Elastic Solid Model Research Articles

Repair of Internal and External Circular Failures Using Winding Technology

The first part of the paper deals with the FEM computation of deformations, stresses and strain in the surrounding area of internal and external circular artificial failures with a set of given geometrical dimensions in steel pipelines. For the investigation of this problem three groups of mechanical models are applied: multilayered elastic shell, 3D elastic solid and 3D elastic-plastic solid FEM models. The aim of this analysis is to clarify the case in which the pipeline fails. When a pipe fails and needs repair or reinforcement, this is called critical case. In the second part of the paper the repaired pipes are investigated. For repairing of the internal and external failures, internal or external multilayered textile composite reinforcements are applied by winding technology. The task is to determine the width of the reinforcement and the number of layers needed for repair. The different mechanical models (multilayered elastic shell, 3D elastic solid and 3D elasto-plastic solid) are compared on the basis of numerical results. The critical cases are determined and the questions of repair are answered also numerically.

유체-구조 상호연성 해석을 위한 입자법 시뮬레이션 기술 개발

Recently, some fluid-structure interaction (FSI) problems involving the fluid impact loads interacting with structures, such as sloshing, slamming, green-water, etc., have been considered, especially in the ocean engineering field. The governing equations for both an elastic solid model and flow model were originally derived from similar continuum mechanics principles. In this study, an elastic model based on a particle method, the MPS method, was developed for simulating the FSI problems. The developed model was first applied to a simple cantilever deflection problem for verification. Then, the model was coupled with the fluid flow model, the PNU (Pusan National University modified)-MPS method, and applied to the numerical investigation of the coupling effects between a cantilever and a mass of water, which has variable density, free-falling to the end of the cantilever.

Second order asymptotics for the propagation speed of interfaces in the Allen‐Cahn phase field model for elastic solids

AbstractFor a phase field model, which consists of the elasticity equations coupled to the Allen‐Cahn equation, we state an asymptotic expansion for the propagation speed of the diffusive interface. The error of the expansion is of order η2, where η is the width of the interface. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ultrasonic evaluation of the hydration degree of the orange peel

The elastic parameters of fruit and vegetables are normally monitored in quality control processes as there is a good correlation to the degrees of firmness, turgidity and humidity. These parameters have been traditionally measured by means of penetration tests, which are destructive. This has resulted in the increased attention recently given to ultrasonic techniques applied to the quality evaluation of horticultural commodities. Nevertheless, since most of the fruit and vegetables display a viscoelastic behavior, the penetration test should be considered to be quasi-static, especially when compared with the speeds associated with the ultrasonic tests. Both methods should provide different values for the elastic parameters. The aim of this work is to study this discrepancy in the values of the elastic parameters and interpret the elastodynamic behavior of the vegetable tissue under an ultrasound test. Thus, the paper presents an ultrasonic nondestructive method to evaluate the elastic parameters of the sweet orange peel at 40kHz. The complete dehydration process of two sets of oranges (Navelina and Ortanique) was monitored for 2months. A linear elastic solid model with viscous losses was numerically solved using a simulation scheme based on a 3D-Spherical FDTD method (Finite-Difference Time-Domain) in order to interpret the results, which proved that the elastic parameters obtained by penetration and ultrasonic tests differ. The method provides an empirical relation between the hydration state and the elastic parameters of the orange peel. Therefore, the proposed ultrasonic test reported in this work is capable of determining the hydration state of the orange simply by measuring the propagation speed of the Rayleigh waves on the orange peel, and hence, can be used as a fruit quality index during postharvest processes.

Modeling of Brain Shift Phenomenon for Different Craniotomies and Solid Models

This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden models, and hyperelastic Mooney‐Rivlin with 2‐ and 5‐parameter models. A pressure on the brain surface at craniotomy region was applied to load the model. The models were solved with the finite elements package ANSYS. The predictions on stress and displacements were compared for three different craniotomies. The difference between the predictions of elastic solid model and a hyperelastic Ogden solid model of maximum brain displacement and maximum effective stress is relevant.

