Details

Title

A finite element implementation of Knowles stored-energy function: theory, coding and applications

Journal title

Archive of Mechanical Engineering

Yearbook

2011

Volume

vol. 58

Numer

No 3

Authors

Keywords

elasticity tensor ; tangent ; modulus tensor ; material Jacobian ; hyperelasticity ; stored-energy potential ; constitutive equation ; finite element method ; FEM

Divisions of PAS

Nauki Techniczne

Coverage

319-346

Publisher

Polish Academy of Sciences, Committee on Machine Building

Date

2011

Type

Artykuły / Articles

Identifier

ISSN 0004-0738, e-ISSN 2300-1895

References

"<i>ABAQUS Verification Manual</i>", ABAQUS, Inc. Providence, 2008. ; Bonet J. (1997), Nonlinear continuum mechanics for finite element analysis. ; Bouchart V.: "<i>Experimental study and micromechanical modeling of the behavior and damage of reinforced elastomers</i>", Ph.D. thesis, University of Sciences and Technologies, 2008, Lille. ; Bouvard J. (2010), A general inelastic internal state variable model for amorphous glassy polymers, Acta Mechanica, 213, 71, doi.org/10.1007/s00707-010-0349-y ; Ciambella J. (2009), On the ABAQUS FEA model of finite viscoelasticity, Rubber Chemistry and Technology, 82, 2, 184, doi.org/10.5254/1.3548243 ; Dettmar J. (2000), A finite element implementation of Mooney-Rivlin's strain energy function in Abaqus. ; Elleuch R. (2006), Viscoelastic Behavior of HDPE Polymer using Tensile and Compressive Loading, Journal of Materials Engineering and Performance, 15, 1, 111, doi.org/10.1361/105994906X83475 ; Fung Y. (1969), Foundations of solid mechanics. ; Holzapfel G. (2010), Nonlinear solid mechanics. ; Jemioło S. (2002), A study on the hyperelastic properties of isotropic materials, 140. ; Knowles J. (1977), The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids, International Journal of Fracture, 13, 611, doi.org/10.1007/BF00017296 ; Knowles J. (1979), On the dissipation associated with equilibrium whocks in finite elasticity, Journal of Elasticity, 9, 131, doi.org/10.1007/BF00041322 ; Knowles J. (1980), Discontinous deformation gradients near the tip of a crack in finite anti-plane shear: an example, Journal of Elasticity, 10, 81, doi.org/10.1007/BF00043136 ; Miehe Ch. (1996), Numerical computation of algorithmic (consistent) tangent moduli in larde-strain computational inelasticity, Computer methods in applied mechanics and engineering, 134, 223, doi.org/10.1016/0045-7825(96)01019-5 ; Ogden R. (1997), Non-linear elastic deformations. ; Ogden R. (2003), Lecture Notes, 6. ; Ostrowska-Maciejewska J. (1994), Mechanics of deformable bodies. ; Ostrowska-Maciejewska J. (2007), Foundations and applications of tensor calculus. ; Perzyna P. (1966), Theory of viscoplasticity. ; Sobieski W. (2008), GNU Fortran with elements of data visualization. ; Soares J. P.: "<i>Constitutive modeling for biodegradable polymers for application in endovascular stents</i>", 2008, Ph.D. thesis, Texas A&M University. ; Soares J. (2010), Deformation-induced hydrolysis of a degradable polymeric cylindrical annulus, Biomechanics and Modeling in Mechanobiology, 9, 177, doi.org/10.1007/s10237-009-0168-z ; Stein E. (2008), Convergence behavior of 3D finite elements for Neo-Hookean material, Engineering Computations: International Journal for Computer-Aided-Engineering and Software, 25, 3, 220, doi.org/10.1108/02644400810857065 ; Skalski K. (2011), Technical Mechanics part XII: Biomechanics. ; Weiss J. A.: "<i>A constitutive model and finite element representation for transversely isotropic soft tissues</i>", 1994, Ph.D. thesis, University of Utah, Salt Lake City.

DOI

10.2478/v10180-011-0021-7

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