Linear Viscoelastic Constitutive Model Research Articles

Linear orthotropic viscoelasticity model for fiber reinforced thermoplastic material based on Prony series

Material properties description and understanding are essential aspects when computational solid mechanics is applied to product development. In order to promote injected fiber reinforced thermoplastic materials for structural applications, it is very relevant to develop material characterization procedures, considering mechanical properties variation in terms of fiber orientation and loading time. Therefore, a methodology considering sample manufacturing, mechanical tests and data treatment is described in this study. The mathematical representation of the material properties was solved by a linear viscoelastic constitutive model described by Prony series, which was properly adapted to orthotropic materials. Due to the large number of proposed constitutive model coefficients, a parameter identification method was employed to define mathematical functions. This procedure promoted good correlation among experimental tests, and analytical and numerical creep models. Such results encourage the use of numerical simulations for the development of structural components with the proposed linear viscoelastic orthotropic constitutive model. A case study was presented to illustrate an industrial application of proposed methodology.

Comparison of solid and fluid constitutive models of bone marrow during trabecular bone compression

The mechanical environment and mechanobiology of bone marrow may play essential roles in bone adaptation, cancer metastasis, and immune cell regulation. However, the location of marrow within the trabecular pore space complicates experimental measurement of marrow mechanics. Computational models provide a means to assess the shear stress and pressure in the marrow during physiological loading, but they rely on accurate inputs for the marrow and the physics assumed for the interaction of bone and marrow. Elastic, viscoelastic, and fluid constitutive properties have all been reported from experimental measurements of marrow properties. It is unclear whether this ambiguity reflects the various length-scales, loading rates, and boundary conditions of the experiments, or if the material models are sufficiently similar as to be interchangeable. To address this question, we analyzed both the mean shear stress and its spatial distribution induced in marrow during compression of trabecular bone cubes when using linear elastic, neo-Hookean, viscoelastic, and power-law fluid constitutive models. Experimentally reported parameters were initially applied for all four constitutive models, resulting in poor agreement. The parameters of the soft solid models were calibrated by linear interpolation so that the volume averaged shear stress agreed with the fluid model for each, but this could only be accomplished on a specimen-by-specimen basis. Following calibration, the root-mean-squared (RMS) difference between the solid and fluid constitutive models was still greater than 26% even when the overall mean shear stress was in close agreement, indicating that the spatial distribution of stress is also sensitive to the constitutive model. As such, the choice of constitutive model should be backed by a strong rationale, and results should be interpreted with care.

Finite Element Analysis of DSSI Effects for a Building of Strategic Importance in Catania (Italy)

Structural response to earthquakes has to be definitely considered a multidisciplinary subject, depending on many factors among which local site effects and dynamic interaction between soil, foundations and structures. The present paper deals with the multidisciplinary Dynamic Soil Structure Interaction (DSSI) analysis concerning the INGV building in Catania (Italy) by means of FEM 2D modelling. The building is a masonry structure situated in an area characterized by a high seismic hazard. The dynamic analysis was performed by adopting seven different accelerograms, scaled at the same PHA with reference to the estimated seismicity of the investigated area. Linear visco-elastic constitutive models were adopted for both the soil and the structure; nevertheless, soil non-linearity is taken into account according to EC8, adopting degraded shear modulus and increased damping ratio. The dynamic response of the system was analysed in the time and frequency domains. The main goals of the paper are: i) to investigate the amplification input effects, considering and not considering the DSSI; ii) to highlight the influence of soil layer variation in the coupled system response; iii) to compare the obtained results with the ones given by simpler 1D free-field soil analyses; iv) to compare the acceleration spectra obtained by 1D and 2D analyses with those provided by Italian technical code, NTC08. The performed analyses show the influence of DSSI in the seismic response of the system in terms of PHA and frequency contents.

Effects of the Variation in Brain Tissue Mechanical Properties on the Intracranial Response of a 6-Year-Old Child.

