Log in

Relevant bibliographies by topics / Strain energy function / Journal articles

To see the other types of publications on this topic, follow the link: Strain energy function.

Journal articles on the topic 'Strain energy function'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Strain energy function.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Yeoh, O. H. "On the Ogden Strain-Energy Function." Rubber Chemistry and Technology 70, no. 2 (May 1, 1997): 175–82. http://dx.doi.org/10.5254/1.3538422.

Full text

Abstract:

Abstract The Ogden strain-energy function for rubber appears to be gaining popularity among users of finite element analysis. This paper discusses some of the special features of this material model. It explains why nonlinear regression analysis of stress-strain data obtained from just one mode of deformation may yield an Ogden strain-energy function that is unsatisfactory for predicting behavior in other deformation modes. It suggests the regression analysis be constrained such that some of the coefficients are chosen based upon the known behavior of rubbery materials.

APA, Harvard, Vancouver, ISO, and other styles

2

Rivlin, Ronald S. "The Valanis–Landel Strain-Energy Function." Journal of Elasticity 73, no. 1-3 (December 2003): 291–97. http://dx.doi.org/10.1023/b:elas.0000029985.16755.4e.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Carroll, M. M. "A Strain Energy Function for Vulcanized Rubbers." Journal of Elasticity 103, no. 2 (November 17, 2010): 173–87. http://dx.doi.org/10.1007/s10659-010-9279-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Stamenovic, D., and T. A. Wilson. "A Strain Energy Function for Lung Parenchyma." Journal of Biomechanical Engineering 107, no. 1 (February 1, 1985): 81–86. http://dx.doi.org/10.1115/1.3138525.

Full text

Abstract:

The strain energy for the air-filled lung is calculated from a model of the parenchymal microstructure. The energy is the sum of the surface energy and the elastic energies of two tissue components. The first of these is the peripheral tissue system that provides the recoil pressure of the saline-filled lung, and the second is the system of line elements that form the free edges of the alveolar walls bordering the alveolar ducts. The computed strain energy is consistent with the observed linear elastic behavior of parenchyma and the data on large deformations around blood vessels.

APA, Harvard, Vancouver, ISO, and other styles

5

Willson, A. J., and P. J. Myers. "A generalisation of Ko's strain-energy function." International Journal of Engineering Science 26, no. 6 (January 1988): 509–17. http://dx.doi.org/10.1016/0020-7225(88)90051-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Doll, S., and K. Schweizerhof. "On the Development of Volumetric Strain Energy Functions." Journal of Applied Mechanics 67, no. 1 (October 12, 1999): 17–21. http://dx.doi.org/10.1115/1.321146.

Full text

Abstract:

To describe elastic material behavior the starting point is the isochoric-volumetric decoupling of the strain energy function. The volumetric part is the central subject of this contribution. First, some volumetric functions given in the literature are discussed with respect to physical conditions, then three new volumetric functions are developed which fulfill all imposed conditions. One proposed function which contains two material parameters in addition to the compressibility parameter is treated in detail. Some parameter fits are carried out on the basis of well-known volumetric strain energy functions and experimental data. A generalization of the proposed function permits an unlimited number of additional material parameters. Dedicated to Professor Franz Ziegler on the occasion of his 60th birthday. [S0021-8936(00)00901-6]

APA, Harvard, Vancouver, ISO, and other styles

7

Takamizawa, Keiichi, and Kozaburo Hayashi. "Strain energy density function and uniform strain hypothesis for arterial mechanics." Journal of Biomechanics 20, no. 1 (January 1987): 7–17. http://dx.doi.org/10.1016/0021-9290(87)90262-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Ling, Yun, Peter A. Engel, Wm L. Brodskey, and Yifan Guo. "Finding the Constitutive Relation for a Specific Elastomer." Journal of Electronic Packaging 115, no. 3 (September 1, 1993): 329–36. http://dx.doi.org/10.1115/1.2909336.

