Stability analysis of dielectric elastomer using the elastic strain energy function with two material constants

The deformation induced by gravity in a solid cylinder is considered. The cylinder is placed on a horizontal frictionless surface with the axis vertical and is treated as an isotropic incompressible elastic material. Further distortion is produced by finite axial compression. Thus the overall deformation is predominantly uniform with a small perturbation superimposed to account for the gravity effects. A particular case is when there is no finite axial compression. The solution then describes the shortening and general infinitesimal deformation associated with the gravitational body force. The results may be used for determining the material constants of soft elastic materials. In particular, the equivalent of Young’s modulus for gelatin has been found by measuring the changes in height of cylindrical specimens when removed from rigid containers and using the appropriate formula derived in the analysis. The results obtained were extremely consistent. In addition, the behaviour of gelatin under finite compression has been examined. By comparing the theoretical predictions with the experimental measurements it is shown that gelatin behaves more as a Mooney material than as a material which has a quadratic form for the associated strain energy function. Values of the two material constants occurring in the Mooney form of the strain energy function are obtained.

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A Strain Energy Function for the Annulus Fibrosus Specified Using Biaxial Experimental Data

10.1115/imece1999-0457 ◽

1999 ◽

Author(s):

Elisa C. Bass ◽

Jeffrey C. Lotz

Keyword(s):

Energy Function ◽

Annulus Fibrosus ◽

Strain Energy ◽

Mechanical Response ◽

Biaxial Tension ◽

Elastic Strain Energy ◽

Strain Energy Function ◽

Constitutive Formulation

Abstract The mechanical behavior of the annulus fibrosus has typically been characterized through the use of uniaxial tests. In contrast, its in vivo constraints are multiaxial and likely result in a mechanical response very different from that observed to date in vitro. The goal of this study was to test the annulus in biaxial tension and use these data to determine an elastic strain energy function for the annulus. Our results demonstrate that the mechanical response of the annulus is dramatically influenced by a biaxial constraint, and that these experiments provide important data for the determination of the constitutive formulation for this strongly anisotropic and nonlinear tissue.

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Modeling of Visco-Hyperelastic Behavior of Foams

Volume 12: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2008-66773 ◽

2008 ◽

Cited By ~ 1

Author(s):

Y. Anani ◽

M. Asghari ◽

R. Naghdabadi

Keyword(s):

Energy Function ◽

Strain Energy ◽

Strain Energy Function ◽

Constitutive Law ◽

Energy Functions ◽

Material Constants ◽

Maxwell Element ◽

Rate Dependent ◽

Dependent Behavior ◽

Strain Energy Functions

In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the ratedependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the ratedependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear elastic materials. Instead, stresses are derived from the principle of virtual work using the stored strain energy potential function. In addition, foams are compressible, therefore classic strain energy functions such as the Ogden strain energy function or the Mooney-Rivlin strain energy function are not suitable to describe hyperelastic behavior of foams. So, strain energy functions must include the effect of compressibility. That means the third principal invariant of the deformation gradient tensor F should enter in strain energy functions. For rate-dependent behavior of foams, history integral constitutive law is used. For the equilibrium spring and the intermediate spring, the same strain energy function is employed. In order to use this stain energy function in history integral equation, the kernel function of it is calculated. The effect of compressibility is considered in rate-dependent behavior of foams too. All material constants were obtained from the results of uniaxial tensile tests. Nonlinear regulation was used to find these constants. In these calculations, Average strain rate was employed to find material constants.

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Mechanical power and hyperelasticity

10.1093/oso/9780198567783.003.0003 ◽

2017 ◽

Author(s):

David J. Steigmann

Keyword(s):

Energy Function ◽

Strain Energy ◽

Strain Energy Function ◽

Mechanical Power ◽

Elastic Materials ◽

Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

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