A theoretical model for the bending of a laminated beam with SMA fiber embedded layer

A theoretical model for the bending of a laminated beam bonded with shape memory alloy (SMA) fiber reinforced layer is presented. The constitutive relations of the SMA layer are obtained by using the method of micromechanics. The bending of the laminated beam is then discussed, and the relationship between bending moment, curvature and temperature are provided. The governing relationships obtained in this paper can be used for theoretical predications of thermomechanical properties of beam-like SMA actuators.     

Crack interaction in bending due to impact

The method of caustics has been applied to investigate crack propagation and interaction between a main propagating edge-crack and a collinear stationary one in plane specimens subjected to impact loading applied in a three-point bending mode. The high sensitivity of the experimental method used, combined with variable collinear crack configurations, has disclosed interesting results, concerning the continuosly variable dynamic stress and strain distributions around the propagating main crack. This arrangement of sensitive cracks was able to verify the existence and relative motion of the neutral zone appearing ahead of the moving crack tip, which separates regions of tensile and compressive transient stress in bent bars.     

An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams

An analytical model to predict the effective fracture toughness of concrete was proposed based on the fictitious crack model. Firstly, the equilibrium equations of forces in the section were formed in combination with the plane section assumption. Then a Lagrange function was presented through the equilibrium equations and the relationship formula between the effective crack length and crack tip opening displacement. Taking into account Lagrange Multiplier Method, the maximum load P_max was obtained, as well as the critical effective crack length a_c. Furthermore, was gained in an analytical manner. Subsequently, some material and structural parameters from other literatures were adopted into the proposed model for the calculation. Compared with the experimental results, most of the calculated values show a good agreement for P_max and a_c. In order to study the influence of the softening curve in the fictitious crack on the calculated fracture parameters, three series of constants determining the shape of the softening curve were chosen in the calculation. The results show that the calculated fracture parameters are not sensitive to the shape of the softening curve. Therefore, only if the elastic modulus E_c and flexural tensile strength f_r were measured, P_max, a_c and can be predicted accurately using the proposed model. Finally, the variations of the calculated fracture parameters with the specimen size and a₀/h (i.e., the ratio of the initial crack length to the depth of the specimen) were studied. It was found that both and the pre-critical crack propagation length Δa_c increase with the specimen size. However, the two parameters increase to the maximums and then decrease gradually with a₀/h. Moreover, the theories of free surface effect were utilized to explain the observed size effects.     

A circular inhomogeneity with interface slip and diffusion under in-plane deformation

We consider the in-plane deformation of a circular elastic inhomogeneity embedded in an infinite elastic matrix subjected to remote uniform stresses or uniform heat flow. The inhomogeneity and matrix have different material properties. The rate-dependent slip and mass transport by stress-driven diffusion concurrently occur on the inhomogeneity/matrix interface. For the remote uniform stress case, it is observed that the internal stresses within the inhomogeneity are quadratic functions of the coordinates x and y, and decay with two relaxation times. Interestingly the average mean stress within the circular inhomogeneity is in fact time-independent. As time approaches infinity, the internal stress field within the inhomogeneity becomes uniform and hydrostatic. In addition the change of strain energy due to the introduction of the circular elastic inhomogeneity is derived, containing various existing results as special cases. Furthermore, a simple condition leading to an internal uniform stress state within the inhomogeneity is found. This condition, which is independent of the elastic properties of the inhomogeneity and matrix, gives a simple relationship between the interface drag and diffusion parameters. For the remote heat flow case, the internal thermal stresses are linear functions of the coordinates x and y and decay only with a single relaxation time. Numerical results are presented to demonstrate the obtained solution and the corresponding physics.     

A fast integral approach for drag force calculation due to oscillatory slip stokes flows

In this paper, we describe an efficient numerical method for modelling oscillatory incompressible slip Stokes flows in three dimensions. The efficiency is achieved by employing an integral approach combined with an accelerated boundary‐element‐method (BEM) solver. First the integral representations for slip flows with two different slip models are formulated. The resulting integral equations are then solved using the BEM combined with the precorrected‐FFT accelerated technique. 3D numerical codes have been developed based on the method described above. These codes are then used to calculate the drag forces on oscillating objects immersed in an unbounded slip flow. Three objects are considered, namely a sphere, a pair of plates and a comb structure. The simulated drag forces on these objects obtained from the two slip models are compared. In the sphere case, the simulated results are also compared with the analytical solutions for both the steady‐state case and the no‐slip oscillatory case and are found to be in good agreement. In addition, qualitative comparison of the simulation results with the experimental results in the plate problem is also presented in this paper. Copyright © 2004 John Wiley & Sons, Ltd.     