Full text

Abstract:

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

APA, Harvard, Vancouver, ISO, and other styles

9

Kim, Nam-Woong, and Kug-Weon Kim. "Prediction of Strain Energy Function for Butyl Rubbers." Transactions of the Korean Society of Mechanical Engineers A 30, no. 10 (October 1, 2006): 1227–34. http://dx.doi.org/10.3795/ksme-a.2006.30.10.1227.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

McCoy, E. L. "The strain energy function in axial plant growth." Journal of Mathematical Biology 27, no. 5 (September 1989): 575–94. http://dx.doi.org/10.1007/bf00288435.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Shariff, M. H. B. M. "Physical invariant strain energy function for passive myocardium." Biomechanics and Modeling in Mechanobiology 12, no. 2 (April 13, 2012): 215–23. http://dx.doi.org/10.1007/s10237-012-0393-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Wang, Xiao-Ming, Hao Li, Zheng-Nan Yin, and Heng Xiao. "MULTIAXIAL STRAIN ENERGY FUNCTIONS OF RUBBERLIKE MATERIALS: AN EXPLICIT APPROACH BASED ON POLYNOMIAL INTERPOLATION." Rubber Chemistry and Technology 87, no. 1 (March 1, 2014): 168–83. http://dx.doi.org/10.5254/rct.13.86960.

Full text

Abstract:

ABSTRACT We propose an explicit approach to obtaining multiaxial strain energy functions for incompressible, isotropic rubberlike materials undergoing large deformations. Via polynomial interpolation, we first obtain two one-dimensional strain energy functions separately from uniaxial data and shear data, and then, from these two, we obtain a multiaxial strain energy function by means of direct procedures based on well-designed logarithmic invariants. This multiaxial strain energy function exactly fits any given data from four benchmark tests, including uniaxial and equibiaxial extension, simple shear, plane–strain extension, and so forth. Furthermore, its predictions for biaxial stretch tests provide good accord with test data. The proposed approach is explicit in a sense without involving the usual procedures both in deriving forms of the multiaxial strain energy function and in estimating a number of unknown parameters.

APA, Harvard, Vancouver, ISO, and other styles

13

Funai, Takashi, Hiroyuki Kataoka, Hideo Yokota, and Taka-aki Suzuki. "Proposal and validation of polyconvex strain-energy function for biological soft tissues." Bio-Medical Materials and Engineering 32, no. 3 (May 18, 2021): 131–44. http://dx.doi.org/10.3233/bme-196015.

Full text

Abstract:

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

APA, Harvard, Vancouver, ISO, and other styles

14

Johnson, A. R., C. J. Quigley, D. G. Young, and J. A. Danik. "Viscohyperelastic Modeling of Rubber Vulcanizates." Tire Science and Technology 21, no. 3 (July 1, 1993): 179–99. http://dx.doi.org/10.2346/1.2139528.

Full text

Abstract:

Abstract The use of internal hyperelastic solids for modeling viscoelastic deformations of rubber vulcanizates is reviewed. The model is applied in one dimension to viscoelastic uniaxial tension and uniaxial shear experiments. Step-strain relaxation tests are used to determine the model's parameters. A hyperelastic energy function, which represents the sum of the internal solids' energy functions, is obtained by least squares fitting a constrained third-order invariant expansion of the Rivlin function to the difference between the step-strain stresses and the relaxed stresses (the standard hyperelastic solid's stresses). The difference energy function is split into two parts and relaxation parameters (related to the rate of change of the internal solids' reference lengths) are selected so that numerically simulated step-strain relaxation stresses approximate the experimental values (at approximately 50 ms). The model is then used to predict the experimental results from a different type of test, cyclic strain data, at three different strain rates (cyclic frequencies). Increased stress due to increased strain rate was indicated by the model for large strains.

APA, Harvard, Vancouver, ISO, and other styles

15

Yeoh, O. H. "Some Forms of the Strain Energy Function for Rubber." Rubber Chemistry and Technology 66, no. 5 (November 1, 1993): 754–71. http://dx.doi.org/10.5254/1.3538343.

Full text

Abstract:

Abstract According to Rivlin's Phenomenological Theory of Rubber Elasticity, the elastic properties of a rubber may be described in terms of a strain energy function which is an infinite power series in the strain invariants I1, I2 and I3. The simplest forms of Rivlin's strain energy function are the neo-Hookean, which is obtained by truncating the infinite series to just the first term in I1, and the Mooney-Rivlin, which retains the first terms in I1 and I2. Recently, we proposed a strain energy function which is a cubic in I1. Conceptually, the proposed function is a material model with a shear modulus that varies with deformation. In this paper, we compare the large strain behavior of rubber as predicted by these forms of the strain energy function. The elastic behavior of swollen rubber is also discussed.