Brain tissue mechanical properties are of importance to investigate child head injury using finite element (FE) method. However, these properties used in child head FE model normally vary in a large range in published literatures because of the insufficient child cadaver experiments. In this work, a head FE model with detailed anatomical structures is developed from the computed tomography (CT) data of a 6-year-old healthy child head. The effects of brain tissue mechanical properties on traumatic brain response are also analyzed by reconstruction of a head impact on engine hood according to Euro-NCAP testing regulation using FE method. The result showed that the variations of brain tissue mechanical parameters in linear viscoelastic constitutive model had different influences on the intracranial response. Furthermore, the opposite trend was obtained in the predicted shear stress and shear strain of brain tissues caused by the variations of mentioned parameters.

Combined primary–secondary system approach to the design of an equipment isolation system with High-Damping Rubber Bearings

Isolating acceleration-sensitive equipment from the motion of the supporting structure represents an effective protection from earthquake damage. In this paper, a passive equipment isolation system composed of High-Damping Rubber Bearings (HDRB) is designed by adopting a coupled approach in which the supporting structure and the isolated equipment are considered as parts of a combined primary–secondary system and analyzed together. This allows for taking into account their dynamic interaction when significant and non-negligible according to the mass ratio and to the frequency ratio. The design methodology is developed by resorting to a reduced-order 2-DOF model of the combined system, a linear visco-elastic constitutive model of the isolation system and to a modal damping constraint depending upon the damping properties of the HDRB and their rubber compound. A 1:5 scale experimental model, consisting of a two-storey steel frame and a heavy block-type mass isolated from the second floor, is subsequently used to exemplify the design methodology and to perform shaking table tests. The dynamic properties of the experimental model are identified and the seismic performance of the equipment isolation system is discussed under a wide selection of seismic inputs, both artificial and natural.

Folding, Stowage, and Deployment of Viscoelastic Tape Springs

This paper presents an experimental and numerical study of the folding, stowage, and deployment behavior of viscoelastic tape springs. Experiments show that during folding the relationship between load and displacement is nonlinear and varies with rate and temperature. In particular, the limit and propagation loads increase with the folding rate but decrease with temperature. During stowage, relaxation behavior leads to a reduction in internal forces that significantly impacts the subsequent deployment dynamics. The deployment behavior starts with a short, dynamic transient that is followed by a steady deployment and ends with a slow creep recovery. Unlike elastic tape springs, localized folds in viscoelastic tape springs do not move during deployment. Finite-element simulations based on a linear viscoelastic constitutive model with an experimentally determined relaxation modulus are shown to accurately reproduce the experimentally observed behavior, and to capture the effects of geometric nonlinearity, time and temperature dependence.

Measuring Cell Mechanics by Optical Alignment Deformation Spectroscopy

Cell mechanical properties are a useful measure of phenotype that can be quantified by cell deformability. There is a lack of high-throughput methods to investigate the mechanical properties of large populations of individual cells. To address this need, we developed optical alignment deformation spectroscopy (OADS), a technique where hydrodynamic interactions between individual cells are used to create deformation. In OADS, a linear optical trap is used to align two incoming cells in a microfluidic cross-flow geometry, allowing hydrodynamic forces to induce a collision between cells at the stagnation point (see figure). After the interaction, the cells leave the stagnation point and a new pair of cells enters the trap. A convenient model cell to characterize OADS is the human erythrocyte because of its well-known mechanical properties. We fit deformation data of erythrocytes to a linear viscoelastic constitutive model (Voigt). This model incorporates a spring and dashpot in parallel, for the elastic (k) and viscous (η) parameters of the cell, respectively. Our measured values of k = 14.5 μN/m and η = 4.9 μN∗s/m compare favorably with literature values. Our results show OADS has potential as an accurate high-throughput individual cell mechanical cytometer.View Large Image | View Hi-Res Image | Download PowerPoint Slide

The Secondary Development of Nonlinear Viscoelastic Constitutive Model Based on ABAQUS

Based on the subroutine VUMAT, user-defined material model in the nonlinear finite element software ABAQUS/EXPLICIT, a nonlinear viscoelastic constitutive model is developed. The validify of the subroutine has been proven through the standard uniaxial tensile model. The shortage of finite element softwares which only have linear viscoelastic constitutive model is remedied. This paper presents the process of developing a material constitutive model and some useful technology. It can be referred for extending the material constitutive model in finite element softwares.

