Pointwise identification of elastic properties in nonlinear hyperelastic membranes-part II: experimental validation

Journal of Applied Mechanics, Transactions ASME

Volumn 76, Issue 6, 2009, Pages 1-8

  Zhao, Xuefeng ^a   Chen, Xiaolin ^b   Lu, Jia ^a  

^a UNIVERSITY OF IOWA   (United States)

^b WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Finite inflation test; Inverse elastostatics; Inverse method; Nonlinear membrane; Parameter identification

Indexed keywords

COMPUTATIONAL DEVELOPMENT; DEFORMED STATE; ELASTIC PARAMETERS; ELASTIC PROPERTIES; EXPERIMENTAL VALIDATIONS; FINITE ELEMENT; GAUSS POINT; HYPERELASTIC MEMBRANES; IDENTIFICATION METHOD; IN-PLANE; INVERSE METHODS; MATERIAL BEHAVIOR; MATERIAL MODELS; NONLINEAR MEMBRANE; OGDEN MODEL; PHYSICAL MEASUREMENT; PREDICTIVE CAPABILITIES; STRESS STRAIN CHARACTERISTICS; SURFACE MESH; THREE-DIMENSIONAL RECONSTRUCTION;

BALLOONS; ELASTICITY; INVERSE PROBLEMS; PARAMETER ESTIMATION; THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

EID: 77249105596     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3130810     Document Type: Article

References (32)

1. Lu, J., and Zhao, X., 2009, "Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes-Part I: Theoretical and Computational Developments," ASME J. Appl. Mech., 76, p. 061013.
2. Rivlin, R. S., and Saunders, D. W., 1951, "Large Elastic Deformations of Isotropic Materials-VII. Experiments on the Deformation of Rubber," Proc. R. Soc. London, Ser. A, 243, pp. 251-288.
3. Govindjee, S., and Mihalic, P. A., 1996, "Computational Methods for Inverse Finite Elastostatics," Comput. Methods Appl. Mech. Eng., 136, pp. 47-57.
4. Govindjee, S., and Mihalic, P. A., 1998, "Computational Methods for Inverse Deformations in Quasi-Incompressible Finite Elasticity," Int. J. Numer. Methods Eng., 43, pp. 821-838.
5. Lu, J., Zhou, X., and Raghavan, M. L., 2007, "Inverse Elastostatic Stress Analysis in Pre-Deformed Biological Structures: Demonstration Using Abdominal Aortic Aneurysm," J. Biomech., 40, pp. 693-696.
6. Lu, J., Zhou, X., and Raghavan, M. L., 2007, "Computational Method of Inverse Elastostatics for Anisotropic Hyperelastic Solids," Int. J. Numer. Methods Eng., 69, pp. 1239-1261.
7. Lu, J., Zhou, X., and Raghavan, M. L., 2008, "Inverse Method of Stress Analysis for Cerebral Aneurysms," Biomech. Model. Mechanobiol., 7, pp. 477-486.
8. Zhou, X., and Lu, J., 2008, "Inverse Formulation for Geometrically Exact Stress Resultant Shells," Int. J. Numer. Methods Eng., 74, pp. 1278-1302.
9. Luhmann, T., Robson, S., Kyle, S., and Harley, I., 2006, Close Range Photogrammetry: Principles, Techniques and Applications, Whittles Publishing, Dunbeath, Caithness, Scotland, UK.
10. Humphrey, J. D., 2002, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer, New York.
11. Rossettos, J. N., 1966, "Nonlinear Membrane Solutions for Symmetrically Loaded Deep Membranes of Revolution," NASA Technical Report No. NASA TN D-3297.
12. Wu, C. H., and Peng, D. Y. P., 1972, "On the Asymptotically Spherical Deformation of Arbitrary Membranes of Revolution Fixed Along an Edge and Inflated by Large Pressures-A Nonlinear Boundary Layer Phenomenon," SIAM J. Appl. Math., 23, pp. 133-152.
13. Hayes, M., and Knops, R. B., 1966, "On Universal Relations in Elasticity Theory," Z. Angew. Math. Phys., 17, pp. 636-639.
14. Beatty, M. F., 1987, "A Class of Universal Relations in Isotropic Elasticity," J. Elast., 17, pp. 113-121.
15. Beatty, M. F., 1989, "A Class of Universal Relations for Constrained, Isotropic Elasticity Materials," Arch. Mech., 80, pp. 299-312.
16. Pucci, E., and Saccomandi, G., 1997, "On Universal Relations in Continuum Mechanics," Continuum Mech. Thermodyn., 9, pp. 61-72.
17. Rivlin, R. S., 2000, "Universal Relations for Elastic Materials," Rendiconti di Matematica e delle sue Applicazioni, Serie VII, 20, pp. 35-55.
18. Rivlin, R. S., 1948, "Large Elastic Deformations of Isotropic Materials, IV. Further Developments of the General Theory," Proc. R. Soc. London, Ser. A, 241, pp. 368-397.
19. Green, A. E., and Adkins, J. E., 1960, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon, Oxford.
20. Treloar, L. R. G., 1944, "Stress-Strain Data for Vulcanized Rubber Under Various Types of Deformation," Trans. Faraday Soc., 40, pp. 59-70.
21. Valanis, K. C., and Landel, R. F., 1967, "The Strain-Energy Function of a Hyperelastic Material in Terms of the Extension Ratios," J. Appl. Phys., 38, pp. 2997-3002.
22. Ogden, R. W., 1972, "Large Deformation Isotropic Elasticity-On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids," Proc. R. Soc. London, Ser. A, 326, pp. 565-584.
23. Ogden, R. W., 1982, "Elastic Deformation of Rubberlike Solids," Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, H. G. Hopkins and M. J. Sewell, eds., Pergamon, Oxford, pp. 499-537.
24. Treloar, L. R. G., 1976, "The Mechanics of Rubber Elasticity," Proc. R. Soc. London, Ser. A, 351, pp. 301-330.
25. Gruttmann, F., and Taylor, R. L., 1992, "Theory and Finite Element Formulation of Rubberlike Membrane Shells Using Principal Stretches," Int. J. Numer. Methods Eng., 35, pp. 1111-1126.
26. Sun, W., and Sacks, M. S., 2005, "Finite Element Implementation of a Generalized Fung-Elastic Constitutive Model for Planar Soft Tissues," Biomech. Model. Mechanobiol., 4, pp. 190-199.
27. Gill, P. E., Murray, W., and Saunders, M. A., 2005, "SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization," SIAM Rev., 47, pp. 99- 131.
28. Humphrey, J. D., Strumpf, R. K., and Yin, F. C. P., 1990, "Determination of a Constitutive Relation for Passive Myocardium, II. Parameter-Estimation," ASME J. Biomech. Eng., 112(3), pp. 340-346.
29. Taylor, R. L., 2003, FEAP User Manual, V7.5.
30. Belytschko, T., Liu, W. K., Organ, D., Fleming, M., and Krysl, P., 1996, "Meshless Methods: An Overview and Recent Developments," Comput. Methods Appl. Mech. Eng., 139, pp. 3-47.
31. Li, S., and Liu, W. K., 2002, "Meshfree and Particle Methods and Their Application," Appl. Mech. Rev., 55, pp. 1-34.
32. Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., 2005, "Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement," Comput. Methods Appl. Mech. Eng., 194, pp. 4135-4195.