APA, Harvard, Vancouver, ISO, and other styles

16

Kang, Taewon. "Theoretical Framework For Describing Strain Energy Function on Biomaterial." Journal of The Korean Society of Manufacturing Technology Engineers 22, no. 1 (February 15, 2013): 50–55. http://dx.doi.org/10.7735/ksmte.2013.22.1.50.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Shariff, M. H. B. M. "Strain Energy Function for Filled and Unfilled Rubberlike Material." Rubber Chemistry and Technology 73, no. 1 (March 1, 2000): 1–18. http://dx.doi.org/10.5254/1.3547576.

Full text

Abstract:

Abstract A general separable form of strain energy function with linear parameters is developed so that if a standard curve fitting method is used only a handful of linear equations need to be solved; the proposed function is formulated in such a way that only a few parameters are required to characterized the rubberlike materials. One of the parameters is the Young's modulus and this could facilitate a curve fitting algorithm if the value of the Young's modulus is known. A single constant, strain energy function is also proposed. The predicted curves agree well with numerous experimental data.

APA, Harvard, Vancouver, ISO, and other styles

18

Bitoh, Yohsuke, Norio Akuzawa, Kenji Urayama, and Toshikazu Takigawa. "Strain energy function of swollen polybutadiene elastomers studied by general biaxial strain testing." Journal of Polymer Science Part B: Polymer Physics 48, no. 6 (March 15, 2010): 721–28. http://dx.doi.org/10.1002/polb.21945.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Woo, Chang Su, Hyun Sung Park, and Wae Gi Shin. "Finite Element Analysis by Using Hyper-Elastic Properties for Rubber Component." Key Engineering Materials 488-489 (September 2011): 190–93. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.190.

Full text

Abstract:

The material modeling of hyper-elastic properties in rubber is generally characterized by the strain energy function. The strain energy functions have been represented either in term of the strain in variants that are functions of the stretch ratios, or directly in terms of the principal stretch. Successful modeling and design of rubber components relies on both the selection of an appropriate strain energy function and an accurate determination of material constants in the function. Material constants in the strain energy functions can be determined from the curve fitting of experimental stress-strain data. The uniaxial tension, equi-biaxial tension and pure shear test were performed to acquire the constants of the strain energy functions which were Mooney-Rivlin and Ogden model. Nonlinear finite element analysis was executed to evaluate the behavior of deformation and strain distribute by using the commercial finite element code. Also, the fatigue tests were carried out to obtain the fatigue failure. Fatigue failure was initiated at the critical location was observed during the fatigue test of rubber component, which was the same result predicted by the finite element analysis.

APA, Harvard, Vancouver, ISO, and other styles

20

Ghaemi, Hamid, A. Spence, and K. Behdinan. "ON THE DEVELOPMENT OF COMPRESSIBLE PSEUDO-STRAIN ENERGY DENSITY FUNCTION FOR HYPERELASTIC MATERIAL: EXPERIMENT, THEORY AND FEM." Transactions of the Canadian Society for Mechanical Engineering 29, no. 3 (September 2005): 459–75. http://dx.doi.org/10.1139/tcsme-2005-0028.

Full text

Abstract:

This study was carried out to develop a compressible pseudo-strain energy function that describes the mechanical behavior of rubber-like materials. The motivation for this work was two fold; first was to define a single-term strain energy function derived from constitutive equations that can describe the mechanical behavior of rubber-like materials and taking into account the coupling between principal stretches and the nearly incompressibility characteristic of elastomers. Second was to implement this strain energy function into the Finite Element Method (FEM) to study the suitability of the model in FEM. A one-term three-dimensional strain energy function based on the principal stretch ratios was proposed. The three dimensional constitutive function was then reduced to describe the behavior of rubber-like materials under biaxial and uniaxial loading condition based on the membrane theory. The work presented here was based on the decoupling of the strain density function into a deviatoric and a volumetric part. Using pure gum, GMS-SS-A40, uniaxial and equi-biaxial experiments were conducted employing different strain rate protocols. The material was assumed to be isotropic and homogenous. The experimental data from uniaxial and biaxial tests were used simultaneously to determine the material parameters of the proposed strain energy function. A GA curve fitting technique was utilized in the material parameter identification. The proposed strain energy function was compared to a few well-known strain energy functions as well as the experimental results. It was determined that the proposed strain energy function predicted the mechanical behavior of rubber-like material with greater accuracy as compared to other models both analytical and numerical results.

