Mixed and Penalty Finite Element Models for the Nonlinear Behavior of Biphasic Soft Tissues in Finite Deformation: Part II — Nonlinear Examples

References

• Almcida , E. S. and Spilker , R. L. ( 1997 ). 'Mixed and penalty finite element models for the nonlinear behavior of biphusic soft tissues in finite deformation: Part I — Alternate formulations' , Int J of Comp Meth in biomech and biomed Engng , 1 , pp. 25 – 46 .
   PubMedGoogle Scholar
• Fortin , M. ( 1981 ). 'Old and new finite elements for incompressible flows' , Int. J. Num. Meth. Fluids , 1 , pp. 347 – 364 .
   Web of Science ®Google Scholar
• Fortin , M. and Fortin , A. ( 1985 ). “ Newer and newer elements for incompressible flow ”, Finite Elements in Fluids , R. H. Gallagher et al., John Wiley and Sons. pp. 171 – 187 .
   Google Scholar
• Ruas , V. ( 1985 ). 'Finite element solution of 3D viscous flow problems using nonstandard degrees of freedom' , Japan Journal of Applied Mathematics , 2 , pp. 415 – 431 .
   Google Scholar
• Almeida , E. S. ( 1995 ). “ Finite Element Formulations for Biological Soft Hydrated Tissues Under Finite Deformation ”, PhD, Rensselaer Polytechnic Institute.
   Google Scholar
• Almeida , E. S. and Spilker , R. L. ( 1997 ). 'An evaluation of mixed and penalty biphasic elements using the linear confined compression problem' , Int. J. Num. Meth. in Engng. , (in review).
   Google Scholar
• Holmes , M. and Mow , V. ( 1990 ). 'The nonlinear characteristics of soft polyelectrolyte gels and hydrated connective tissues in ultrafiltration' , J. biomech. , 23 , pp. 1145 – 1156 .
   PubMed Web of Science ®Google Scholar
• Reed , M. B. ( 1984 ). 'An investigation of numerical errors in the analysis of consolidation by finite elements' , Int. J. Num. and Anal. Meth. Geomech. , 8 , pp. 243 – 257 .
   Google Scholar
• Vermeer , P. A. and Verruijt , A. ( 1981 ). 'An accuracy condition for consolidation by finite elements' , Int. J. Num. and Anal. Meth. Geomech. , 5 , pp. 1 – 14 .
   Web of Science ®Google Scholar
• Holmes , M. H. ( 1986 ). 'Finite deformation of soft tissue: Analysis of a mixture model in uni-axial compression' , J. biomech. Engng. , 108 , pp. 372 – 381 .
   PubMed Web of Science ®Google Scholar
• Suh , J. -K. ( 1989 ). “ A Finite Element Formulation for Nonlinear Behavior of Biphasic Hydrated Soft Tissue Under Finite Deformation ”, Ph.D., Rensselaer Polytechnic Institute. ,
   Google Scholar
• Spilker , R. L. and Suh , J. -K. ( 1990 ). 'Formulation and evaluation of a finite element model of soft hydrated tissue' , Computers and Structures , 35 , pp. 425 – 439 .
   Google Scholar
• Fung , Y. C. ( 1993 ). Biomechanics: Mechanical Properties of Living Tissues. , 2nd Edition, New York , NY , Springer-Verlag.
   Google Scholar
• Mow , V. C. , Ratcliffe , A. and Poole , A. R. ( 1992 ). 'Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures' , Biomat. , 13 , pp. 67 – 97 .
   PubMed Web of Science ®Google Scholar
• Soslowsky , L. J. , Flatow , E. L. , Bigliani , L. U. , Pawluk , R. J. , Ateshian , G. A. and Mow , V. C. ( 1992 ), 'Quantitation of in situ contact areas at the glenohumeral joint: A biomechanical study' , J. Orthop. Res. , 10 , pp. 524 – 534 .
   PubMed Web of Science ®Google Scholar
• Soslowsky , L. J. ( 1991 ). “ Studies on Diarthrodial Joint Biomechanics with Special to the Shoulder ”, Ph. D. , Columbia University.
   Google Scholar
• Donzelli , P. S. ( 1995 ). “ A Mixed-Penalty Contact Finite Element Formulation for Biphasic Soft Tissues ”, PhD, Rensselaer Polytechnic Institute.
   Google Scholar
• Donzelli , P. S. and Spilker , R. L. ( 1985 ). “ Investigation of gleno-humeral contact by the finite element method ”, Transactions of the Orthopaedic Research Society , Orlando , FL , ORS., pp. 684.
   Google Scholar
• Donzelli , P. S. , Spilker , R. L. , Ateshian , G. A. and Mow , V. C. ( 1997 ). 'A finite element investigation of contact between transversely isotropic layers of biphasic tissue'. J. Biomech. , (submitted for publication).
   Google Scholar
• Hou , J. S. , Holmes , M. H. , Lai , W. M. and Mow , V. C. ( 1989 ). 'Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications'. J. Biomech. Engng. , 111 , pp. 78 – 87 .
   PubMed Web of Science ®Google Scholar
• Suh , J.-K. , Spilker , R. L. and Holmes , M. H. ( 1991 ). ‘A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation ’. Int. J. Num. Meth. in Engng. , 32 , pp. 1411 – 1439 .
   Web of Science ®Google Scholar
• Cohen , B. , Gardner , T. R. and Ateshian , G. A. ( 1993 ). “ The influence of transverse isotropy on cartilage indentation behavior — A study of the human humeral head ”. Transactions Orthopaedic Research Society , Chicago , ORS. pp, 185.
   Google Scholar
• Bathe , K. J. ( 1982 ). Finite Element Procedures in Engineering Analysis , Englewood Cliffs , NJ , Prentice-Hall.
   Google Scholar