Continuum modeling of a composite material with internal resonators

Two continuum methods were investigated for modeling the dynamic behavior of an acoustic metamaterial in the form of a composite material with internal resonators. First, an effective homogeneous classical continuum model was proposed. The effective elastic constants for this continuum are obtained by taking the static equivalence between the continuum and the composite, while the effective mass density adopts the form of a second order tensor. The second model is also a continuum model that is described by two displacement variables. In addition to the usual displacement vector, a displacement vector for the motion of the resonator mass is included, thus making this multi-displacement model quite different from the classical model for elastic solids. It was shown that the dispersion relations predicted by the proposed two approaches were practically the same. The accuracy of the dispersion curves was verified by finite element analyses. Simplicity is the main advantage of the first approach. However, it has to adopt an unusual frequency-dependent effective mass density which may become negative in certain frequency range. On the other hand, the multi-displacement model can be constructed based on the actual material properties of the composite and, in general, is more versatile for further extensions to complex microstructures.

The influence of the cohesive process zone in hydraulic fracturing modelling

This paper studies the importance of the cohesive zone in the modelling of a fluid driven fracture under plain strain conditions. The fracture is driven by pumping of an incompressible viscous fluid at the fracture inlet. Rock deformation is modeled for linear elastic and poroelastic solids. Fluid flow in the fracture is modeled by lubrication theory. The cohesive zone approach is used as the fracture propagation criterion. Finite element analysis was used to compute the solution for the crack length, the fracture opening and propagation pressure as a function of the time and distance from the wellbore. It is demonstrated that the crack profiles and the propagation pressures are larger in the case of elastic-softening cohesive model compared to the results of the rigid-softening cohesive model for both elastic and poroelastic cohesive solids. It is found that the results are affected by the slope of the loading branch of the cohesive model and they are nearly unaffected from the exact form of the softening branch. Furthermore, the size of the process zone, the fracture geometry and the propagation pressure increase with increasing confining stresses. These results may explain partially the discrepancies in net-pressures between field measurements and conventional model predictions.

Experimental and numerical investigations of external reinforced damaged pipelines

The lifetime management of different engineering structures and structural elements is one of the important technical-economic problems nowadays. The purpose of the paper is to present the role of the external reinforcing on the structural integrity of industrial and transporting steel pipelines, based on experimental and numerical investigations. External reinforcement was developed using carbon fibre polymer matrix composite (PMC). Fatigue and burst tests were performed on pipeline sections containing natural and artificial metal loss defects, and girth welds including weld defects (passed and not passed quality). Both unreinforced and reinforced pipeline sections were examined. For the FEM investigation of the problem three groups of mechanical models are applied: multilayered elastic shell, 3D elastic solid and 3D elastic-plastic solid FEM models. The aim of this numerical analysis is to clarify the deformation, stresses and strains in the surrounding area of defects both in the steel pipe and in the composite reinforcement. A further task is to determine numerically the width of the reinforcement and the number of layers needed for reinforcement or repair. The applicability of the hybrid structure (steel + PMC) was demonstrated by means of the experimental and the numerical results.

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.

Relativistic mechanics of neutron superfluid in (magneto)elastic star crust

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure.

Macroscale constitutive modeling of kinking nonlinear elastic solids

A large class of solids has recently been identified as kinking nonlinear elastic (KNE) solids because they deform predominantly by the formation of dislocation-based, incipient and regular kink bands [M.W. Barsoum, A. Murugaiah, S.R. Kalidindi, T. Zhen, Phys. Rev. Lett. 92 (2004) 255508 1–4; M.W. Barsoum, T. Zhen, A. Zhou, S. Basu, S.R. Kalidindi, Phys. Rev. B (2005) 134101 1–8]. The incipient kink bands are fully reversible and have been shown to be the hysteretic mesoscopic units invoked to explain the nonlinear elastic deformation in rocks. In this paper, we present a theoretical framework to model the macroscale aspects of the nonlinear elastic behavior of KNE solids in a uniaxial stress state. The theory assumes that the probability of kinking is given by Weibull statistics. Despite its simplicity, the model captures reasonably well the fully reversible, hysteretic, rate-independent, and discrete memory aspects of the macroscale behavior of KNE solids in the nonlinear elastic regime.

Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust

This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.