APA, Harvard, Vancouver, ISO, and other styles

21

Norris, A. N., and D. L. Johnson. "Nonlinear Elasticity of Granular Media." Journal of Applied Mechanics 64, no. 1 (March 1, 1997): 39–49. http://dx.doi.org/10.1115/1.2787292.

Full text

Abstract:

The finite and incremental elasticity of a random packing of identical spheres is derived using energy methods. We consider different models for the contact forces between spheres, all of which are based upon or related to the fundamental Hertz theory; we consider only the special cases of perfect friction (no tangential slip) or no tangential friction. The existence of a strain energy function for the medium depends critically upon the type of contact. If the tangential contact stiffness is independent of the normal force, then the energy is well defined for all values of the macroscopic strain. Otherwise, the strain energy of the system is path dependent, in general. However, the concept of a quadratic strain energy function is always well defined for incremental motion superimposed on large confining stress and strain. For all models considered, we derive the changes in wave speeds due to incremental strains. For the models based upon an energy function we derive expressions for the third-order elastic constants as a function of confining pressure.

APA, Harvard, Vancouver, ISO, and other styles

22

Johnson, Arthur R., and Ross G. Stacer. "Rubber Viscoelasticity Using the Physically Constrained System's Stretches as Internal Variables." Rubber Chemistry and Technology 66, no. 4 (September 1, 1993): 567–77. http://dx.doi.org/10.5254/1.3538329.

Full text

Abstract:

Abstract The simulation of rubber viscoelasticity with the tube reptation model for topological interactions is investigated for large dynamic strains. The chemically crosslinked (CC) system of molecules acts as a constraint box per unit volume for the physically constrained (PC) system and carries the PC system during the deformation process. A stick—slip model is used to simulate the interaction between the CC and PC systems Stretch ratios describe the history of the PC system's energy. Rubber energy density functions for both the CC and time dependent PC systems are shown to model large strain viscoelastic deformations. In this approach the energy is split into two terms. The long term energy function for the CC molecules represents one part and a time dependent energy function for the PC molecules comprises the second part. The PC systems' stretches then appear as internal variables in the expression of the total energy. The relaxation of the PC molecules during a general deformation is determined by the history of the CC system's strain state and the box (tube) stick—slip relaxation equation(s). Examples are presented in which step-strain relaxation test data and strain rate data are simulated for large deformations of a rubber compound with differing short and long term energy functions.

APA, Harvard, Vancouver, ISO, and other styles

23

Degener, M., D. H. Hodges, and D. Petersen. "Analytical and Experimental Study of Beam Torsional Stiffness With Large Axial Elongation." Journal of Applied Mechanics 55, no. 1 (March 1, 1988): 171–78. http://dx.doi.org/10.1115/1.3173624.

Full text

Abstract:

The axial force and effective torsional stiffness versus axial elongation are investigated analytically and experimentally for a beam of circular cross section and made of an incompressible material that can sustain large elastic deformation. An approach based on a strain energy function identical to that used in linear elasticity, except with its strain components replaced by those of some finite-deformation tensor, would be expected to provide only limited predictive capability for this large-strain problem. Indeed, such an approach based on Green strain components (commonly referred to as the geometrically nonlinear theory of elasticity) incorrectly predicts a change in volume and predicts the wrong trend regarding the experimentally determined axial force and effective torsional stiffness. On the other hand, use of the same strain energy function, only with the Hencky logarithmic strain components, correctly predicts constant volume and provides excellent agreement with experimental data for lateral contraction, tensile force, and torsional stiffness—even when the axial elongation is large. For strain measures other than Hencky, the strain energy function must be modified to consistently account for large strains. For comparison, theoretical curves derived from a modified Green strain energy function are added. This approach provides results identical to those of the Neo-Hookean formulation for incompressible materials yielding fair agreement with the experimental results for coupled tension and torsion. An alternative approach, proposed in the present paper and based on a modified Almansi strain energy function, provides very good agreement with experimental data and is somewhat easier to manage than the Hencky strain energy approach.

APA, Harvard, Vancouver, ISO, and other styles

24

Shariff, Mohd Halim Bin Mohd, and Jose Merodio. "Residually Stressed Fiber Reinforced Solids: A Spectral Approach." Materials 13, no. 18 (September 14, 2020): 4076. http://dx.doi.org/10.3390/ma13184076.

