Mooney-Rivlin Strain Energy Function Research Articles

다구찌 방법을 이용한 고분자 전해질 연료전지 가스켓의 강건 구조 설계

In this paper, robust structural design of the PEMFC stack gasket is pursued with Taguchi method by considering the noise factor in stack assembly. The study of noise problem in stacking is required to secure the safety and performance improvement of PEMFC stack. The design parameters in the Taguchi method are selected so that the structural responses are insensitive to the noise factors. In the gasket analysis, a Mooney-Rivlin strain energy function is used to consider hyperelasticity between load and displacement. By uni-axial and equi-biaxial tension tests of the gasket, the material properties are determined for the use in robust design of PEMFC gasket. The robust design of the PEMFC stack may provide structural reliability

고분자 전해질 연료전지 가스켓 및 GDL의 구조 해석

In this paper, structural behavior of Gasket and GDL of a PEMFC stack is studied to improve the performance and to secure the safety. In the Gasket analysis Mooney-Rivlin strain energy function is used to consider hyperelasticity of load and displacement. The material properties is determined by testing specimens of the gasket at uni-axial and equi-biaxial mode and compared with finite element analysis results. By measuring a thickness change, the material property of GDL is determined. The pressure drop of a unit cell is measured along the channel for the clamping force. A cross sectional change of channel base on the experimental data is obtained experimentally and compare with FEM analysis results.

Determination of the Constitutive Constants of Non-Linear Viscoelastic Materials

A simple method for computing the strain and the time dependent constants for non-linear viscoelastic materials is presented. The method is based on the finite time increment formulation of the convolution integral, and is applicable for materials which exhibit separable strain and time variables. The strain-dependent function can take any form including the hyperelastic potentials such as the Mooney-Rivlin strain energy function. The time-dependent function is based on the Prony series. The attraction of the method is that true material constants can be computed for any deformation history.

BIDIRECTIONAL MODELLING OF HIGH-DAMPING RUBBER BEARINGS

High-damping rubber (HDR) bearings are used in seismic isolation applications for buildings and bridges, although no models are currently available for the accurate description of the shear force-deformation response under bidirectional loading. A strain rate-independent, phenomenological model is presented which effectively represents the stiffness, damping, and degradation response of HDR bearings. The model decomposes the resisting force vector as the sum of an elastic component in the direction of the displacement vector and a hysteretic force component parallel to the velocity vector. The elastic component is obtained from a generalised Mooney—Rivlin strain energy function, and the hysteretic component is described by an approach similar to bounding sur-face plasticity. Degradation is decomposed into long term (“scragging”) and short term (“Mullins' effect”) components. Calibration is carried out over a series of bidirectional test data, and the model is shown to provide a good match of slow strain-rate experimental data using a unique set of material parameters for all tests. A testing protocol and calibration of the model for use in design of structures with HDR bearings are discussed.

Radial oscillations of thin cylindrical and spherical shells: investigation of Lie point symmetries for arbitrary strain-energy functions

The Lie point symmetry structure of the second order differential equations which describe non-linear radial oscillations of thin-walled hyperelastic cylindrical and spherical shells is investigated. The differential equations depend on the strain-energy function and on the net applied surface pressure. If the net applied surface pressure is time independent, the differential equations admit the Lie point symmetry corresponding to time translational invariance for arbitrary strain-energy functions. Other Lie point symmetries exist for each equation only for special classes of strain-energy function. For the cylindrical shell the special class includes the Mooney–Rivlin strain-energy function and the differential equation reduces to the Ermakov–Pinney equation. A new solution is obtained for a specific time dependent net applied surface pressure. For the spherical shell the special class does not include the Mooney–Rivlin strain-energy function. For free oscillations the differential equation reduces to the Ermakov–Pinney equation but there also exists a special net applied surface pressure and for this pressure the differential equation is more general than the Ermakov–Pinney equation.

On Non-Linear Radial Oscillations of an Incompressible, Hyperelastic Spherical Shell

Non-linear radial oscillations of a thin-walled spherical shell of incompressible isotropic hyperelastic material are considered. The oscillations are described by a second order differential equation which depends on the strain-energy function and the net applied pressure at the surfaces. The condition on the strain-energy function for the differential equation to be an Ermakov-Pinney equation is derived. It is shown the condition is not satisfied by a Mooney-Rivlin strain-energy function. The Lie point symmetry structure of the differential equation for a Mooney-Rivlin material is determined. Three approximate solutions are derived for free oscillations of a neo-Hookean material. The approximate solutions have the form of non-linear superpositions similar to the solutions for the non-linear radial oscillations of a thin-walled cylindrical tube.

