Abstract: Publication date: Available online 18 December 2019Source: Advances in Applied MechanicsAuthor(s): Jian-Ying Wu, Vinh Phu Nguyen, Chi Thanh Nguyen, Danas Sutula, Sina Sinaie, Stephane Bordas Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, a major concern in structural designs. Computational modeling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights into understanding the fracture processes of many materials such as concrete, rock, ceramic, metals, and biological soft tissues. This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician. PFMs are the regularized versions of the variational approach to fracture which generalizes Griffith's theory for brittle fracture. They can handle topologically complex fractures such as initiation, intersecting, and branching cracks in both two and three dimensions with a quite straightforward implementation. One of our aims is to justify the gaining popularity of PFMs. To this end, both theoretical and computational aspects are discussed and extensive benchmark problems (for quasi-static and dynamic brittle/cohesive fracture) that are successfully and unsuccessfully solved with PFMs are presented. Unresolved issues for further investigations are also documented.

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 RouhaniAbstractPhotonic 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.