Full text

Abstract:

We use a spectral approach to model residually stressed elastic solids that can be applied to carbon fiber reinforced solids with a preferred direction; since the spectral formulation is more general than the classical-invariant formulation, it facilitates the search for an adequate constitutive equation for these solids. The constitutive equation is governed by spectral invariants, where each of them has a direct meaning, and are functions of the preferred direction, the residual stress tensor and the right stretch tensor. Invariants that have a transparent interpretation are useful in assisting the construction of a stringent experiment to seek a specific form of strain energy function. A separable nonlinear (finite strain) strain energy function containing single-variable functions is postulated and the associated infinitesimal strain energy function is straightforwardly obtained from its finite strain counterpart. We prove that only 11 invariants are independent. Some illustrative boundary value calculations are given. The proposed strain energy function can be simply transformed to admit the mechanical influence of compressed fibers to be partially or fully excluded.

APA, Harvard, Vancouver, ISO, and other styles

25

Klisch, Stephen M. "A Bimodular Polyconvex Anisotropic Strain Energy Function for Articular Cartilage." Journal of Biomechanical Engineering 129, no. 2 (September 15, 2006): 250–58. http://dx.doi.org/10.1115/1.2486225.

Full text

Abstract:

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex “strong interaction terms” for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson’s ratios, as well as axial stress–axial strain responses, in tension and compression for finite deformations.

APA, Harvard, Vancouver, ISO, and other styles

26

Shen, Y., K. Chandrashekhara, W. F. Breig, and L. R. Oliver. "Neural Network Based Constitutive Model for Rubber Material." Rubber Chemistry and Technology 77, no. 2 (May 1, 2004): 257–77. http://dx.doi.org/10.5254/1.3547822.

Full text

Abstract:

Abstract Rubber hyperelasticity is characterized by a strain energy function. The strain energy functions fall primarily into two categories: one based on statistical thermodynamics, the other based on the phenomenological approach of treating the material as a continuum. This work is focused on the phenomenological approach. To determine the constants in the strain energy function by this method, curve fitting of rubber test data is required. A review of the available strain energy functions based on the phenomenological approach shows that it requires much effort to obtain a curve fitting with good accuracy. To overcome this problem, a novel method of defining rubber strain energy function by Feedforward Backpropagation Neural Network is presented. The calculation of strain energy and its derivatives by neural network is explained in detail. The preparation of the neural network training data from rubber test data is described. Curve fitting results are given to show the effectiveness and accuracy of the neural network approach. A material model based on the neural network approach is implemented and applied to the simulation of V-ribbed belt tracking using the commercial finite element code ABAQUS.

APA, Harvard, Vancouver, ISO, and other styles

27

WEIZSÄCKER, H. W., G. A. HOLZAPFEL, G. W. DESCH, and K. PASCALE. "Strain Energy Density Function for Arteries from Different Topographical Sites." Biomedizinische Technik/Biomedical Engineering 40, s2 (1995): 139–41. http://dx.doi.org/10.1515/bmte.1995.40.s2.139.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Rivlin, Ronald S. "Restrictions on the Strain-Energy Function for an Elastic Material." Mathematics and Mechanics of Solids 9, no. 2 (April 2004): 131–39. http://dx.doi.org/10.1177/1081286504042589.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Nah, C., G. B. Lee, J. Y. Lim, Y. H. Kim, R. SenGupta, and A. N. Gent. "Problems in determining the elastic strain energy function for rubber." International Journal of Non-Linear Mechanics 45, no. 3 (April 2010): 232–35. http://dx.doi.org/10.1016/j.ijnonlinmec.2009.11.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Itskov, M., A. E. Ehret, and D. Mavrilas. "A polyconvex anisotropic strain–energy function for soft collagenous tissues." Biomechanics and Modeling in Mechanobiology 5, no. 1 (December 14, 2005): 17–26. http://dx.doi.org/10.1007/s10237-005-0006-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Chaplain, M. A. J. "The Strain Energy Function of an Ideal Plant Cell Wall." Journal of Theoretical Biology 163, no. 1 (July 1993): 77–97. http://dx.doi.org/10.1006/jtbi.1993.1108.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Markert, Bernd, Wolfgang Ehlers, and Nils Karajan. "A general polyconvex strain-energy function for fiber-reinforced materials." PAMM 5, no. 1 (December 2005): 245–46. http://dx.doi.org/10.1002/pamm.200510099.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Darijani, H., R. Naghdabadi, and M. H. Kargarnovin. "Hyperelastic materials modelling using a strain measure consistent with the strain energy postulates." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 3 (October 26, 2009): 591–602. http://dx.doi.org/10.1243/09544062jmes1590.