Finite Amplitude Azimuthal Shear Waves in a Compressible Hyperelastic Solid

Lagrangian equations of motion for finite amplitude azimuthal shear wave propagation in a compressible isotropic hyperelastic solid are obtained in conservation form with a source term. A Godunov-type finite difference procedure is used along with these equations to obtain numerical solutions for wave propagation emanating from a cylindrical cavity, of fixed radius, whose surface is subjected to the sudden application of a spatially uniform azimuthal shearing stress. Results are presented for waves propagating radially outwards; however, the numerical procedure can also be used to obtain solutions if waves are reflected radially inwards from a cylindrical outer surface of the medium. A class of strain energy functions is considered, which is a compressible generalization of the Mooney-Rivlin strain energy function, and it is shown that, for this class, an azimuthal shear wave can not propagate without a coupled longitudinal wave. This is in contrast to the problem of finite amplitude plane shear wave propagation with the neo-Hookean generalization, for which a shear wave can propagate without a coupled longitudinal wave. The plane problem is discussed briefly for comparison with the azimuthal problem.

Non-linear radial oscillations of a thin-walled double-layer hyperelastic cylindrical tube

Non-linear radial oscillations of an infinitely long, double-layer, hyperelastic thin-walled cylindrical tube of incompressible material are considered. Conditions are derived on the strain-energy functions of each layer for the radial equation of motion to reduce to the Ermakov-Pinney equation. The conditions are satisfied by the Mooney-Rivlin strain-energy function. Non-linear superposition theory for the solution of the Ermakov-Pinney equation in terms of two linearly independent solutions of the time dependent linear harmonic oscillator equation is reviewed and applied. Exact solutions for the inner radius of the double-layer, thin-walled cylinder are derived for free oscillations and for the Heaviside step loading boundary condition. The radial oscillations of single-layer and double-layer cylindrical tubes of the same thickness and subjected to the same boundary conditions are analysed and compared. The conclusions deduced for the composite cylindrical tube may have application to the dynamics of composite bodies.

Thixotropic behaviour of rubber under dynamic loading histories: Experiments and theory

In the first part of this essay we investigate the thermomechanical behaviour of carbon black-filled rubber under dynamic loading conditions. The loadings consist of static predeformations which are superimposed by small sinusoidal oscillations. The frequency was varied between 0.1 Hz and 100 Hz, the deformation amplitude between 0.006 and 0.06, the temperature between 253 K and 373 K and the storage and dissipation moduli measured. The data show that the frequency dependence of the moduli is of the powerlaw type. They also depend on the deformation amplitude and the temperature. If the temperature is constant, increasing amplitudes lead to decreasing moduli. As discussed by Payne (1965), this behaviour can be interpreted in terms of a thixotropic change. If, on the other hand, the deformation amplitude is kept constant, increasing temperature levels lead to decreasing moduli. In the second part of this work we develop a constitutive theory to represent the material behaviour observed. We consider the dissipation principle of thermodynamics and formulate the model for three-dimensional finite deformations. To describe thermal expansion effects, we decompose the deformation gradient into a thermal and a mechanical part as proposed by Lu and Pister (1975). We prescribe the thermal part by a constitutive function and assume the mechanical part to be the driving force for the stress tensor. As motivated in earlier works we split the total stress into an equilibrium stress and a rate-dependent overstress. We represent the equilibrium stress using a modified Mooney-Rivlin strain energy function and the overstress by a series of Maxwell elements whose springs are of Neo-Hookean type. Both the kinematic tensors and the associated stress measures are defined by using the concept of dual variables proposed by Haupt and Tsakmakis (1989). In order to represent the thixotropic effects, the viscosities depend on the temperature and the deformation history. The history dependence is implied by an internal variable which is a measure for the deformation amplitude and has a relaxation property as discussed by Payne (1965). To determine the material parameters, we linearise the constitutive equations with respect to the static predeformation and take the analytical solution for harmonic strain-controlled loadings into account. Numerical simulations demonstrate that the constitutive theory describes all phenomena experimentally observed with a fairly good approximation. The model is compatible with the second law of thermodynamics in the form of the Clausius Duhem inequality.

Azimuthal shearing and transverse deflection of an annular elastic membrane

We consider an annular membrane which has its outer rim fixed and its inner rim displaced normal to the reference plane and twisted. The resulting deformation is assumed to be axisymmetric and a direct two-dimensional formulation is adopted. The analysis is based on the Mooney-Rivlin strain energy function for isotropic elastic solids. The formation of wrinkles is accommodated in an approximate way by introducing a relaxed strain energy function. We first study the problem without twist, including a case in which wrinkling occurs, and then we investigate the full problem with twisting present. In both cases, the equations of equilibrium are reduced to a first order system of ordinary differential equations and solved numerically. Using convexity conditions, we discuss the local stability of the computed deformations.

The dynamic response of a stretched circular hyperelastic membrane subjected to normal impact

Finite amplitude wave propagation in a circular isotropic hyperelastic membrane, initially subjected to an equibiaxial stretch which is followed by a suddenly applied pressure or normal impact of a projectile, is considered. Axially symmetric deformation is assumed, and the governing equations, in Lagrangian form, are expressed in terms of the principal components of Biot stress and the principal stretches. These equations are a system of first first order quasi-linear partial differential equations in conservation form with a source term. Solutions, obtained by the method of characteristics and a finite difference scheme, are presented graphically for particular cases of the Mooney-Rivlin strain energy function.