liquids. Recent research indicates that dynamical heterogeneity, spatio-temporal fluctuations in local dynamical behavior, might help…
The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework…
We propose a new conceptual approach to reach unattained dissipative properties based on the friction of slender concentric sliding columns. We begin by searching for the optimal topology in the simplest telescopic system of two concentric…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
This paper focuses on the homogenization of high-contrast dielectric elastomer composites, materials that deform in response to electrical stimulation. The considered heterogeneous material consisting of an ambient material with inserted…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…
The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional…
Acoustic transparency is the capability of a medium to transmit mechanical waves to adjacent media, without scattering. This characteristic can be achieved by carefully engineering the acoustic impedance of the medium -- a combination of…
The ability to control forces between sub-micron-scale building blocks offers considerable potential for designing new materials through self-assembly. A typical paradigm is to first identify a particular (crystal) structure that has some…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress-strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation…
Since its introduction more than 60 years ago, the Hashin-Shtrikman upper bound has stood as the theoretical limit for the stiffness of isotropic composites and porous solids, acting as an important reference against which the moduli of…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
High entropy alloys gained significant scientific interest in recent years due to their enhanced mechanical properties including high yield strength combined with outstanding ductility. The strength of these materials originates from their…