Lamb Wave Scattering from Rivets

For structures with large surface areas, a full integrity evaluation can be a time-consuming operation. Lamb wave techniques allow this evaluation to be performed with waves propagating along one dimension of the inspection area while the probing transducers are moved in the perpendicular dimension, giving information about the presence of flaws within the entire scanned area. For riveted structures the scattering of the Lamb waves from the rivets is often the dominant feature in the measured response, masking the more subtle effects of Lamb wave interactions with the flaws of interest [1]. In this paper we consider the scattering of lowest mode symmetric and antisymmetric Lamb waves from model rivets, and derive analytic expressions for the scattered fields. With solutions of this type the disruptive effects of the rivets can be “processed out” of measured data in order to expose the signals which are due to the flaws in the structure

Characterization of the Internal Microstructures of Granular Materials Using Computerized Tomography

In developing micromechanical models of constitutive behavior, granular materials are treated as ensembles of discrete particles. The macroscopic mechanical properties of these materials are derived from force-deformation relations [1], which describe the behavior of particle-to-particle contacts at the microscopic level. The occurrence and behavior of these contacts are controlled by the packing structures in the granular system. The packing structures used in many current approaches to modeling granular materials are either regular [2,3,4] or numerically-generated random packings [5]. To properly account for actual particle packings, however, it is desirable to develop an experimental technique for direct observation. In this paper, the microstructures of simplified materials (laboratory packed spherical particles) are investigated using X-ray computerized tomography (CT), which provides a non-intrusive way to obtain cross-sectional images of material samples. Series of these digital images are then processed to reconstruct the three-dimensional internal structure of the sample using numerical techniques. Scanning and image analysis results for a sample made of glass spheres are presented in this paper, demonstrating the potential of CT technology in identifying the microstructures of granular materials

Thermoelastic Waves in Microstructured Solids

Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in microstructured solids under thermal loading

Solid Friction from stick-slip to pinning and aging

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between wacroscopic hard rough solids, whose main dynamical features are well described by the Rice-Ruina rate and state dependent constitutive law. We show that it results from two combined effects : (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure (ii) geometric aging, i.e. slow growth of the real arrea of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsoprtion-induced metastability.Comment: 28 page

New Mechanics of Traumatic Brain Injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinationsComment: 18 pages, 1 figure, Late

Multiscale analysis of materials with anisotropic microstructure as micropolar continua

Multiscale procedures are often adopted for the continuum modeling of materials composed of a specific micro-structure. Generally, in mechanics of materials only two-scales are linked. In this work the original (fine) micro-scale description, thought as a composite material made of matrix and fibers/particles/crystals which can interact among them, and a scale-dependent continuum (coarse) macro-scale are linked via an energy equivalence criterion. In particular the multiscale strategy is proposed for deriving the constitutive relations of anisotropic composites with periodic microstructure and allows us to reduce the typically high computational cost of fully microscopic numerical analyses. At the microscopic level the material is described as a lattice system while at the macroscopic level the continuum is a micropolar continuum, whose material particles are endowed with orientation besides position. The derived constitutive relations account for shape, texture and orientation of inclusions as well as internal scale parameters, which account for size effects even in the elastic regime in the presence of geometrical and/or load singularities. Applications of this procedure concern polycrystals, wherein an important descriptor of the underlying microstructure gives the orientation of the crystal lattice of each grain, fiber reinforced composites, as well as masonry-like materials. In order to investigate the effects of micropolar constants in the presence of material non central symmetries, some numerical finite element simulations, with elements specifically formulated for micropolar media, are presented. The performed simulations, which extend several parametric analyses earlier performed [1], involve two-dimensional media, in the linear framework, subjected to compression loads distributed in a small portion of the medium

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain-gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant is introduced, in addition to the standard Lamé constants . The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics

On the coupling of local 3D solutions and global 2D shell theory in structural mechanics

Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories. To circumvent, or at least alleviate this issue, authors proposed in their former works an in-plane-out-of-plane separated representation able to capture rich 3D behaviors while keeping the computational complexity of 2D simulations. However, that procedure it was revealed to be too intrusive for being introduced into existing commercial softwares. Moreover, experience indicated that such enriched descriptions are only compulsory locally, in some regions or structure components. In the present paper we propose an enrichment procedure able to address 3D local behaviors, preserving the direct minimally-invasive coupling with existing plate and shell discretizations. The proposed strategy will be extended to inelastic behaviors and structural dynamics