Full text

Abstract:

In this article, a strain energy density function of the Saint Venant—Kirchhoff type is expressed in terms of a Lagrangian deformation measure. Applying the governing postulates to the form of the strain energy density, the mathematical expression of this measure is determined. It is observed that this measure, which is consistent with the strain energy postulates, is a strain type with the characteristic function more rational than that of the Seth—Hill strain measures for hyperelastic materials modelling. In addition, the material parameters are calculated using a novel procedure that is based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to evaluate the performance of the proposed model of the strain energy density, some test data of pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and predictions of the model for incompressible and compressible isotropic materials.

APA, Harvard, Vancouver, ISO, and other styles

34

Kobayashi, H., and R. Vanderby. "New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials." Journal of Applied Mechanics 72, no. 6 (February 11, 2005): 843–51. http://dx.doi.org/10.1115/1.2041661.

Full text

Abstract:

Acoustoelastic analysis has usually been applied to compressible engineering materials. Many materials (e.g., rubber and biologic materials) are “nearly” incompressible and often assumed incompressible in their constitutive equations. These material models do not admit dilatational waves for acoustoelastic analysis. Other constitutive models (for these materials) admit compressibility but still do not model dilatational waves with fidelity (shown herein). In this article a new strain energy function is formulated to model dilatational wave propagation in nearly incompressible, isotropic materials. This strain energy function requires four material constants and is a function of Cauchy–Green deformation tensor invariants. This function and existing (compressible) strain energy functions are compared based upon their ability to predict dilatational wave propagation in uniaxially prestressed rubber. Results demonstrate deficiencies in existing functions and the usefulness of our new function for acoustoelastic applications. Our results also indicate that acoustoelastic analysis has great potential for the accurate prediction of active or residual stresses in nearly incompressible materials.

APA, Harvard, Vancouver, ISO, and other styles

35

Liu, J., K. Kim, M. Golshan, D. Laundy, and A. M. Korsunsky. "Energy calibration and full-pattern refinement for strain analysis using energy-dispersive and monochromatic X-ray diffraction." Journal of Applied Crystallography 38, no. 4 (July 13, 2005): 661–67. http://dx.doi.org/10.1107/s0021889805016663.

Full text

Abstract:

Precise channel-to-energy conversion is very important in full-pattern refinement in energy-dispersive X-ray diffraction. Careful examination shows that the channel-to-energy conversion is not entirely linear, which presents an obstacle to obtaining accurate quantitative data for lattice strains by pattern refinement. In order to establish an accurate quadratic channel-to-energy conversion function, aMatlabprogram was written to find the best quadratic coefficient and hence the whole energy conversion function. Then this energy conversion function was used to perform a whole-pattern fitting of the energy-dispersive X-ray diffraction pattern of a Ti64 sample. The strain across the Ti64 bar calculated from the fitting results has been compared with values obtained by single-wavelength X-ray diffraction utilizing a Laue monochromator.

APA, Harvard, Vancouver, ISO, and other styles

36

Vahapoğlu, Vahap, and Sami Karadeniz. "Constitutive Equations for Isotropic Rubber-Like Materials Using Phenomenological Approach: A Bibliography (1930–2003)." Rubber Chemistry and Technology 79, no. 3 (July 1, 2006): 489–99. http://dx.doi.org/10.5254/1.3547947.

Full text

Abstract:

Abstract To describe the elastic behavior of rubber-like materials, numerous specific forms of strain energy functions have been proposed in the literature. This bibliography provides a list of references on the strain energy functions for rubber-like materials on isothermal condition using the phenomenological approach. The published works, either containing the strain energy function proposals or the discussions on such proposals, based upon the phenomenological approach, are classified.

APA, Harvard, Vancouver, ISO, and other styles

37

Bruhns, O. T., H. Xiao, and A. Meyers. "Constitutive inequalities for an isotropic elastic strain-energy function based on Hencky's logarithmic strain tensor." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, no. 2013 (September 8, 2001): 2207–26. http://dx.doi.org/10.1098/rspa.2001.0818.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Sang, Jian Bing, Bo Liu, Zhi Liang Wang, Su Fang Xing, and Jie Chen. "Application and Research of Numerical Simulation for Rubber Like Material with MSC.Marc." Materials Science Forum 575-578 (April 2008): 854–58. http://dx.doi.org/10.4028/www.scientific.net/msf.575-578.854.

