Ogden Strain Energy Function Research Articles

Constitutive behaviors of a silicone rubber at high strain rates

Silicone rubber is a macromolecule polymer, and can suffer a large deformation. In the paper, the silicone rubber specimens are tested at a series of strain rates by modified SHPB techniques. Based on the experimental data, a constitutive model of the silicone rubber is built up based on Ogden strain energy functions. An interesting phenomenon- localized damage cycle, so called lag circle- shows up in the tested specimen under high strain-rates loading. The diameters of the damage cycle are associated with strain-rate and specimen's size. A formulation about the relations between the diameter and the strain-rate, specimen's size is presented.

고무부품의 유한요소해석을 위한 재료시험 및 비선형 재료물성에 관한 연구

Mechanical testing methods to determine the material constants for large deformation nonlinear finite element analysis were demonstrated for natural rubber. Uniaxial tension, uniaxial compression, equi-biaxial tension and pure shear tests of rubber specimens are performed to achieve the stress-strain curves. The stress-strain curves are obtained after between 5 and 10 cycles to consider the Mullins effect. Mooney and Ogden strain-energy density functions, which are typical form of the hyperelastic material, are determined and compared with each other. The material constants using only uniaxial tension data are about 20% higher than those obtained by any other test data set. The experimental equations of shear elastic modulus on the hardness and maximum strain are presented using multiple regression method. Large deformation finite element analysis of automotive transmission mount using different material constants is performed and the load-displacement curves are compared with experiments. The selection of material constant in large deformation finite element analysis depend on the strain level of component in service.br/

Heel–shoe interactions and the durability of EVA foam running-shoe midsoles

A finite element analysis (FEA) was made of the stress distribution in the heelpad and a running shoe midsole, using heelpad properties deduced from published force-deflection data, and measured foam properties. The heelpad has a lower initial shear modulus than the foam (100 vs. 1050 kPa), but a higher bulk modulus. The heelpad is more non-linear, with a higher Ogden strain energy function exponent than the foam (30 vs. 4). Measurements of plantar pressure distribution in running shoes confirmed the FEA. The peak plantar pressure increased on average by 100% after 500 km run. Scanning electron microscopy shows that structural damage (wrinkling of faces and some holes) occurred in the foam after 750 km run. Fatigue of the foam reduces heelstrike cushioning, and is a possible cause of running injuries.

Modelling Indentation of Bread Crumb by Finite Element Analysis

Finite element analysis (FEA) has the potential for shedding light on the complex mechanical behaviour of many food products. In this paper, the *HYPERFOAM material model in the ABAQUS/Standard FEA package was applied to study the mechanical properties of the crumb of white bread loaves. The applicability of this material model was validated by uniaxial compression stress–strain data. Overall stress–strain curves of low-density bread crumb were well predicted by FEA; altering Poisson's ratio in the simulations (0 and 0·21) made little difference unless the strain was greater than 0·35 for denser crumbs. Experimental compressive Young's modulus and critical stress were well correlated to their counterparts predicted from the FEA material constants in the Ogden strain energy function. The crumb, with characteristics defined by the compressive material constants, was meshed by four-node axisymmetric continuum elements of uniform size to simulate indentation of the crumb. Two cylindrical flat-ended and two spherical indenters were modelled as *RIGID SURFACE. With the axisymmetric indentation FEA model, the load–displacement curves generated from cylindrical indentation were well predicted, whereas those from spherical indenters were under-predicted.

Finite deformations of a hyperelastic, compressible and fibre reinforced tube

Finite torsion and axial stretch of a long, hyperelastic, compressible and circular tube is studied for the design of a prototype of small diameter vascular prosthesis. The analysis is carried out in the context of the finite elasticity theory by using a class of Ogden strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The highly non-linear differential equations with variable coefficients governing the problem are solved numerically using a Runge–Kutta method. For different prestresses supported by the tube, the effects of the combined deformation on the stress distributions are presented.

