On the implementation of a wrinkling, hyperelastic membrane model for skin and other materials

References

• Arcaro VF. 2007. Finite element analysis of 3D isotropic membrane structures. Campinas, Brazil: Vinicius F. Arcaro; [cited 2008 June 16]. Available from: http://www.arcaro.org/tension/main.htm
   Google Scholar
• Arruda , EM and Boyce , MC . 1993 . A three-dimensional constitutive model for the large stretch behaviour of rubber elastic materials . J Mech Phys Solids , 41 : 389 – 412 .
   Web of Science ®Google Scholar
• Bischoff , JE , Arruda , EM and Grosh , K . 2000 . Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model . J Biomech , 33 : 645 – 652 .
   PubMed Web of Science ®Google Scholar
• Bouzidi , R and Van , AL . 2004 . Numerical solution of hyperelastic membranes by energy minimisation . Comput Struct , 82 : 1961 – 1969 .
   Google Scholar
• Crisfield , MA . 1991 . Non-linear finite element analysis of solids and structures , Chichester : Wiley .
   Google Scholar
• Crisfield , MA . 1997 . Non-linear finite element analysis of solids and structures. Volume 2: advanced topics , Chichester : Wiley .
   Google Scholar
• Crisfield , MA and Wills , J . 1989 . Analysis of R/C panels using different concrete models . J Eng Mech ASCE , 115 ( 3 ) : 578 – 597 .
   Google Scholar
• Da Costa , V , Wei , R , Lim , R , Sun , CH , Brown , JJ and Wong , BJ . 2008 . Nondestructive imaging of live human keloid and facial tissue using multiphoton microscopy . Arch Facial Plast Surg , 10 ( 1 ) : 38 – 43 .
   Google Scholar
• Danielson , DA . 1973 . Human skin as an elastic membrane . J Biomech , 6 ( 5 ) : 539 – 546 .
   Google Scholar
• Delalleau , A , Josse , G , Lagarde , JM , Zahouani , H and Bergheau , JM . 2006 . Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test . J Biomech , 39 ( 9 ) : 1603 – 1610 .
   PubMed Web of Science ®Google Scholar
• Diaby , A , Van , AL and Wielgosz , C . 2006 . Buckling and wrinkling of prestressed membranes . Finite Elem Anal Des , 42 : 992 – 1001 .
   Google Scholar
• Diridollou , S , Black , D , Lagarde , JM , Gall , Y , Berson , M , Vabre , V , Patat , F and Vaillant , L . 2000 . Sex- and site-dependent variations in the thickness and mechanical properties of human skin in vivo . Int J Cosmet Sci , 22 ( 6 ) : 421 – 435 .
   PubMedGoogle Scholar
• Dunn , MG , Silver , FH and Swann , DA . 1985 . Mechanical analysis of hypertrophic scar tissue: structural basis for apparent increased rigidity . J Invest Dermatol , 84 : 9 – 13 .
   PubMed Web of Science ®Google Scholar
• Evans SL, Holt CA, Mahmud J, Ozturk H, Saidi K, Shrive NG. 2007a. Measuring the mechanical properties of skin using digital image correlation and nonlinear finite element analysis. Paper presented at: 2nd International Conference on Mechanics of Biomaterials and Tissues, Kauai, Hawaii.
   Google Scholar
• Evans SL, Holt CA, Ozturk H, Saidi K, Shrive NG. 2007b. Measuring soft tissue properties using digital image correlation and finite element modelling. Paper presented at: 13th International Conference on Experimental Mechanics, Alexandroupolis, Greece.M
   Google Scholar
• Flynn , C and McCormack , BA . 2008 . A simplified model of scar contraction . J Biomech , 41 ( 7 ) : 1582 – 1589 .
   Google Scholar
• Gil , AJ and Bonet , J . 2006 . Finite element analysis of prestressed structural membranes . Finite Elem Anal Des , 42 : 683 – 697 .
   Google Scholar
• Hager , WW and Zhang , H. 2005 . A new conjugate gradient method with guaranteed descent and an efficient line search . SIAM J Optimization , 16 : 170 – 192 .