Full text

Abstract:

This paper starts with a discussion on the theory of finite deformation and various types strain energy functions of rubber like material, the material parameter of elastic law of Gao[3] is estimated by experiment and numerical simulation. Because there are various types of strain energy functions, a user subroutine is programmed to implement the strain energy function of Gao[3] into the program of MSC.Marc, which offers a convenient method to analyze the stress and strain of rubber-like material with the strain energy function that is needed. Two examples will be presented in this paper to demonstrate the use of the framework for rubber like materials. One is to simulate a foam tube in compression. The other one is to simulate a rectangle board with a circular hole. After numerical analysis, it is proved the numerical results based on Gao model are in perfect agreement with the results based on Mooney model and the estimated material parameters are valid.

APA, Harvard, Vancouver, ISO, and other styles

39

Elata, D., and M. B. Rubin. "Isotropy of Strain Energy Functions Which Depend Only on a Finite Number of Directional Strain Measures." Journal of Applied Mechanics 61, no. 2 (June 1, 1994): 284–89. http://dx.doi.org/10.1115/1.2901442.

Full text

Abstract:

Motivated by studies of low-density materials and fiber-dominated composites, we consider an elastic material whose strain energy function depends only on a finite number of directional strain measures, which correspond to the strains of material fibers in specific material directions. It is shown that an arbitrary set of six distinct direction vectors can be used to define six symmetric base tensors which span the space of all symmetric second-order tensors. Using these base tensors and their reciprocal tensors we develop a representation for the strain tensor in terms of six directional strain measures. The functional form of the strain energy of a general anisotropic nonlinear elastic material may then be expressed in terms of these directional strain measures. Next, we consider general nonlinear isotropic response by developing explicit functional forms for three independent strain invariants in terms of these directional strain measures. Finally, with reference to previous work, we discuss isotropy of specific functional forms of directional strain measures associated with up to 15 directions in space.

APA, Harvard, Vancouver, ISO, and other styles

40

Khisaeva, Z. F., and M. Ostoja-Starzewski. "Mesoscale bounds in finite elasticity and thermoelasticity of random composites." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2068 (January 17, 2006): 1167–80. http://dx.doi.org/10.1098/rspa.2005.1614.

Full text

Abstract:

Under consideration is the problem of size and response of the Representative Volume Element (RVE) in the setting of finite elasticity of statistically homogeneous and ergodic random microstructures. Through the application of variational principles, a scale dependent hierarchy of strain energy functions (i.e. mesoscale bounds) is derived for the effective strain energy function of the RVE. In order to account for thermoelastic effects, the variational principles are first generalized, and then analogous bounds on the effective thermoelastic response are derived. It is also shown that, in contradiction to results obtained for random linear composites, the hierarchy on the effective strain energy function in nonlinear elasticity cannot be split into volumetric and isochoric terms, while the hierarchy on the effective free energy function cannot be divided into purely mechanical and thermal contributions.

APA, Harvard, Vancouver, ISO, and other styles

41

Termonia, Yves. "Multiaxial deformation of polymers: strain energy density function and time dependence." Macromolecules 25, no. 19 (September 1992): 5008–12. http://dx.doi.org/10.1021/ma00045a029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Singh, Fateh, V. K. Katiyar, and B. P. Singh. "A new strain energy function to characterize apple and potato tissues." Journal of Food Engineering 118, no. 2 (September 2013): 178–87. http://dx.doi.org/10.1016/j.jfoodeng.2013.04.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Rothermel, Taylor M., Zaw Win, and Patrick W. Alford. "Large-deformation strain energy density function for vascular smooth muscle cells." Journal of Biomechanics 111 (October 2020): 110005. http://dx.doi.org/10.1016/j.jbiomech.2020.110005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Miroshnychenko, Dmitri, and W. A. Green. "Heuristic search for a predictive strain-energy function in nonlinear elasticity." International Journal of Solids and Structures 46, no. 2 (January 2009): 271–86. http://dx.doi.org/10.1016/j.ijsolstr.2008.08.037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Sokolis, Dimitrios P. "Strain-energy function and three-dimensional stress distribution in esophageal biomechanics." Journal of Biomechanics 43, no. 14 (October 2010): 2753–64. http://dx.doi.org/10.1016/j.jbiomech.2010.06.007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

SUI, Y. K., X. R. PENG, J. L. FENG, and H. L. YE. "TOPOLOGY OPTIMIZATION OF STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BY INDEPENDENT CONTINUUM MAP METHOD." International Journal of Computational Methods 03, no. 03 (September 2006): 295–319. http://dx.doi.org/10.1142/s0219876206000758.