Finite element analysis of base isolated buildings subjected to earthquake loads

A finite element formulation modelling hyperelastic quasi-incompressible rubber-like materials (elastomers) is developed which takes into account large displacements and large elastic strains as well as inelastic effects. The capacity of laminated rubber-like materials to support high loads in compression and large displacements in shear is the principal reason for their use in devices for seismic base isolation of structures. The energy-dissipation capacity of these devices is increased by using high damping rubber, which is an elastomer incorporating carbon black particles, or having lead-plug insertion. The Ogden strain energy function has been used as a basis for the material model implemented in a total Lagrangian formulation, the strain being decomposed into its deviatory and volumetric parts and the pressure variable being condensed at element level. Mooney–Rivlin and neo-Hooke strain energy functions can also be used by simply changing the parameters of the model. The stress–strain hysteresis, which appears when these devices are subjected to dynamic or quasi-static cyclic loads, has been modelled by frequency dependent viscoelastic and plastic constitutive models. The bearings have been modelled by means of an equivalent single element capable of describing the composite behaviour of the actual isolation system. The proposed model is validated using available experimental results and it is proved to be a powerful tool in dealing with different bearings. Finally, results for a six-storey base isolated building subjected to the El Centro earthquake are given. Copyright © 1999 John Wiley & Sons, Ltd.

On the Ogden Strain-Energy Function

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.

The relaxation and deformational properties of a carbon‐black filled elastomer in biaxial tension

AbstractBiaxial stress relaxation data acquired for a carbon‐black‐filled elastomer are analyzed. Consistent with previously published simple‐tension and pure‐shear results for this elastomer, the biaxial relaxation behavior is also found to be a separable function of time and strain effects. A departure from separability is observed at the larger strain; this might be a manifestation of strain‐induced crystallization. An analysis of the biaxial results together with the earlier reported simple‐tension and pure‐shear data reveals that the deformational dependence of this elastomer obeys the Valanis—Landel hypothesis up to moderate deformations. The Ogden strain energy function is found to be an excellent analytical representation of all of the multiaxial data. Large relative errors found at small tensile strains between the data and the Ogden fit are attributed to carbon black structural effects.

Wave speeds in rotating thick-walled elastic tubes

The wave speeds in rotating thick-walled circular cylinders of incompressible, isotropic, hyperelastic material at finite deformation are investigated. It is proved that pure torsional, longitudinal and breathing mode vibrations no longer exist when rotation is initiated. Numerical results are given for a number of different situations when an empirical three term Ogden strain-energy function is used. Comparisons are made with the corresponding results for membrane shells and solid cylinders.

Surface instabilities on an equibiaxially stretched elastic half-space

The existence of non-homogeneous modes of deformation in an equibiaxially stretched elastic half-space is investigated. The surface of the half-space is assumed to be traction-free.It is shown that three different eigenmodal deformations are possible, according as the cube of the critical stretch is greater than, less than, or equal to ¾.For the class of strain-energy functions due to Ogden (9), necessary conditions for bifurcation are deduced-for equibiaxial tension. Results are given and discussed for single-term, as well as two- and three-term Ogden strain-energy functions, for equibiaxial tension and compression.

The deformation of rubber cylinders and tubes by rotation

AbstractA detailed analytical and numerical study is made of the deformation of highly elastic circular cylinders and tubes produced by steady rotation about the axis of symmetry. Explicit results are obtained through the use of Ogden's strain–energy function for incompressible isotropic elastic materials which, as well as being analytically convenient, is capable of reproducing accurately the observed isothermal behaviour of vulcanized rubber over a wide range of deformations. The three problems of steady rotation considered here concern (i) a tube shrink-fitted to a rigid spindle, (ii)an unconstrained tube, and (iii) a solid cylinder. In each case a set of restictions on the material constans appearing in the strain–energy function is stated which ensures that a tubular of cylindrical shape-preserving deformation exists for all angular spees and that, for problems (i) and (iii), there is no other solution. In connection with problems (ii) and (iii) values of the material constans are also given which correspond to the bifuraction or non-existence of soultions. Enegry consideration are used to determine the local stability of the various solutions obtained.