Linear Material Properties Research Articles

Experimental evaluation of an elastic foundation model to predict contact pressures in knee replacements

Computational wear prediction is an attractive concept for evaluating new total knee replacement designs prior to physical testing and implementation. An important hurdle to such technology is the lack of in vivo contact pressure predictions. To address this issue, this study evaluates a computationally efficient simulation approach that combines the advantages of rigid and deformable body modeling. The hybrid method uses rigid body dynamics to predict body positions and orientations and elastic foundation theory to predict contact pressures between general three-dimensional surfaces. To evaluate the method, we performed static pressure experiments with a commercial knee implant in neutral alignment using flexion angles of 0, 30, 60, and 90° and loads of 750, 1500, 2250, and 3000 N. Using manufacturer CAD geometry for the same implant, an elastic foundation model with linear or nonlinear polyethylene material properties was implemented within a commercial multibody dynamics software program. The model's ability to predict experimental peak and average contact pressures simultaneously was evaluated by performing dynamic simulations to find the static configuration. Both the linear and nonlinear material models predicted the average contact pressure data well, while only the linear material model could simultaneously predict the trends in the peak contact pressure data. This novel modeling approach is sufficiently fast and accurate to be used in design sensitivity and optimization studies of knee implant mechanics and ultimately wear.

Poly(p-phenylenevinylene) derivatives: new promising materials for nonlinear all-optical waveguide switching

Several new derivatives of poly(p-phenylenevinylene) (PPV) are investigated regarding their linear and nonlinear optical material and waveguide properties, including their nonlinear photonic bandgap properties that are induced by photoablated periodic Bragg gratings. The new materials were prepared by means of the polycondensation route, which yields polymers with excellent solubilities and film-forming properties. Comparative data suggest that the new polycondensation-type MEH-PPV (completely soluble, strictly linear and fully conjugated), in particular, is the most promising polymer under investigation to fulfill the requirements for all-optical switching in planar waveguide photonic bandgap structures. UV-photobleaching techniques and photoablation in the UV, VIS, and near-infrared ranges at different pulse durations are investigated. Homogeneous submicrometer gratings that serve as Bragg reflectors have been fabricated in MEH-PPV thin films by application of these methods. The great potential of this type of materials for nonlinear all-optical switching applications that arises from their unique optical properties and their patterning behavior is discussed in detail. Numerical simulations of a switching device based on gap-soliton formation in a nonlinear periodic waveguide structure with the newly obtained material data have been carried out. We show that one can expect photonic bandgap all-optical switching in MEH-PPV planar waveguides. Device performance considering different grating parameters is discussed.

Time-Dependent Circumferential Deformation of Cortical Bone Upon Internal Radial Loading

Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.

Homogenization of linear and of debonding composites using the BEM

A homogenization of microstructure in composites is presented in this paper. Homogenization of composite structures has been solved by many authors, and many numerical methods have been used, particularly when the elastic material behavior of composites was considered. When dealing with linear material properties of such structures, a large background not only in numerical methods but also in mathematical theories are successively developed. A little different situation occurs when in some respect nonlinear material is studied. First, linear problem is solved by the BEM, then we consider possible debond or change of the fiber–matrix interfacial boundary if the debond appears, and both fiber and matrix are elastic. Such a problem is strongly nonlinear. In order to simplify the computations, influence matrices are calculated. Once they are available, Uzawa's algorithm can be applied for solving the debonding process.

Wall Stress Studies of Abdominal Aortic Aneurysm in a Clinical Model

To estimate when an abdominal aortic aneurysm (AAA) may rupture, it is necessary to understand the forces responsible for this event. We investigated the wall stresses in an AAA in a clinical model. Using CT scans of the AAA, the diameter and wall thickness were measured and the model of the aneurysm was created. The wall stresses were determined using a finite element analysis in which the aorta was considered isotropic with linear material properties and was loaded with a pressure of 120 mmHg. The AAA was eccentric with a length of 10.5 cm, a diameter of 2.5 to 5.9 cm, and a wall thickness of 1.0 to 2.0 mm. The aneurysm had specific areas of high stress. On the inner surface the highest stress was 0.4 N/mm2 and occurred along two circumferentially oriented belts--one at the bulb and the other just below. The stress was longitudinal at the anterior region of the bulb and circumferential elsewhere, suggesting that a rupture caused by this stress will result in a circumferential tear at the anterior portion of the bulb and a longitudinal tear elsewhere. In the mid-surface the highest stress was 0.37 N/mm2 and occurred at two locations: the posterior region of the bulb and anteriorly just below. The stress was circumferential, suggesting that the rupture caused by this stress will produce a longitudinal tear. The location and orientation of the maximum stress were influenced more by the tethering force than by the wall thickness, luminal pressure, or wall stiffness. In conclusion, the rupture of an AAA is most likely to occur on the inner surface at the bulb. Such analytical approaches could lead to a better understanding of the aneurysm rupture and may be instrumental in planning surgical interventions.

