Abstract
The objective of this chapter is to provide a structured review of constitutive models of skin mechanics valid for finite deformations, with special emphasis on state-of-the-art anisotropic formulations which are essential in most advanced modelling applications. The fundamental structural and material characteristics of the skin, necessary for understanding its mechanics and for the formulation of constitutive equations, are briefly presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burns T et al (2004) Rook’s textbook of dermatology, 7th edn. Blackwell Science, Oxford
Silver FH, Siperko LM, Seehra GP (2003) Mechanobiology of force transduction in dermal tissue. Skin Res Technol 9(1):3–23
Dandekar K, Raju BI, Srinivasan MA (2003) 3-D finite-element models of human and monkey fingertips to investigate the mechanics of tactile sense. J Biomech Eng-Trans ASME 125(5):682–691
Xu F, Lu T (2011) Introduction to skin biothermomechanics and thermal pain. Springer, Heidelberg, p 414
Limbert G (2017) Mathematical and computational modelling of skin biophysics – a review. Proc R Soc A Math Phys Eng Sci 473(2203):1–39
Jor JWY et al (2013) Computational and experimental characterization of skin mechanics: identifying current challenges and future directions. Wiley Interdiscip Rev Syst Biol Med 5(5):539–556
Benítez JM, Montáns FJ (2017) The mechanical behavior of skin: structures and models for the finite element analysis. Comput Struct 190:75–107
Li W (2015) Modelling methods for in vitro biomechanical properties of the skin: a review. Biomed Eng Lett 5(4):241–250
Fung YC (1981) Biomechanics: mechanical properties of living tissues. Springer, New York
Humphrey JD (2003) Continuum biomechanics of soft biological tissues. Proc R Soci A Math Phys Eng Sci 459(2029):3–46
Lanir Y (2016) Multi-scale structural modeling of soft tissues mechanics and mechanobiology. J Elast 129(1–2):7–48
Hamed J, Matthew BP (2018) Skin mechanical properties and modeling: a review. Proc Inst Mech Eng Part H J Eng Med 232:323–343. https://doi.org/10.1177/0954411918759801
Shimizu H (2007) Shimizu’s textbook of dermatology. Hokkaido University Press - Nakayama Shoten, Sapporo, p 564
Buganza Tepole A, Kuhl E (2014) Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Comput Methods Biomech Biomed Eng 19:13–30
Kvistedal YA, Nielsen PMF (2009) Estimating material parameters of human skin in vivo. Biomech Model Mechanobiol 8(1):1–8
Lanir Y (1987) Skin mechanics. In: Skalak R, Chien S (eds) Handbook of bioengineering. McGraw-Hill, New York
Vierkötter A, Krutmann J (2012) Environmental influences on skin aging and ethnic-specific manifestations. Dermato-endocrinol 4(3):227–231
Silver FH, Freeman JW, DeVore D (2001) Viscoelastic properties of human skin and processed dermis. Skin Res Technol 7(1):18–23
Limbert G (2014) State-of-the-art constitutive models of skin biomechanics. In: Querleux B (ed) Computational biophysics of the skin. Pan Stanford, Singapore, pp 95–131
Marieb EN, Hoehn K (2010) Human anatomy & physiology, 8th edn. Pearson International Edition, San Francisco, p 1114
Chan LS (1997) Human skin basement membrane in health and autoimmune diseases. Front Biosci 2:343–352
Leyva-Mendivil MF et al (2015) A mechanistic insight into the mechanical role of the stratum corneum during stretching and compression of the skin. J Mech Behav Biomed Mater 49(0):197–219
Leyva-Mendivil MF et al (2017) Skin microstructure is a key contributor to its friction behaviour. Tribol Lett 65(1):12
Biniek K, Levi K, Dauskardt RH (2012) Solar UV radiation reduces the barrier function of human skin. Proc Natl Acad Sci USA 109(42):17111–17116
Wu KS, van Osdol WW, Dauskardt RH (2006) Mechanical properties of human stratum corneum: effects of temperature, hydration, and chemical treatment. Biomaterials 27(5):785–795
Ciarletta P, Ben Amar M (2012) Papillary networks in the dermal-epidermal junction of skin: a biomechanical model. Mech Res Commun 42:68–76
Burgeson RE, Christiano AM (1997) The dermal-epidermal junction. Curr Opin Cell Biol 9:651–658
Ribeiro JF et al (2013) Skin collagen fiber molecular order: a pattern of distributional fiber orientation as assessed by optical anisotropy and image analysis. PLoS One 8(1):e54724
Gosline J et al (2002) Elastic proteins: biological roles and mechanical properties. Philos Trans R Soc Lond B Biol Sci 357(1418):121–132
Sherratt MJ (2013) Age-related tissue stiffening: cause and effect. Adv Wound Care 2(1):11–17
Langer K (1861) Zur Anatomie und Physiologie der Haut. Über die Spaltbarkeit der Cutis. Sitzungsbericht der Mathematisch-naturwissenschaftlichen Classe der Wiener Kaiserlichen Academie der Wissenschaften Abt, p 44
Langer K (1978) On the anatomy and physiology of the skin: I. The cleavability of the cutis. Br J Plast Surg 31(1):3–8