   Web of Science ®Google Scholar
• Hencky , H . 1915 . On the stress state in circular plates with vanishing bending stiffness . Z Math Phys , 63 : 311 – 317 .
   Google Scholar
• Hendriks , FM , Brokken , D , van Eemeren , JTWM , Oomens , CWJ , Baaijens , FPT and Horsten , JBAM . 2003 . A numerical–experimental method to characterize the non-linear mechanical behaviour of human skin . Skin Res Technol , 9 ( 3 ) : 274 – 283 .
   PubMed Web of Science ®Google Scholar
• Hendriks , FM , Brokken , D , Oomens , CWJ , Bader , DL and Baaijens , FPT . 2006 . The relative contribution of different skin layers to the mechanical behaviour of human skin in vivo using suction experiments . Med Eng Phys , 28 : 259 – 266 .
   PubMed Web of Science ®Google Scholar
• Holzapfel , GA . 2000 . Nonlinear solid mechanics: a continuum approach for engineering , Chichester : Wiley .
   Google Scholar
• Jacquet , E , Josse , G , Khatyr , F and Garcin , C . 2008 . A new experimental method for measuring skin's natural tension . Skin Res Technol , 14 ( 1 ) : 1 – 7 .
   Google Scholar
• Jansen , LH and Rottier , PB . 1958 . Some mechanical properties of human abdominal skin measured on excised strips: a study of their dependence on age and how they are influenced by the presence of striae . Dermatologica , 117 : 65 – 183 .
   Google Scholar
• Kvistedal YA. 2004. Investigating stress–strain properties of in vivo human skin using multiaxial loading experiments and finite element modelling [thesis]. [Auckland]: University of Auckland.
   Google Scholar
• Lanir , Y . 1983 . Constitutive equations for fibrous connective tissues . J Biomech , 16 ( 1 ) : 1 – 12 .
   PubMed Web of Science ®Google Scholar
• Miller , RK , Hedgepeth , JM , Weingarten , VI , Das , P and Kahyai , S . 1985 . Finite element analysis of partly wrinkled membranes . Comput Struct , 20 ( 1–3 ) : 631 – 639 .
   Google Scholar
• Newton , TA . 1990 . A simple algorithm for finding eigenvalues and eigenvectors for 2 × 2 matrices . Am Math Mon , 97 ( 1 ) : 57 – 60 .
   Google Scholar
• Ogden , RW . 1972 . Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubberlike solids . Proc R Soc Lond , 326 : 565 – 584 .
   Web of Science ®Google Scholar
• Roddeman , DG , Drukker , J , Oomens , CW and Janssen , JD . 1987 . The wrinkling of thin membranes. Parts I & II . Trans ASME: J Appl Mech , 54 ( 4 ) : 884 – 892 .
   Google Scholar
• Shergold , OA and Fleck , NA . 2004 . Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin . Proc R Soc Lond A , 460 ( 2050 ) : 3037 – 3058 .
   Web of Science ®Google Scholar
• Stekelenburg , A , Oomens , CWJ , Strijkers , GJ , Nicolay , K and Bader , DL . 2006 . Compression-induced deep tissue injury examined with magnetic resonance imaging and histology . J Appl Physiol , 100 ( 6 ) : 1946 – 1954 .
   PubMed Web of Science ®Google Scholar
• Tong , P and Fung , YC . 1976 . The stress–strain relationship for the skin . J Biomech , 9 ( 10 ) : 649 – 657 .
   PubMedGoogle Scholar
• Valanis , KC and Landel , RF . 1978 . The strain–energy function for a hyperelastic material in terms of extension ratios . J Appl Phys , 11 : 1969 – 1978 .
   Google Scholar
• Wagner , H . 1929 . Flat sheet metal girder with very thin metal web . Z Flugtechnik Motorlurftschiffahrt , 20 : 200 – 314 .
   Google Scholar
• Wu , X , Levenston , ME and Chaikof , EL . 2006 . A constitutive model for protein-based materials . Biomaterials , 27 ( 30 ) : 5315 – 5325 .
   Google Scholar