Nonlinear Coupled Seismic Sliding Analysis of Earth Structures

Earthquake-induced sliding displacements of earth structures are generally evaluated using simplified sliding block analyses that do not accurately model the seismic response of the sliding mass nor the seismic forces along the slide plane. The decoupled approximation introduced to capture each of these effects separately is generally believed to be conservative. However, recent studies using linear viscoelastic sliding mass models have revealed instances where the decoupled approximation is unconservative. In this paper, a coupled analytical model that captures simultaneously the fully nonlinear response of the sliding mass (necessary for intense motions) and the nonlinear stick-slip sliding response along the slide plane is presented. The proposed sliding model is validated against shaking table experiments of deformable soil columns sliding down an inclined plane. The effect of sliding on the response of earth structures is evaluated, and comparisons are made between sliding displacements calculated using coupled and decoupled analytical procedures with linear and nonlinear material properties. Nonlinearity resulting from stick-slip episodes is often the dominant source of nonlinearity in this problem. The decoupled approximation was unconservative primarily for intense ground motions for systems with low values of ky, larger values of ky/kmax, and high period ratios (Ts/Tm). Results indicate that a decoupled analysis is adequate for earth structures that are not expected to experience intense, near-fault motions. However, for projects undergoing intense, near-fault ground motions, a fully nonlinear, coupled stick-slip analysis is recommended.

Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient

The nature of the singular field around the crack in functionally graded material (FGM) is analyzed parametrically using finite element method. The numerical simulations are carried out by varying the location of the crack in the graded region for different material gradients. Using linear material property variation in the gradient zone, the influence of material gradient and the crack position on the fracture parameters such as complex stress intensity factor (SIF) and energy release rate are studied. The crack opening displacement profiles of FGM are compared with the homogeneous and bimaterial counterparts. The analysis shows that the fracture parameters of FGM approach that of the bimaterial as the material gradient is increased, regardless of the position of the crack in the graded region. The extent of applicability of the homogenous crack tip fields around the crack in FGM is analyzed, and the results show that the size of the homogeneous field reduces with the increase in material gradient. Static fracture experiments are conducted on epoxy based FGM to determine complex SIF with electrical strain gages, using the homogeneous field equations to convert the strains to SIF. The measured SIF values compare favorably with the numerical results providing a limited experimental validation of the computations and the use of homogeneous field for FGM.

Interstitial fluid pressurization during confined compression cyclical loading of articular cartilage.

The objective of this study was to experimentally verify the well-accepted but untested hypothesis that cartilage interstitial fluid pressurizes variously under the action of an applied cyclical stress in confined compression over a range of loading frequencies, contributing significantly to the cartilage dynamic stiffness. Eighteen bovine cartilage cylindrical samples were tested under load control using a porous indenter in a confined compression chamber fitted with a microchip pressure transducer at its bottom. Over a static stress of 130 kPa, a cyclical stress of amplitude 33 kPa was applied with the indenter at frequencies ranging from 0.0001 to 0.1 Hz. The cartilage interstitial fluid pressure and deformation were measured simultaneously as a function of time. The displacement response at the lowest tested frequency was curvefitted in the time domain to determine the linear biphasic material properties, H(A) = 0.70+/-0.10 MPa and k0=2.4x10(-16)+/-0.64x10(-16) m4/N s. These properties were employed in the biphasic theory to predict the interstitial fluid pressure response and compare it to experiment, resulting in nonlinear coefficients of determination ranging from r2 = 0.89+/-0.15 to 0.96+/-0.03 depending on frequency. It was found for the samples of this study that above a characteristic frequency of 0.00044 Hz, the magnitude and phase of fluid pressurization matched the applied stress, reducing the tissue strain at the impermeable bottom surface to nearly zero. The findings of this study verify the hypothesis that cartilage dynamic stiffness derives primarily from flow-dependent viscoelasticity as predicted by the linear biphasic theory; they demonstrate experimentally the significance of interstitial fluid pressurization as the fundamental mechanism of cartilage load support over a wide range of frequencies.