The Mechanical Properties of Caladium Petiole

Abstract: In this study, the mechanical properties of Caladium (Caladium × hortulanun Birdsey) petiole were investigated. The petiole was considered as a composite beam which consists of rind and core parts. To classify the mechanical properties of rind and core part of petioles, two‐phase three‐point bending tests were conducted on the specimens cut from petioles. Linear beam theory was used to convert the time‐dependent bending forces, during the three‐point bending tests, to relaxation moduli. The result shows that the mechanical properties of rind and core parts of Caladium are very different. The relaxation modulus of rind is approximate 40 times higher than relaxation modulus of core at time = 600 s after applying bending load, and the relaxation time distribution of core is wider than the relaxation time distribution of core. The three‐ and seven‐parameter linear viscoelastic constitutive models were used to describe the time‐dependent relaxation moduli of rind and core of caladium petiole. The fitted results show that the seven‐parameter Wiechert model can describe the viscoelastic behaviour of Caladium petiole very well. The finite element analysis was used to assess the error of this test methodology. The reaction force error because of the tapered diameter of specimens is about 12%.

On the large deflections of linear viscoelastic beams

The quasi-static response and the stored and dissipated energies due to large deflections of a slender inextensible beam made of a linear viscoelastic material and subjected to a time-dependent inclined concentrated load at the free end are investigated. The beam cross-section is considered prismatic, the self-weight is disregarded and the material is initially stress free. The set of four first-order non-linear partial integro-differential equations obtained from geometrical compatibility, equilibrium of forces and moments, and linear viscoelastic constitutive relation is numerically solved using a one-parameter shooting method combined with a fourth-order Runge–Kutta algorithm. An analytical expression is derived to divide the energy supplied by the external load into conserved and dissipated parts. For the case study presented, a three-parameter solid linear viscoelastic constitutive model is employed and a step load is applied. The variables are made non-dimensional, so four parameters govern the problem: the ratio between the final and initial relaxation moduli, the load magnitude, the angle of inclination and the unloading time. A finite-element model is also performed to compare and validate the analytical and numerical formulations. Results are presented for encastré curvature and tip displacement versus time, geometrical configuration, load versus tip displacement, total work done by the external force, stored and dissipated energies versus time, energy per unit length along arc length for three times and versus time for two beam sections.

Modelling of length scale effects in viscoelastic materials

A length scale dependent linear viscoelastic constitutive model is developed. First, a generalized Maxwell model that can describe standard linear viscoelasticity is considered. The model is then generalized to include effects of viscous strain gradients. The formulation of additional boundary conditions resulting from the strain gradient terms is discussed. It is shown that the boundary conditions can be formulated in terms of a surface energy. As an example, the thermal expansion of a thin polymeric film on an elastic substrate is analyzed. It is shown that the relative thermal expansion in the thickness direction of the film decreases for sufficiently small film thicknesses, in accordance with experimental observations. This effect cannot be captured by a standard thermo-viscoelastic theory, which gives a constant thermal expansion independent of film thickness.

