Abstract: Publication date: Available online 10 May 2019Source: Advances in Applied MechanicsAuthor(s): Raj Kumar Pal, Javier Vila, Massimo Ruzzene Recent breakthroughs in condensed matter physics are opening new directions in band engineering and wave manipulation. Specifically, challenging the notions of reciprocity, time-reversal symmetry, and sensitivity to defects in wave propagation may disrupt ways in which mechanical metamaterials are designed and employed, and may enable totally new functionalities. Nonreciprocity and topologically protected wave propagation will have profound implications on how stimuli and information are transmitted within materials, or how energy can be guided and steered so that its effects may be controlled or mitigated.This chapter introduces one basic approach to generate topologically protected edge-bound wave propagation in mechanical metamaterials. The concept is based on breaking inversion symmetry within the geometry of a unit cell of a periodic media, and in joining periodic assemblies that are inverted copies of each other. Such inversion leads to topologically different structures, as quantified by associated dispersion topological invariants. A nontrivial interface is thus produced which supports the propagation of defect and backscattering-immune edge states. The concept is first illustrated in a one-dimensional spring mass lattice, which is the simplest configuration that supports the considered broken inversion symmetry and the resulting interface bound modes. Next, the presentation is extended to a conceptual discrete two-dimensional hexagonal lattice, which provides the required symmetries for the nucleation of isolated Dirac points in reciprocal space with inverted topological invariants at the high symmetry points. This lattice forms the basis for the design of a continuous elastic hexagonal lattice, whose dispersion topology is investigated first numerically and then probed experimentally to demonstrate the existence of the predicted edge modes. The results shown for this continuous lattice demonstrate the effectiveness of the approach followed for the generation of topology inverted lattices and the production of nontrivial interfaces. Such procedure can be extended to a variety of structural configurations which can be exploited for designs of components that are capable of guiding elastic waves along predefined paths, or isolate vibrations to specific spatial locations.

Abstract: Publication date: Available online 10 May 2019Source: Advances in Applied MechanicsAuthor(s): Pattabhi Ramaiah Budarapu, Xiaoying Zhuang, Timon Rabczuk, Stephane P.A. Bordas Material behavior and microstructure geometries at small scales strongly influence the physical behavior at higher scales. For example, defects like cracks and dislocations evolve at lower scales and will strongly impact the material properties (mechanical, electrical, thermal, and chemical) at the macroscale. We summarize the recent developments in computational methods to simulate material behavior on multiple scales. We provide details on different techniques at various length scales: quantum, atomistic and coarse-grained models, and various continuum-based models. Furthermore, multiscale methods are broadly divided into: hierarchical, semiconcurrent, and concurrent techniques, and we review a number of modern hierarchical and semiconcurrent multiscale methods such as virtual atom cluster model, homogenization techniques, representative volume element-based methods and structural reconstruction based on Wang tiles. We also go through popular concurrent multiscale methods for fracture applications, such as extended bridging scale and extended bridging domain methods and discuss in detail adaptivity, coarse graining techniques, and their interactions. Computer implementation aspects of specific problems in the context of molecular as well as multiscale framework are also addressed for two- and three-dimensional crack growth problems. The chapter ends with conclusions and future prospects of multiscale methods.

Abstract: Publication date: Available online 3 January 2019Source: Advances in Applied MechanicsAuthor(s): Yan Pennec, Yabin Jin, Bahram Djafari Rouhani Photonic and phononic crystals provide a novel and alternative platform for sensing material properties with high sensitivity. The sensor aims to determine properties of the fluid such as its nature, concentration or temperature, employing specific features in the photonic and phononic transmission spectra. The dependence of such frequency dips or peaks where the transmission takes place is correlated to material properties, specifically to the acoustic or optical refractive index through the light and sound velocity of the fluid. Looking at both phononic and photonic behaviors within one single platform increases the ability to determine the fluid properties by cross correlating the optical and acoustic data. The capability of the concept is demonstrated through two different structures for which different specific applications can be reached. The first one is made of a two-dimensional crystal constituted of infinite cylindrical holes in a silicon substrate where one row of holes oriented perpendicular to the propagation direction is filled with a liquid. In the second one, the transmissions of optical and acoustic waves are normally impinging upon a periodic perforated silicon plate where the embedded medium is a liquid. Finally, we introduce acoustic metamaterials made of hollow pillars deposited on a plate for sensing purposes. Such crystals can exhibit confined whispering gallery modes around the hollow parts of the pillars. Filling the hollow parts with a fluid gives rise to new localized modes, which depend on the physical properties and height of the fluid. In all the investigated cases, we show an ultra-sensitivity to the light and sound velocities for different fluids, considered as the analyte, depending on their nature, concentrations or temperature.

Abstract: Publication date: Available online 12 November 2018Source: Advances in Applied MechanicsAuthor(s): Clémence L. Bacquet, Hasan Al Ba’ba’a, Michael J. Frazier, Mostafa Nouh, Mahmoud I. Hussein Resonant elastic metamaterials are artificial material systems that exhibit unique dynamical properties shaped by the intrinsic interaction between resonances and traveling dispersive waves. In this chapter, we provide a technical review of the recently proposed concept of dissipation emergence in elastic metamaterials. This concept is termed “metadamping.” Unlike conventional materials used to dampen vibrations where the damping capacity is affected by the atomic configuration, defects, and/or rheological properties, here the level of dissipation is controlled via the dynamics of the metamaterial's resonant substructures. In this manner, it is possible to create a net material system that is both stiff and highly damped, to absorb vehicle vibrations for example. The chapter starts with a motivation and introduction of metadamping, and then presents an in-depth analysis and parametric study of metadamping in the context of both locally and nonlocally resonant elastic metamaterials modeled as mass-spring-dashpot systems. The effect of the core damping model (e.g., viscous vs nonviscous) is also examined. Finally, a review is given of metadamping in a pillared beam that has recently been investigated by experiments, simulations, and theory.

Abstract: Publication date: Available online 17 October 2018Source: Advances in Applied MechanicsAuthor(s): Javier Segurado, Ricardo A. Lebensohn, Javier LLorca This paper reviews the current state of the art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modeling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Finally, current challenges and future research directions in this field are summarized.