Establishing Linear Viscoelastic Conditions for Asphalt Binders

The linear viscoelastic regime is defined in terms of the constitutive relationship between the stress and the strain. The set of equations that define the fundamental linear viscoelastic material properties in the time and frequency domains and their relationship to one another is based on the validity of the linearity principle. A material must obey two simultaneous conditions to be linear viscoelastic: the homogeneity (also called proportionality) condition and the superposition principle. On the basis of these considerations a testing procedure was developed to check linear viscoelastic conditions for tests performed on asphalt binders with the dynamic shear rheometer (DSR), the bending beam rheometer (BBR), and direct tension (DT). The testing procedure for the DSR requires performing strain sweeps and multiwave single-point tests. For the BBR, tests performed using different constant loads are required. In addition, the recovery part of the specification test is recorded. For the DT, tests performed at different strain rates and relaxation tests performed at different strain levels are required. When applied to asphalt binder data, the testing procedure found no departure from viscoelastic conditions for the DSR and BBR test data. However, the DT procedure indicated a departure from linear viscoelastic conditions.

A boundary element formulation using higher order curvilinear edge elements

A boundary element method in terms of the field variable is applied to three-dimensional magnetostatic problems. We propose higher order edge elements of quadrilateral shape for the field approximation on curved surfaces. The tangential component of the unknown field variable is interpolated by the edge element. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by TEAM Workshop problem 13 assuming linear material properties.

A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques

This paper presents an original three dimensional (3D) analytical general solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar and its applications to some experimental methods of material behaviour testing to improve their accuracy. One application is to take into account the wave dispersion effects in the split Hopkinson pressure bar (SHPB) setup composed of viscoelastic bars. Another is to eliminate the geometrical effects in an impulse test in which the linear viscoelastic material properties can be deduced from the change in the wave shape due to the propagation between two points of measurement in a specimen bar.

Evolution of the molecular weight distribution and linear viscoelastic rheological properties during the reactive extrusion of polypropylene

AbstractHomogeneous and nonhomogeneous reactive extrusion of polypropylene is modeled using random chain scission statistics coupled with the double reptation mixing rule. In this manner, the evolution of both the molecular weight distribution and the linear viscoelastic material properties is quantitatively predicted for the reactive extrusion–pelletization process. Dispersion in the level of random chain scission has little impact on the MFI for a given average level of chain scission; however, dispersion does generate a marked increase in the recoverable compliance (melt elasticity) relative to the ideal homogeneous random chain scission case. Methods to quantitatively determine the degree of cracking dispersion in processing equipment are identified. Quality control issues such as blending materials of known linear viscoelastic properties to obtain a desired property set is considered in the context of known empirical relations consistent with the double reptation model. Simple mixing rules for the melt flow index and the steady‐state recoverable compliance involving only single component MFI and Je information are derived. © 1995 John Wiley & Sons, Inc.

3D coupled electromagnetic and structural finite element analysis of motional eddy current problems

A finite element technique is described that fully couples structural and electromagnetic analysis in the time domain. One finite element model,with both linear and nonlinear structural and electromagnetic material properties, is solved in two or three dimensions. Displacements computed versus time for the TEAM12 eddy current 3D problem and for a nonlinear axisymmetric solenoid are shown to agree closely with measurements. >

Material Damping Analysis of a Smart Hybrid Composite Lamina

This paper addresses an analytical approach to evaluate the inherent material Specific Damping Capacity (SDC) of a smart hybrid fiber reinforced polymer composite lamina. Analytical equations for the material specific damping capacity have been derived by assuming a linear viscoelastic material property for the constituent fiber-matrix system. The damping properties corresponding to all the six in-plane and out-of-plane applied stresses were considered. Numerical studies are carried out by considering examples for which results are available in the literature. In order to demonstrate the versatility of the present method, the damping analysis of a typical shape memory alloy fiber reinforced hybrid composite lamina has also been made.

Effects of the superposition of compaction and tectonic strain during folding of a multilayer sequence—model and observations

Sedimentary rocks deformed at shallow crustal depth can show a wide variety of planar, linear and mixed planar-linear fabrics depending on their structural position within folds. A model has been developed which tries to explain this variation in fabric development in terms of the strain states that it represents. We analyse the finite strain states that may develop during compaction and subsequent buckle folding of sedimentary multilayers composed of a regular alternation of competent and incompetent beds. The geometric properties of the multilayer during buckling have been analysed from a finite element model characterized by: linear viscous material properties, a viscosity contrast μ 1/ μ 2 = 40, and a ratio of incompetent to competent layer thickness d 2/ d 1 = 1. Sequential matrix multiplication allows the determination of the finite strain states for all stages of fold development. Finite strain states predicted from the model appear to be in good agreement with observations of fabric development in naturally deformed rocks from the Southern Apennines. During progressive deformation in the model, the finite strain ellipsoid in the limb regions of folded incompetent layers is consistently oblate, and the XY plane lies at a small angle to bedding as a consequence of previous compaction. Natural cleavage consistently lies at a low angle to bedding in folded argillites from the Southern Apennines and it can be interpreted to represent the XY plane of the total finite strain ellipsoid in strongly compacted sediments, and not that of tectonic deformation alone. In the hinge regions of open folds, finite strains predicted in the incompetent layers of the model are of prolate type, and they become oblate as the interlimb angle decreases; the presence of a ‘true’ pencil structure in open folds and of a spaced cleavage associated with a ‘regular’ pencil structure in more close folds, often noted in the case study of the Southern Apennines, most probably reflects this change from prolate to oblate strain in the hinge zones as folding proceeds.

