Authors:Julius Kaplunov; Danila Prikazchikov Abstract: Publication date: Available online 13 April 2017 Source:Advances in Applied Mechanics Author(s): Julius Kaplunov, Danila A. Prikazchikov Explicit asymptotic formulations are derived for Rayleigh and Rayleigh-type interfacial and edge waves. The hyperbolic–elliptic duality of surface and interfacial waves is established, along with the parabolic–elliptic duality of the dispersive edge wave on a Kirchhoff plate. The effects of anisotropy, piezoelectricity, thin elastic coatings, and mixed boundary conditions are taken into consideration. The advantages of the developed approach are illustrated by steady-state and transient problems for a moving load on an elastic half-space.

Authors:E.C. Aifantis Abstract: Publication date: Available online 4 October 2016 Source:Advances in Applied Mechanics Author(s): E.C. Aifantis A combined theoretical/numerical/experimental program is outlined for extending the internal length gradient (ILG) approach to consider time lags, stochasticity, and multiphysics couplings. Through this extension, it is possible to discuss the interplay between deformation internal lengths (ILs) and ILs induced by thermal, diffusion, or electric field gradients. Size-dependent multiphysics stability diagrams are obtained, and size-dependent serrated stress–strain curves are interpreted through combined gradient-stochastic models. When differential equations are not available for describing material behavior, a Tsallis nonextensive thermodynamic formulation is employed to characterize statistical properties. A novel multiscale coarse-graining technique, the equation-free method (EFM), is suggested for bridging length scales, and the same is done for determining ILs through novel laboratory tests by employing specimens with fabricated gradient micro-/nanostructures. The extension of ILG framework to consider fractional derivatives and fractal media is explored. Three apparently different emerging research areas of current scientific/technological/biomedical interest are discussed: (i) plastic instabilities and size effects in nanocrystalline (NC)/ultrafine grain (UFG) and bulk metallic glass (BMG) materials; (ii) chemomechanical damage, electromechanical degradation, and photomechanical aging in energetic materials; (iii) brain tissue and neural cell modeling. Finally, a number of benchmark problems are considered in more detail. They include gradient chemoelasticity for Li-ion battery electrodes; gradient piezoelectric and flexoelectric materials; elimination of singularities from crack tips; derivation of size-dependent stability diagrams for shear banding in BMGs; modeling of serrated size-dependent stress–strain curves in micro-/nanopillars; description of serrations and multifractal patterns through Tsallis q-statistics; and an extension of gradient elasticity/plasticity models to include fractional derivatives and fractal media.

Authors:M. Ostoja-Starzewski; S. Kale; P. Karimi; A. Malyarenko; B. Raghavan; S.I. Ranganathan; J. Zhang Abstract: Publication date: Available online 14 September 2016 Source:Advances in Applied Mechanics Author(s): M. Ostoja-Starzewski, S. Kale, P. Karimi, A. Malyarenko, B. Raghavan, S.I. Ranganathan, J. Zhang The problem of effective properties of material microstructures has received considerable attention over the past half a century. By effective (or overall, macroscopic, global) is meant the response assuming the existence of a representative volume element (RVE) on which a homogeneous continuum is being set up. Since the efforts over the past quarter century have been shifting to the problem of the size of RVE, this chapter reviews the results and challenges in this broad field for a wide range of materials. For the most part, the approach employed to assess the scaling to the RVE is based on the Hill–Mandel macrohomogeneity condition. This leads to bounds that explicitly involve the size of a mesoscale domain—this domain also being called a statistical volume element (SVE)—relative to the microscale and the type of boundary conditions applied to this domain. In general, the trend to pass from the SVE to RVE depends on random geometry and mechanical properties of the microstructure, and displays certain, possibly universal tendencies. This chapter discusses that issue first for linear elastic materials, where a scaling function plays a key role to concisely grasp the SVE-to-RVE scaling. This sets the stage for treatment of nonlinear and or/inelastic random materials, including elasto-plastic, viscoelastic, permeable, and thermoelastic classes. This methodology can be extended to homogenization of random media by micropolar (Cosserat) rather than by classical (Cauchy) continua as well as to homogenization under stationary (standing wave) or transient (wavefront) loading conditions. The final topic treated in this chapter is the formulation of continuum mechanics accounting for the violations of second law of thermodynamics, which have been studied on a molecular level in statistical physics over the past two decades. We end with an overview of open directions and challenges of this research field.