A stratified model to predict dispersion in trabecular bone

Frequency-dependent phase velocity (dispersion) has previously been measured in trabecular bone by several groups. In contrast to most biologic tissues, phase velocity in trabecular bone tends to decrease with frequency. A stratified model, consisting of alternating layers of bone and marrow (in vivo) or water (in vitro), has been employed in an attempt to explain this phenomenon. Frequency-dependent phase velocity was measured from 300 to 700 kHz in 1) phantoms consisting of regularly spaced thin parallel layers of polystyrene sheets in water and 2) 30 calcaneus samples in vitro. For the polystyrene phantoms, the agreement between theory and experiment was good. For the calcaneus samples, the model has some limited usefulness (uncertainty of about 5%) in predicting average phase velocity. More importantly, the model seems to perform consistently well for predicting the frequency dependence of phase velocity in calcaneus.     

Ellipsometry of the liquid-vapor interface close to the critical point: A theoretical analysis

It is shown that the ellipsometric coefficient for a liquid-vapor interface may be written as the sum of three contributions. The first is given by Drude's formula. The second contribution is due to capillary wave fluctuations. Finally, the third contribution is due to fluctuations of the density profile around the Fisk-Widom profile with a wavelength up to roughly the bulk correlation length and thus short compared to the capillary length. Close to the critical point the first two contributions scale as (T - T _c ) ^- . The expression for the third contribution contains an integral over the excess density correlation function over wave vectors large compared to the inverse bulk correlation length. The scaling behavior of the third contribution is probably such that this term becomes unimportant close to the critical point. The formulae given in this paper only for the liquid-vapor interface may be used for a binary fluid if one makes the usual substitutions. An experimental analysis of the ellipsometric coefficient for binary fluids close to the critical point by Schmidt [1] indicates that the sum of the first two terms predicts a value which is somewhat to large but which has the correct scaling behavior. A discussion of this difference in amplitude is given.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Finite Element Analysis of sheet metal bending process to predict the springback

Springback remains a major concern in sheet metal forming process. Springback, shape discrepancy between fully loaded and unloaded configuration due to elastic recovery of material, is mainly affected by geometrical parameters, material properties of sheet and lubrication condition between the blank and the tool. A total-elastic–incremental-plastic (TEIP) algorithm, for large deformation and large rotational problems, was incorporated in indigenous Finite Element software. This software was used to predict the springback in a typical sheet metal bending process and to investigate the influence of these parameters on springback. The results of simulation are validated with own experiments and published experimental results.     

A constitutive model for frictional slip on rock interfaces

The shear stress required for frictional slip on rock interfaces is known to depend on the history of the slip velocity. At least one physical model that predicts this behavior also indicates that memory of past normal stresses may persist. A constitutive equation that incorporates memory of both past slip velocities and past normal stresses is proposed, and the appropriate physical property functions are identified. Once measured, these functions allow the computation of the shear stress on a slipping interface for general loading histories.     

The polycrystalline plasticity due to slip and twinning during magnesium alloy forming

In order to simulate the magnesium alloy-forming processes accurately, it is necessary to consider the plastic anisotropy. In this paper, a new rate-independent constitutive model for polycrystalline plastic deformation by slip and twinning has been formulated, and then introduced into a FEM program. Metal flow is assumed to occur by crystallographic slip on given slip and twinning systems within each crystal. Each integration point represents a single crystal. Then uniaxial compression and cup drawing of Mg alloy are studied by using a rate-independent polycrystalline plasticity finite element analysis. In this paper, the ear distributions of the polycrystal are predicted for different typical initial orientation cases. The values of the twinning factors associated with slip system deformation are deduced. It is found that the twinning factors vary with the value of the stress. The basal slip and twinning system plays the dominant role in the deformation of magnesium alloy, which might be the most important contribution to strain hardening.     

A system model to predict the results of ultrasonic scattering experiments

A system model is presented for the computation of ultrasonic scattering experiments. It includes a two-dimensional transducer model, whose diffraction field is given as an elastic plane wave spectral decomposition. An electromechanical reciprocity theorem is used to calculate the voltage at the terminal of the receiver. As a flaw-model, we use a strip-like crack, whose scattered field is calculated by the elastodynamic Huygens principle including mode conversion effects. Results in the time domain are presented for LLT- and 45° -tandem inspection situations and compared with measurements. Agreement between the model predictions and experimental results is typical to within 2 dB for average scan amplitudes.     