On Interface Crack Growth in Composite Plates

Analysis of fracture growth, and in particular at interfaces, is pertinent not only to load-carrying members in composite structures but also as regards, e.g., adhesive joints, thin films, and coatings. Ordinarily linear fracture mechanics then constitutes the common tool to solve two-dimensional problems occasionally based on beam theory. In the present more general effort, an analysis is first carried out for determination of the energy release rate at general loading of multilayered plates with local crack advance either at interfaces or parallel to such. The procedure is accomplished for arbitrary hyperelastic material properties within von Karman plate theory and the results are expressed by aid of an Eshelby energy momentum tensor. By a feasible superposition it is then shown that the original nonlinear plate problem may be reduced to that of an equivalent beam in case of linear material properties. As a consequence of the so-established principle, the magnitude of mode-dependent singular stress amplitude factors is then directly determinable from earlier two-dimensional linear beam solutions for isotropic and anisotropic bimaterials and relevant at determination of cohesive and adhesive fracture. The procedure is illustrated by an analysis of combined buckling and crack growth of a delaminated plate having a nontrivial crack contour.

Linear viscoelastic analysis with random material properties

Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic processes caused by random linear viscoelastic material properties. Separation of variable as well as integral transform correspondence principles are formulated and discussed in detail. The statistical differential equation of the moment characteristic functional is derived, but rather than solving the highly complex functional equation, solutions are formulated in terms of first and second order statistical properties. Both Gaussian and beta distributions are considered for the probability density distributions of creep and relaxation functions and their effectiveness is evaluated. In order to illustrate the developed general theory, specific examples of beam bending and pressurized hollow cylinders are solved. The influence of various parameters contributing to the creep and relaxation correlation functions is evaluated and the relationship between deterministic and stochastic bounds is also investigated. It is shown that deterministic bounds based on material data spread are unrealistic in the presence of random viscoelastic properties, since the do not correctly predict the limits of this stochastic process.

Micromechanical modeling of powder compacts—I. Unit problems for sintering and traction induced deformation

A micromechanical model has been developed for the constitutive behavior of powder compacts based on unit models for the interaction between individual particles. In this paper, the first of two companion papers, two unit problems have been formulated for the study of inter-particle behavior. These correspond to the cases of deformation by external tractions and local surface tension forces. The contact area between individual particles is used to characterize the state of the powder compact. Specific numerical results are presented for linear viscous material properties and are compared with existing models. The choice of unit problems for sintering has been discussed at length and some ambiguities in the traditional method of modeling viscous sintering are pointed out. The results of this study are used in the companion paper [ Acta metall. 36, 2563 (1988)] to develop a model for the sintering and compaction of discrete packings.

Coupled Heat and Moisture Flow Through Soils

A method for numerically modeling the transient coupled heat and moisture flow in a multi‐dimensional soil domain subjected to time‐dependent heat and moisture generation is presented. The computer program, TRUCHAM, which is based on the Philip and DeVries model for flow in soils, utilizes an integrated finite difference procedure. The technique accommodates different types of linear and nonlinear boundary conditions and material properties. Validation of the program has been made with data from exact solutions, controlled laboratory experiments and field tests. This program will be useful in solving many heat and mass transport problems encountered in the field of underground power cables, heat storage and nuclear waste disposal programs.

The Theory of One-Dimensional Consolidation of Saturated Clays: III. Existing Testing Procedures and Analyses

Abstract The successful calculation of the progress of consolidation requires that both the theory used to model the field problem and the material properties used by the theory must be appropriate and suitable. Thus the testing procedure must provide reliable and consistent information on the material behavior. Further, the test procedure must be accompanied by methods of analysis that will produce values of the material properties that are appropriate to the theory. This paper presents a summary of the existing laboratory methods that are used to determine the consolidation properties of soils. Emphasis is placed on the analysis of the test data. It is shown that all the methods that are currently used contain inherent simplifying assumptions. These methods are restricted in their applicability to problems where linear or constant material properties or both are good approximations to real behavior.