Authors:Alain Goriely; Silvia Budday; Ellen Kuhl Pages: 79 - 139 Abstract: Publication date: 2015 Source:Advances in Applied Mechanics, Volume 48 Author(s): Alain Goriely, Silvia Budday, Ellen Kuhl Arguably, the brain is the most complex organ in the human body, and, at the same time, the least well understood. Today, more than ever before, the human brain has become a subject of narcissistic study and fascination. The fields of neuroscience, neurology, neurosurgery, and neuroradiology have seen tremendous progress over the past two decades; yet, the field of neuromechanics remains underappreciated and poorly understood. Here, we show that mechanical stretch, strain, stress, and force play a critical role in modulating the structure and function of the brain. We discuss the role of neuromechanics across the scales, from individual neurons via neuronal tissue to the whole brain. We review current research highlights and discuss challenges and potential future directions. Using the nonlinear field theories of mechanics, we illustrate three phenomena which are tightly regulated by mechanical factors: neuroelasticity, the extremely soft behavior of the brain independent of time; neurodevelopment, the evolution of the brain at extremely long time scales; and neurodamage, the degradation of the brain at extremely short time scales. We hope that this review will become a starting point for a multidisciplinary approach to the mechanics of the brain with potential impact in preventing, diagnosing, and treating neurological disorders.

Authors:Mokarram Hossain; Paul Steinmann Abstract: Publication date: Available online 23 November 2015 Source:Advances in Applied Mechanics Author(s): Mokarram Hossain, Paul Steinmann A temporal evolution of material parameters may appear in many fields; as a paradigm the curing process of polymeric materials is here considered. Thereby, a systematic overview is presented in this contribution whereby modeling various aspects of the polymer curing process under different types of loads are investigated. Physically based, small and finite strain curing models have been developed that can work under a purely mechanical load where the time dependence of the material parameters appearing in the models are considered. The curing process of polymers under a purely mechanical load is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. To work under various classes of coupled loads, e.g., thermomechanical, magnetomechanical, and electromechanical loads, the initially developed modeling framework suited for a mechanical load is extended. Thereby, capturing the curing process in the presence of a magnetomechanical or an electromechanical load becomes even more challenging. In the current contribution, thermodynamically consistent small and finite strain constitutive frameworks are revisited which are based either on a direct time-dependent formulation or on a degree of cure-dependent formulation. The degree of cure is a key parameter in the curing (reaction) kinetics. Both our mechanical and several coupled modeling frameworks are in line with a rate-type hypoelastic approach. Some representative numerical examples are discussed under various forms of mechanical and nonmechanical loads which show the capability of different constitutive formulations to capture major phenomena observed during the curing process of polymers.

Authors:Syed N. Khaderi; Jaap M.J. den Toonder; Patrick R. Onck Pages: 1 - 78 Abstract: Publication date: Available online 21 November 2015 Source:Advances in Applied Mechanics Author(s): S.N. Khaderi, J.M.J. den Toonder, P.R. Onck Cilia are tiny hair-like structures that cover the surfaces of biological cells. One of their functions is to generate flow. Artificial cilia are mechanical actuators that are designed to mimic the motion of natural cilia in order to create fluid transport in microchannels. These fluid propulsion systems have potential for application in lab-on-a-chip devices that are used, e.g., for point-of-care diagnosis. The artificial cilia can be actuated through various means such as light, magnetic fields and electric fields. One of the main challenges in the design of artificial cilia is to find the cilia geometry and spacing, microchannel geometry, external actuation field, and frequency of operation, for which the fluid transported and the pressure generated are maximal. Various researchers have attempted to provide answers to these questions using computational models and experimental studies. The main feature of the computational models is that they accurately capture the interaction between the external actuation field (such as electric or magnetic fields), the motion of the artificial cilia and the fluid flow. In this chapter, we (i) give a brief overview of the existing modeling approaches, (ii) give an in-depth description of a recently developed modeling framework, and (iii) provide an overview of the most important results and insights that has led to our current understanding of the fluid propulsion using magnetically driven artificial cilia.