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Register a new userOn static chiral Milton-Briane-Willis continuum mechanics
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Recent static experiments on twist effects in chiral three-dimensional mechanical metamaterials have been discussed in the context of micropolar Eringen continuum mechanics, which is a generalization of Cauchy elasticity. For cubic symmetry, Eringen elasticity comprises nine additional parameters with respect to Cauchy elasticity, of which three directly influence chiral effects. Here, we discuss the behavior of the static case of an alternative generalization of Cauchy elasticity, the Milton-Briane-Willis equations. We show that in the homogeneous static cubic case only one additional parameter with respect to Cauchy elasticity results, which directly influences chiral effects. We show that the Milton-Briane-Willis equations qualitatively describe the experimentally observed chiral twist effects, too. We connect the behavior to a characteristic length scale.
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New connections between static elastic cloaking, low frequency elastic wave scattering and neutral inclusions are established in the context of two dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core-shell composite cylinder as a neutral elastic inclusion. Two types of neutral inclusion are distinguished, textit{weak} and textit{strong} with the former equivalent to low frequency transparency {and the classical Christensen and Lo generalised self-consistent result for in-plane shear from 1979. Our introduction of the textit{strong neutral inclusion} is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed unphysical materials.} The relationships between low frequency transparency, static cloaking and neutral inclusions provide the material designer with options for achieving elastic cloaking in the quasi-static limit.
Implicit electron-density solvation models based on joint density-functional theory offer a computationally efficient solution to the problem of calculating thermodynamic quantities of solvated systems from firstprinciples quantum mechanics. However, despite much recent interest in such models, to date the applicability of such models in the plane-wave context to non-aqueous solvents has been limited because the determination of the model parameters requires fitting to a large database of experimental solvation energies for each new solvent considered. This work presents an alternate approach which allows development of new iso-density models for a large class of protic and aprotic solvents from only simple, single-molecule ab initio calculations and readily available bulk thermodynamic data.
We explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloakss designs are strikingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigor in transposition of existing cloakss designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars.
When a liquid film lies on a non-wettable substrate, the configuration is unstable and the film then retracts from a solid substrate to form droplets. This phenomenon, known as dewetting, commonly leads to undesirable morphological changes. Nevertheless, recent works have demonstrated the possibility to harness dewetting by employing templated substrates with a degree of precision on par with advanced lithographic processes for high-performance nanophotonic applications. Since resonant behavior is highly sensitive to geometrical changes, predicting quantitatively dewetting dynamics is of high interest. In this work, we develop a continuum model that predicts the evolution of a thin film on a patterned substrate, from the initial reflow to the nucleation and growth of holes. We provide an operative framework based on macroscopic measurements to model the intermolecular interactions at the origin of the dewetting process, involving length scales that span from sub-nanometer to micron range. A comparison of experimental and simulated results shows that the model can accurately predict the final distributions, thereby offering novel predictive tools to tailor the optical response of dewetted nanostructures.
Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.
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