A comprehensive model to predict acoustic absorption factor of porous mixes

The aim of this study is to define an experimental model to predict acoustic absorption properties of porous asphalt concretes (PAC) as a function of composition and volumetric characteristics of mixes. The model can be used for the mix design of PAC and it enables to individuate which composition parameters to operate on in order to obtain optimum acoustic performances of low noise porous pavements. In order to define the experimental model, a large number of asphalt concrete samples, with high void content and composed of both different aggregate grading and different bitumen percentages were compacted in laboratory. Noise absorption spectra were determined on these samples by means of the stationary wave impedance tube. The measured amplitudes of the acoustic absorption spectrum were fitted by the Neithalath microstructural model in order to determine, for each sample, the pore geometry which allows to reproduce the measured acoustic absorption spectrum. After that, the pore geometry was related to composition and volumetric characteristics of mixes by means of multivariate regression techniques. By this way, the acoustic absorption spectrum of PAC can be predicted as function of specific composition parameters.     

A constitutive model for interface friction

A new adhering-slipping rate constitutive model for interface friction is formulated. The model is fully three-dimensional in nature, but rate-independent, isothermal and isotropic in character. The conditions imposed by the requirement that the interface constitutive model be independent of an observer are carefully examined, and the new consititute model is objective or invariant under a change in observer. An incrementally objective, implicit time-integration procedure for the model is also developed. Although idealized, the model should be useful for a first-order accounting of frictional behavior at dry, unlubricated contacting interfaces in quasistatic deformation processing operations of metallic workpieces with rigid tools.     

A physics-based model to predict micro-pitting lives of lubricated point contacts

This paper proposes a physics-based model to predict the onset of micro-pit formation for lubricated point contacts of rough surfaces. A mixed elastohydrodynamic lubrication model is employed to predict the surface normal and tangential tractions for a stress prediction model to determine the resultant stress histories. The boundary element approach is used in the stress model to fully capture the measured three-dimensional topographies of the contacting rough surfaces, allowing an accurate prediction of the localized stress concentrations that dictate the occurrence of micro-pits. In the process, the method of coordinate transformation and the indirect approach of rigid body motion are devised to eliminate the kernel singularities. A novel numerical procedure is also developed to minimize any Gaussian quadrature numerical error in the integration of the near singular kernels. The fatigue damage is then evaluated employing a multi-axial fatigue criterion. The proposed micro-pitting life prediction methodology is demonstrated using an example ball-on-disk contact problem.     

A continuous damage fracture model to predict formability of sheet metal

A continuous damage fracture model, which consists of a fracture criterion and a continuum damage constitutive law was proposed in this paper to calculate formability of sheet metal. In this model, an extension of the McClintock void growth model was selected as the fracture criterion to be incorporated with a coupled damage‐plasticity Gurson‐type constitutive law. Also, by introducing a Lode angle dependent parameter to define the loading asymmetry condition, the shear effect was phenomenologically taken into account. The proposed fracture model was implemented in user defined material subroutines in ABAQUS. The model was calibrated and correlated by the uniaxial tension, shear and notched specimens tests. Application of the fracture criterion for the Limit dome height tests was discussed and the simulation results were compared with the experimental data.     

A micromechanical model to predict the flow of soft particle glasses

Soft particle glasses form a broad family of materials made of deformable particles, as diverse as microgels, emulsion droplets, star polymers, block copolymer micelles and proteins, which are jammed at volume fractions where they are in contact and interact via soft elastic repulsions. Despite a great variety of particle elasticity, soft glasses have many generic features in common. They behave like weak elastic solids at rest but flow very much like liquids above the yield stress. This unique feature is exploited to process high-performance coatings, solid inks, ceramic pastes, textured food and personal care products. Much of the understanding of these materials at volume fractions relevant in applications is empirical, and a theory connecting macroscopic flow behaviour to microstructure and particle properties remains a formidable challenge. Here we propose a micromechanical three-dimensional model that quantitatively predicts the nonlinear rheology of soft particle glasses. The shear stress and the normal stress differences depend on both the dynamic pair distribution function and the solvent-mediated EHD interactions among the deformed particles. The predictions, which have no adjustable parameters, are successfully validated with experiments on concentrated emulsions and polyelectrolyte microgel pastes, highlighting the universality of the flow properties of soft glasses. These results provide a framework for designing new soft additives with a desired rheological response.     

Nonlinear thermal bending response of FGM plates due to heat conduction

Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves. The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions. The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis.