A relative gradient theory for layered materials

It is possible to remedy certain difficulties with the description of short wave length phenomena and interfacial slip in standard models of a laminated material by considering the bending stiffness of the layers. If the couple or moment stresses are assumed to be proportional to the relative deformation gradient, then the bending effect disappears for vanishing interface slip, and the model correctly reduces to an isotropic standard continuum. In earlier Cosserat-type models this was not the case. Laminated materials of the kind considered here occur naturally as layered rock, or at a different scale, in synthetic layered materials and composites. Similarities to the situation in regular dislocation structures with couple stresses, also make these ideas relevant to single slip in crystalline materials. Application of the theory to a one-dimensional model for layered beams demonstrates agreement with exact results at the extremes of zero and infinite interface stiffness. Moreover, comparison with finite element calculations confirm the accuracy of the prediction for intermediate interfacial stiffness.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Texture alignment in simple shear

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is coupled to a director theory to add specific orientation of grains to describe anisotropic microstructure. The numerical solution is based on an implicit form of the Material Point Method developed by Moresi et al. [1].

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Rhythmic variations in pain, stiffness, and manual dexterity in hand osteoarthritis

Objective: To explore circadian variation in pain, stiffness, and manual dexterity inpatients with hand osteoarthritis (OA). Methods: Twenty one patients with hand OA, as defined by ACR criteria (17 women, four men, mean age 62.2 years, range 52-74 years) self rated pain and stiffness on separate 10 cm horizontal visual analogue scales and performed bead intubation coordinometry (BIC) six times each day (on waking up, at bedtime, and every four hours in between) for 10 consecutive days. Each series (using data with the trend removed if there was a significant trend) was analysed for circadian rhythmicity by a cosine. vector technique (single cosinor). With individual data expressed as the percentage of the mean, group rhythm characteristics at period 24 hours were summarised for each variable by population mean cosinor analysis. Results: Individual analyses identified significant circadian rhythms at pless than or equal to0.05 for pain (n=15/21), stiffness (n=16/20), and dexterity (n=18/21), and a significant circadian rhythm on a group basis was identified for pain (p=0.013), stiffness (p

Age does not influence the bone response to treadmill exercise in female rats

Purpose: Because it is believed that bone may respond to exercise differently at different ages, we compared bone responses in immature and mature rats after 12 wk of treadmill running. Methods: Twenty-two immature (5-wk-old) and 21 mature (17-wk-old) female Sprague Dawley rats were randomized into a running (trained, N = 10 immature, 9 mature) or a control group (controls, N 12 immature, 12 mature) before sacrifice 12 wk later. Rats ran on a treadmill five times per week for 60-70 min at speeds up to 26 m.min(-1). Both at baseline and after intervention, we measured total body, lumbar spine, and proximal femoral bone mineral, as well as total body soft tissue composition using dual-energy x-ray absorptiometry (DXA) in vivo. After sacrificing the animals, we measured dynamic and static histomorphometry and three-point bending strength of the tibia. Results: Running training was associated with greater differences in tibial subperiosteal area, cortical cross-sectional area, peak load, stiffness, and moment of inertia in immature and mature rats (P < 0.05). The trained rats had greater periosteal bone formation rates (P < 0.01) than controls, but there was no difference in tibial trabecular bone histomorphometry. Similar running-related gains were seen in DXA lumbar spine area (P = 0.04) and bone mineral content (BMC; P = 0.03) at both ages. For total body bone area and BMC, the immature trained group increased significantly compared with controls (P < 0.05), whereas the mature trained group gained less than did controls (P < 0.01). Conclusion: In this in vivo model, where a similar physical training program was performed by immature and mature female rats, we demonstrated that both age groups were sensitive to loading and that bone strength gains appeared to result more from changes in bone geometry than from improved material properties.

Spinal stiffness changes throughout the respiratory cycle

Posteroanterior stiffness of the lumbar spine is influenced by factors, including trunk muscle activity and intra-abdominal pressure (IAP). Because these factors vary with breathing, this study investigated whether stiffness is modulated in a cyclical manner with respiration. A further aim was to investigate the relationship between stiffness and IAP or abdominal and paraspinal muscle activity. Stiffness was measured from force-displacement responses of a posteroanterior force applied over the spinous process of L-2 and L-4. Recordings were made of IAP and electromyographic activity from L-4/L-2 erector spinae, abdominal muscles, and chest wall. Stiffness was measured with the lung volume held at the extremes of tidal volume and at greater and lesser volumes. Stiffness at L-4 and L-2 increased above base-level values at functional residual capacity (L-2 14.9 N/mm and L-4 15.3 N/mm) with both inspiratory and expiratory efforts. The increase was related to the respiratory effort and was greatest during maximum expiration (L-2 24.9 N/mm and L-4 23.9 N/mm). The results indicate that changes in trunk muscle activity and IAP with respiratory efforts modulate spinal stiffness. In addition, the diaphragm may augment spinal stiffness via attachment of its crural fibers to the lumbar vertebrae.

Theoretical and experimental studies of unbraced tubular trusses allowing for torsional stiffness

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters. (C) 2004 Elsevier Ltd. All rights reserved.