Equivalent Elasticity Research Articles

Stress–strain relations in elastoplastic solids with Dugdale-type cracks

Mechanical behavior of a two-dimensional elastoplastic solid with rectilinear cracks is investigated. Plastic strip model is used to reduce plasticity problem to the equivalent linear elasticity formulation. Two realizations of the mixed mode plastic strip model are considered: in-line plastic strips as proposed by Becker and Gross [Int. J. Fract. 37 (1988) 163], and inclined plastic strips of Panasyuk and Savruk [Appl. Mech. Rev. 47 (1994) 151]. The effective mechanical response predictions are based on the procedure presented in Kachanov et al., [Appl. Mech. Rev. 47 (1994) 151]. Stress–strain relations are obtained for parallel and randomly oriented non-interacting cracks. Results are compared with known elastic solutions.

Computation of equivalent material properties of woven fabric composites using homogenization technique

Reliable three-dimensional models of woven fabric composites had scarcely been proposed for their geometric complexity. Simplified models, mostly one- or two-dimensional, currently used are not considered effective enough because of their oversimplifications. In this paper, the equivalent thermal conductivities and elasticity properties of woven fabric composites are computed using homogenization technique. The computational results show that the strength and thermal conductivity linearly increase with fiber volume fraction and that the variations of undulation of fibers has little effect on equivalent material properties. Homogenization technique is proved useful in the study of woven fabric composites and may find a lot more applications in the area.

Diffusion with critically correlated traps and the slow relaxation of the longest-wavelength mode.

We study diffusion on a substrate with permanent traps distributed with critical positional correlation, modeled by their placement on the perimeters of a critical percolation cluster. We perform a numerical analysis of the vibrational density of states and the largest eigenvalue of the equivalent scalar elasticity problem using the method of Arnoldi and Saad. We show that the critical trap correlation increases the exponent appearing in the stretched exponential behavior of the low frequency density of states by approximately a factor of two as compared to the case of no correlations. A finite size scaling hypothesis of the largest eigenvalue is proposed and its relation to the density of states is given. The numerical analysis of this scaling postulate leads to the estimation of the stretch exponent in good agreement with the density of states result.

A discrete-continuum hybrid model for vibrational energy transfer at the gas–solid interface. II. The quantal evolution of coupled localized-collective motions

We analyze a new approach to the vibration of inhomogeneous surfaces whereby surface defects and their surroundings are properly treated as discrete atoms while the remainder of the solid is represented by an elastic continuum of equivalent mass density and elasticity with quantized vibrational waves. Such a hybrid treatment is aimed at describing defect-local motion while fully coupled to collective vibrational waves in a quantum-mechanical fashion appropriate to inelastic gas–surface scattering. We assess how the hybrid model reproduces the response of the surface by following the quantum-statistical moments of vibrational displacements as the collision progresses. The results suggest that the discrete-continuum approach can provide a powerful tool for describing collisional excitation of defect-laden surfaces within a fully quantal treatment of surface motion.

Invariance of ankle dynamic stiffness during fatiguing muscle contractions

Our objective was to determine the effect of muscle fatigue on the dynamic stiffness of the human ankle. Four subjects were required to maintain constant-force contractions of tibialis anterior until the required force could no longer be maintained. Repeated pseudo-random displacements of ankle angular position were applied throughout each contraction. The dynamic relation between ankle angular position and ankle torque was identified by determining non-parametric compliance impulse response functions (CIRFs). The CIRFs were redetermined every 2.55s throughout the sustained contractions to provide a quantitative measure of changes in ankle stiffness dynamics. Inspection of these CIRFs revealed little change in shape or magnitude throughout the contractions, despite large increases in tibialis anterior EMG. The dynamics were further quantified by estimating the equivalent joint inertia, viscosity and elasticity associated with each CIRF. As each contraction progressed, the inertial and elastic terms remained constant whereas the viscous term decreased slightly. These findings demonstrate that fatigue of tibialis anterior during sustained constant mean force contractions results in little change in the mechanical dynamics of the human ankle.

Time Varying Stress in Ligaments of Perforated Plates with Reference to Prestressed Concrete Reactor Vessels

The work described herein relates to the prediction of stresses in materials which exhibit time varying strains with particular reference to the ligaments of perforated circular concrete slabs, subjected to long-term radial prestress and uniform elevated temperature. The perforations are reinforced with steel liners and arranged in a square central lattice symmetrical about two orthogonal axes. Special reference is made to the distribution of stress in the standpipe region of prestressed concrete cylindrical pressure or containment vessels for gas cooled reactors. In order to assess the stress distribution around the perforated zone of a circular slab, a method of analysis was developed by the author, based on the “Equivalent Elastic Modulus” of the perforated zone and the “Effective Modulus Method”, utilizing experimental data obtained from tests performed on model specimens. The object of this paper is to extend the above method of analysis into the perforated region, and assess the long-term stresses i...

Propagation of ultrasonic waves in porous ceramics

Theoretical problems concerning the propagation of ultrasonic waves in a porous medium are outlined. The propagation velocity of longitudinal ultrasonic waves in an elastic medium with spherical gaseous inclusions is considered in detail. The calculation method adopted consists of determining equivalent elasticity moduli of the porous medium. The calculation of these moduli is based on the work of H. Mackenzie on media containing spherical gaseous inclusions of various diameters. The theoretical results obtained for the propagation velocity of ultrasonic waves, are compared with those measured on electrical porcelain, the latter constituting a model of a porous medium. Also a method allowing for the effect of composition of the porcelain mass to be taken into account, is described. The results of measurements of the propagation velocity of a longitudinal wave are found to be in good agreement with theoretical data. This conformity allows for non-destructive tests of products containing spherical gaseous inclusions.