Multi-scale goal-oriented adaptive modeling of random heterogeneous materials

This paper addresses the general problem of modeling local features of the response of highly heterogeneous elastic materials with random distributions of the material constituents. The theory and methodologies of goal-oriented adaptive modeling of heterogeneous materials [Oden, J.T., Vemaganti, K., 2000a. Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. Part I: Error estimates and adaptive algorithms. J. Comp. Phys. 164, 22–47; Oden, J.T., Vemaganti, K., 2000b. Adaptive modeling of composite structures: modeling error estimation. Int. J. Comput. Civil Str. Eng. 1, 1–16; Vemaganti, K., Oden, J.T., 2001. Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. Part II: A computational environment for adaptive modeling of heterogeneous elastic solids. Comput. Methods Appl. Mech. Eng. 190, 6089–6124; Romkes, A., Vemaganti, K., Oden, J.T., 2004. The extension of the GOALS algorithm to the analysis of elastostatics problems of random heterogeneous materials. ICES Report 04-45, The University of Texas at Austin] are extended to incorporate uncertainty in the material data by using classical Monte Carlo methods for calculating local quantities of interest. Techniques for estimating modeling error are extended to cases in which the material data are random variables. Several numerical examples involving two-phase composites with random material properties are given.

Long‐period tidal factors at Antarctica Syowa Station determined from 10 years of superconducting gravimeter data

We determined long‐period gravimetric tidal parameters from 10 years of superconducting gravimeter observations at Syowa Station in Antarctica. The obtained amplitude and phase lead for the Mm wave were 6.106 ± 0.030 μGal (μGal = 10−8 m s−2), 0.32° ± 0.28°, respectively, and those for the Mf wave were 11.657 ± 0.018 μGal, 0.78° ± 0.09°, respectively. We also determined the parameters of other tidal constituents with periods of 6 to 32 days; Mqm, Msqm, Mtm, Mstm, Msf, Msm, and their frequency dependence was estimated by means of a weighted least squares method. The observed values, corrected by the four ocean tide models of Schwiderski, NAO.99L, FES99, and TPXO6.0, were compared with the theoretical values calculated from the elastic and inelastic solid Earth tide models by Dehant et al. Even though the values of the ocean tide corrections have relatively large discrepancies between the four models and it is still difficult to discuss the degree of inelasticity of the Earth for this frequency band, we can say that the observations favor the inelastic Earth model rather than the elastic model.

Reflection and Refraction of Elastic Waves in Solids at Finite Temperatures up to Melting Points

On the basis of the recently proposed thermo-mechanical continuum model for elastic solids, several quantities characterizing reflection and refraction in solids, that is, amplitude ratios among incident, reflected and refracted waves, reflectivity, transmissivity, critical angle and temperature gap at an interface, are analyzed and discussed in a wide temperature range including a melting point as a limiting case.

Microscale modeling of kinking nonlinear elastic solids

Recently we identified and classified a class of solids as kinking nonlinear elastic (KNE) because they deform by the formation of kink bands. KNE solids represent a large family that include, among others, layered ternary carbides and nitrides, layered oxides and semiconductors, zinc, cadmium, graphite, ice, and the layered silicates, such as mica, present in nonlinear mesoscopic elastic solids. Herein we present a microscale model that accounts for the mechanical response of KNE solids to compressive stresses and apply it to two very different solids: ${\mathrm{Ti}}_{3}{\mathrm{SiC}}_{2}$ and graphite. Building on the Frank and Stroh model put forth in the 1950's for the formation of kink bands, we developed a comprehensive theory that accounts for the contributions of incipient kink bands (IKBs) and dislocations pile-ups produced by normal glide processes to the nonlinear strains and stored strain energies. The theory provides estimates for the densities of IKBs, the dislocation densities, both from the IKBs and dislocation pileups, as well as the energy dissipated by the motion of the dislocations.

Unconfined creep compression of chondrocytes

The study of single cell mechanics offers a valuable tool for understanding cellular milieus. Specific knowledge of chondrocyte biomechanics could lead to elucidation of disease etiologies and the biomechanical factors most critical to stimulating regenerative processes in articular cartilage. Recent studies in our laboratory have suggested that it may be acceptable to approximate the shape of a single chondrocyte as a disc. This geometry is easily utilized for generating models of unconfined compression. In this study, three continuum mechanics models of increasing complexity were formulated and used to fit unconfined compression creep data. Creep curves were obtained from middle/deep zone chondrocytes ( n=15) and separately fit using the three continuum models. The linear elastic solid model yielded a Young's modulus of 2.55±0.85 kPa. The viscoelastic model (adapted from the Kelvin model) generated an instantaneous modulus of 2.47±0.85 kPa, a relaxed modulus of 1.48±0.35 kPa, and an apparent viscosity of 1.92±1.80 kPa-s. Finally, a linear biphasic model produced an aggregate modulus of 2.58±0.87 kPa, a permeability of 2.57×10 −12±3.09 m 4/N-s, and a Poisson's ratio of 0.069±0.021. The results of this study demonstrate that similar values for the cell modulus can be obtained from three models of increasing complexity. The elastic model provides an easy method for determining the cell modulus, however, the viscoelastic and biphasic models generate additional material properties that are important for characterizing the transient response of compressed chondrocytes.