Full text

Abstract:

We establish topology optimization model in terms of Independent Continuum Map method (ICM), so as to avoid the difficulties caused by multiple objective functions of compliance, owing to referring to weight as objective function. Using the distorted-strain-energy criterion, we transform stress constraints on all elements into structure strain-energy constraints in global sense. Then, the problem of topological optimum of continuum structure subjected to global strain-energy constraints is formulated and solved. The process of optimization is conducted through three basic steps which include the computation of the minimum strain energy of structure corresponding to the maximum strain-energy under the load case due to prescribing weight constraint, the determination of the allowable strain-energy of structure for every load case by using a formula from our numerical tests, as well as the establishment and solution of optimization model with the weight function due to all allowable strain energies. A strategy that is available to cope with complicated load ill-posedness in terms of different complementary approaches one by one is presented in the present work. Several numerical examples demonstrate that the topology path of transferring forces can be obtained more readily by global strain energy constraints rather than local stress constraints, and the problem of load ill-posedness can be tackled very well by the weighting method with regard to structural strain energy as weighting coefficient.

APA, Harvard, Vancouver, ISO, and other styles

47

SHIMIZU, Shun, Jungju LEE, Kenji URAYAMA, and Toshikazu TAKIGAWA. "Strain Energy Function of Poly(Propylene Oxide) and Polybutadiene Elastomers Estimated by General Biaxial Strain Testing." Journal of the Society of Materials Science, Japan 62, no. 1 (2013): 18–21. http://dx.doi.org/10.2472/jsms.62.18.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Kakavas, P. A. "A new development of the strain energy function for hyperelastic materials using a logarithmic strain approach." Journal of Applied Polymer Science 77, no. 3 (July 18, 2000): 660–72. http://dx.doi.org/10.1002/(sici)1097-4628(20000718)77:3<660::aid-app21>3.0.co;2-a.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Yeoh, O. H. "Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates." Rubber Chemistry and Technology 63, no. 5 (November 1, 1990): 792–805. http://dx.doi.org/10.5254/1.3538289.

Full text

Abstract:

Abstract A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy function has been shown to permit the prediction of stress/strain behavior in different deformation modes from data obtained in one simple deformation mode. This circumvents the need for a rather difficult experiment in general biaxial extension. The simple form of the proposed function also simplifies the regression analysis. This strain-energy function is consistent with the general Rivlin strain-energy function and is easily obtained from the popular third-order deformation approximation. Thus, it is already available in many existing finite-element analysis programs.

APA, Harvard, Vancouver, ISO, and other styles

50

Martin, Robert J., Ionel-Dumitrel Ghiba, and Patrizio Neff. "A polyconvex extension of the logarithmic Hencky strain energy." Analysis and Applications 17, no. 03 (May 2019): 349–61. http://dx.doi.org/10.1142/s0219530518500173.

Full text

Abstract:

Adapting a method introduced by Ball, Muite, Schryvers and Tirry, we construct a polyconvex isotropic energy function [Formula: see text] which is equal to the classical Hencky strain energy [Formula: see text] in a neighborhood of the identity matrix 𝟙; here, [Formula: see text] denotes the set of [Formula: see text]-matrices with positive determinant, [Formula: see text] denotes the deformation gradient, [Formula: see text] is the corresponding stretch tensor, [Formula: see text] is the principal matrix logarithm of [Formula: see text], [Formula: see text] is the trace operator, [Formula: see text] is the Frobenius matrix norm and [Formula: see text] is the deviatoric part of [Formula: see text]. The extension can also be chosen to be coercive, in which case Ball’s classical theorems for the existence of energy minimizers under appropriate boundary conditions are immediately applicable. We also generalize the approach to energy functions [Formula: see text] in the so-called Valanis–Landel form [Formula: see text] with [Formula: see text], where [Formula: see text] denote the singular values of [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!