Stochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case

In this research, an incompressible, isotropic, nonlinear elastic rectangular block and a circular cylindrical sector are studied under bending and straightening moments, respectively. Analytical approaches are presented on implementing of the left Cauchy–Green tensor and Cauchy stresses. In addition, finite element analysis of both problems is carried out using UHYPER user-defined subroutine in ABAQUS to verify the analytical methods. Four different invariant-based strain energy functions, including neo-Hookean, Mooney–Rivlin, Arruda–Boyce, and recently proposed polynomial Exp-Exp models, are examined, and the results are compared. Material parameters of silicon rubber for the strain energy functions are identified by applying an optimization procedure. Finite element method results confirmed the analytical approach with great compatibility. Results showed that the length of the unbent beam does not affect the stress. Likewise, the initial angle of curved structure does not affect the unbending moment and stresses. Moreover, the Exp-Exp model had a slightly different result rather than other strain energies, which means that this model is more conservative than its counterparts. Furthermore, the Exp-Exp strain energy function is calibrated for tissue-like phantom and is compared with experimental data.

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On the identifiability of the stored energy function of hyperelastic materials from sensor data at the boundary

Inverse Problems ◽

10.1088/0266-5611/30/10/105002 ◽

2014 ◽

Vol 30 (10) ◽

pp. 105002 ◽

Cited By ~ 6

Author(s):

Thomas Schuster ◽

Arne Wöstehoff

Keyword(s):

Energy Function ◽

Sensor Data ◽

Stored Energy ◽

Hyperelastic Materials

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MATHEMATICAL ANALYSIS OF NONLINEAR BONDED JOINT MODELS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202504003349 ◽

2004 ◽

Vol 14 (04) ◽

pp. 535-556 ◽

Cited By ~ 10

Author(s):

FRANCOISE KRASUCKI ◽

ARNAUD MÜNCH ◽

YVES OUSSET

Keyword(s):

Mathematical Analysis ◽

Energy Function ◽

Three Dimensional ◽

Expansion Method ◽

Limit Problem ◽

Stored Energy ◽

Joint Models ◽

Numerical Application ◽

Energy Functions ◽

The One

Within the framework of nonlinear elasticity, we consider the problem of two adherents joined along their common surface by a thin soft adhesive. Two stored energy functions are considered: the stored energy function of Saint Venant–Kirchhoff and the stored energy function of Ciarlet–Geymonat. Using the asymptotic expansion method, the limit energy associated to each of these stored energy functions is obtained. The aim of this paper is to give a rigorous mathematical analysis of the formally derived limit problem. We show that the limit problem associated to the Saint Venant–Kirchhoff case admits at least one solution and the limit problem associated to the Ciarlet–Geymonat case admits exactly one solution. An analytical comparison in the one-dimensional case and a three-dimensional numerical application are also presented.

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A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications

Archive of Mechanical Engineering ◽

10.2478/v10180-011-0021-7 ◽

2011 ◽

Vol 58 (3) ◽

pp. 319-346 ◽

Cited By ~ 16

Author(s):

Cyprian Suchocki

Keyword(s):

Finite Element ◽

Energy Function ◽

Function Theory ◽

Constitutive Models ◽

Elasticity Tensor ◽

Stored Energy ◽

Energy Potential ◽

Hyperelastic Materials ◽

Finite Element Implementation ◽

Living Tissues

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

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