Unconfined creep compression of chondrocytes

The study of single cell mechanics offers a valuable tool for understanding cellular milieus. Specific knowledge of chondrocyte biomechanics could lead to elucidation of disease etiologies and the biomechanical factors most critical to stimulating regenerative processes in articular cartilage. Recent studies in our laboratory have suggested that it may be acceptable to approximate the shape of a single chondrocyte as a disc. This geometry is easily utilized for generating models of unconfined compression. In this study, three continuum mechanics models of increasing complexity were formulated and used to fit unconfined compression creep data. Creep curves were obtained from middle/deep zone chondrocytes ( n =15) and separately fit using the three continuum models. The linear elastic solid model yielded a Young's modulus of 2.55±0.85 kPa. The viscoelastic model (adapted from the Kelvin model) generated an instantaneous modulus of 2.47±0.85 kPa, a relaxed modulus of 1.48±0.35 kPa, and an apparent viscosity of 1.92±1.80 kPa-s. Finally, a linear biphasic model produced an aggregate modulus of 2.58±0.87 kPa, a permeability of 2.57×10 −12 ±3.09 m 4 /N-s, and a Poisson's ratio of 0.069±0.021. The results of this study demonstrate that similar values for the cell modulus can be obtained from three models of increasing complexity. The elastic model provides an easy method for determining the cell modulus, however, the viscoelastic and biphasic models generate additional material properties that are important for characterizing the transient response of compressed chondrocytes.

Adaptive modeling of wave propagation in heterogeneous elastic solids

This manuscript presents the results of a detailed research investigation on a fundamental problem in wave mechanics: the propagation of stress waves in heterogeneous elastic solids. The theory and methodologies of hierarchical modeling of heterogeneous materials [J. Comput. Phys. 164 (2000) 22; Int. J. Comp. Civil Str. Engrg. 1 (2000) 1; Goal-oriented Adaptive Modeling of Heterogeneous Elastic Solids, Ph.D. thesis, The University of Texas at Austin, 2000; Comput. Methods Appl. Mech. Engrg. 190 (2001) 6089] are extended to elastodynamic cases to make possible the control of the modeling error in the local average stress. One-dimensional numerical applications are given.

Characterization of Time-Varying Properties and Regional Strains in Myocardial Ischemia

Mechanical dysfunction plays an important role in the pathological progress of myocardial ischemia and is directly related to the prognosis of the patient. The crucial index of myocardial mechanics, regional time-varying elastance, and stress, however, could not be measured directly in clinical practice. This review outlines the steps to deduct myocardial mechanical performance from medical imaging modalities and modeling. The first step is to reconstruct three-dimensional cardiac motion by combining image data and geometric model of the heart. SPAMM-MRI (spatial modulation of magnetization) image, because of its high spatial–temporal resolution and ability to track material point of moving myocardium, is an ideal image modality for such a task. Several geometry models focused on SPAMM-MRI data analysis are discussed in detail, including some that assume cardiac shapes and some that extract the motion information from the tagging and subsequent model building by interpolation. Once the geometry of the heart at different time point is established, the second step is to calculate motion index from it. While different indices have been proposed, such as endocardium excursion, heart wall thickening, cardiac torsion, regional myocardial strain has the advantage of less affected by global heart motion and neighborhood myocardium. It is a key index to bridge cardiac MRI image and regional myocardial mechanical model. Finally, the three-dimensional strain distribution is used to compute myocardium stress and marterial property. Animal experiment, however, has shown that myocardial elastance changes throughout the cardiac cycle. The use of time-varying elastance model instead of elastic solid continuum model can thus provide a more accurate description of regional myocardium mechanics.