A Numerical Model for Risk of Ball-Impact Injury to Baseball Pitchers

Metal baseball bats produce higher ball exit velocity (BEV) than wood bats, increasing the risk of impact injuries to infield players. In this paper, maximum BEV from a wood and a metal bat were determined using the finite element method. Three-dimensional (3-D) bat kinematics at the instant of impact were determined from high-speed videography (N = 17 high-performance batters). A linear viscoelastic constitutive model was developed for stiffer and softer types of baseballs. The risk of impact injury was determined using available movement time data for adult pitchers; the data indicate that 0.400 s is required to evade a batted ball. The highest BEV (61.5 m.s(-1)) was obtained from the metal bat and the stiffer ball model, equating to 0.282 s of available movement time. For five impacts along the long axis of each bat, the "best case scenario" resulted from the wood bat and the softer ball (46.0 m.s(-1), 0.377 s). The performance difference between the bats was attributed to the preimpact linear velocity of the bat impact point and to differences in orientation on the horizontal plane. Reducing the swing moment of the baseball bat, and the shear and relaxation modulii of the baseball, increased the available movement time.

An experimental investigation of normal and shear stress interaction of an epoxy resin and model predictions

AbstractThe axial‐torsional interaction of an epoxy resin was investigated by subjecting thin‐walled tubular specimens to combined normal and shear stress components. It is shown that a superimposed normal stress (tensile or compressive) or hydrostatic pressure will influence shear creep behavior. Similarly, a superposed shear stress affects the normal stress response of the resin. The axial‐torsional stress interaction is also observed in transient stress responses under different strain paths, and in the creep deformation with non‐proportional stress histories. Urear viscoelastic constitutive models are unable to predict the aforementioned behaviors. Two typical nonlinear viscoelastic constitutive models are examined with respect to their capabilities to predict the observed response. It Is shown that the predictions of these two models agree only qualitatively but not quantitatively with the experimental results.

Identification of linear viscoelastic constitutive models

Accelerations induce in the brain mechanical stresses that may explain the loss of consciousness feared by fighter pilots. In this study, the brain is modelled as a multi-domain structure and a finite element method is used to identify the constitutive law parameters of each domain and then to analyse the stress level in the brain. The loading and observed strain rates induced by hypergravity seem to indicate a quasi-static behaviour of the brain structure. A general procedure has been developed to characterise the behaviour of a structure including several domains. Each of them is assumed to be isotropic and homogeneous with a linear viscoelastic behaviour. These constitutive laws were identified using only the displacements of several nodes on the envelope discarding the displacements between domains at the interaction surfaces. These interfaces may be buried inside the structure and not connected with the external surface. Two validation examples are proposed to show the reliability and effectiveness of the method.

Time-Dependent Behaviour and Viscoelastic Constitutive Modelling of an Epoxy Polymer

The time-dependent behaviour of a cold cure epoxy polymer was investigated by different types of tests including compression, tension, biaxial loading, strain recovery, stress relaxation, creep and cyclic creep. This epoxy showed nonlinear viscoelastic behaviour since strains were fully recovered after stresses were removed and sufficient time was allowed for the recovery. A linear viscoelastic constitutive model has been extended to the nonlinear regime, and used to simulate the test results. It was found that the model is capable of predicting the observed trends for different types of tests. With one set of specified material constants, the model provides a fairly good prediction for several types of tests. However, this trend may not hold for other types of tests, for which the material constants were not calibrated, although the general trend would be predicted satisfactorily.

Time-Dependent Behaviour and Viscoelastic Constitutive Modelling of an Epoxy Polymer

The time-dependent behaviour of a cold cure epoxy polymer was investigated by different types of tests including compression, tension, biaxial loading, strain recovery, stress relaxation, creep and cyclic creep. This epoxy showed nonlinear viscoelastic behaviour since strains were fully recovered after stresses were removed and sufficient time was allowed for the recovery. A linear viscoelastic constitutive model has been extended to the nonlinear regime, and used to simulate the test results. It was found that the model is capable of predicting the observed trends for different types of tests. With one set of specified material constants, the model provides a fairly good prediction for several types of tests. However, this trend may not hold for other types of tests, for which the material constants were not calibrated, although the general trend would be predicted satisfactorily.