Langer K (1978) On the anatomy and physiology of the skin: II. Skin tension (with 1 figure). Br J Plast Surg 31(2):93–106
Ní Annaidh A et al (2011) Characterization of the anisotropic mechanical properties of excised human skin. J Mech Behav Biomed Mater 5(1):139–148
Alexander H, Cook TH (1977) Accounting for natural tension in the mechanical testing of human skin. J Invest Dermatol 69:310–314
Flynn C, Stavness I, Lloyd J, Fels S (2015) A finite element model of the face including an orthotropic skin model under in vivo tension. Comput Methods Biomech Biomed Eng 18:571–582. https://doi.org/10.1080/10255842.2013.820720
Deroy C et al (2016) Non-invasive evaluation of skin tension lines with elastic waves. Skin Res Technol 23:326–335
Rosado C et al (2016) About the in vivo quantitation of skin anisotropy. Skin Res Technol 23:429–436. https://doi.org/10.1111/srt.12353
Wan Abas WAB (1994) Biaxial tension test of human skin in vivo. Biomed Mater Eng 4:473–486
Ní Annaidh A et al (2012) Automated estimation of collagen fibre dispersion in the dermis and its contribution to the anisotropic behaviour of skin. Ann Biomed Eng 40(8):1666–1678
Ottenio M et al (2015) Strain rate and anisotropy effects on the tensile failure characteristics of human skin. J Mech Behav Biomed Mater 41:241–250
Kvistedal YA, Nielsen PMF (2004) Investigating stress-strain properties of in-vivo human skin using multiaxial loading experiments and finite element modeling. In: Proceedings of the 26th annual international conference of the IEEE engineering in medicine and biology society, vols 1–7, 26, pp 5096–5099
Batisse D et al (2002) Influence of age on the wrinkling capacities of skin. Skin Res Technol 8(3):148–154
Delalleau A et al (2006) Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test. J Biomech 39:1603–1610
Diridollou S et al (2000) In vivo model of the mechanical properties of the human skin under suction. Skin Res Technol 6(4):214–221
Dobrev Hq (2000) Use of Cutometer to assess epidermal hydration. Skin Res Technol 6(4):239–244
Hendriks FM et al (2003) A numerical-experimental method to characterize the non-linear mechanical behaviour of human skin. Skin Res Technol 9(3):274–283
Weickenmeier J, Jabareen M, Mazza E (2015) Suction based mechanical characterization of superficial facial soft tissues. J Biomech 48(16):4279–4286
Pensalfini M et al (2018) Location-specific mechanical response and morphology of facial soft tissues. J Mech Behav Biomed Mater 78(Suppl C):108–115
Müller B et al (2018) A novel ultra-light suction device for mechanical characterization of skin. PLoS One 13(8):e0201440
Tonge TK et al (2013) Full-field bulge test for planar anisotropic tissues: Part I – Experimental methods applied to human skin tissue. Acta Biomater 9(4):5913–5925
Geerligs M et al (2011) Linear shear response of the upper skin layers. Biorheology 48(3–4):229–245
Geerligs M et al (2011) In vitro indentation to determine the mechanical properties of epidermis. J Biomech 44:1176–1181
Lamers E et al (2013) Large amplitude oscillatory shear properties of human skin. J Mech Behav Biomed Mater 28:462–470
Lanir Y, Fung YC (1974) Two-dimensional mechanical properties of rabbit skin—II: Experimental results. J Biomech 7:171–182
Wong WLE, Joyce TJ, Goh KL (2016) Resolving the viscoelasticity and anisotropy dependence of the mechanical properties of skin from a porcine model. Biomech Model Mechanobiol 15(2):433–446
Veronda DR, Westmann R (1970) Mechanical characterization of skin – finite deformations. J Biomech 3:111–124
Marino M (2016) Molecular and intermolecular effects in collagen fibril mechanics: a multiscale analytical model compared with atomistic and experimental studies. Biomech Model Mechanobiol 15(1):133–154
Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. In: Spencer AJM (ed) Continuum theory of the mechanics of fibre-reinforced composites. Springer, Vienna, pp 1–32
Šolinc U, Korelc J (2015) A simple way to improved formulation of FE2 analysis. Comput Mech 56(5):905–915
Saeb S, Steinmann P, Javili A (2016) Aspects of computational homogenization at finite deformations: a unifying review from Reuss’ to Voigt’s bound. Appl Mech Rev 68(5):050801–050801-33
Leyva-Mendivil MF et al (2017) Implications of multi-asperity contact for shear stress distribution in the viable epidermis – an image-based finite element study. Biotribology 11:110–123
Young PG et al (2008) An efficient approach to converting three-dimensional image data into highly accurate computational models. Philos Trans R Soc A Math Phys Eng Sci 366(1878):3155–3173
Limbert G et al (2010) Trabecular bone strains around a dental implant and associated micromotions—a micro-CT-based three-dimensional finite element study. J Biomech 43(7):1251–1261
Linder-Ganz E et al (2007) Assessment of mechanical conditions in sub-dermal tissues during sitting: a combined experimental-MRI and finite element approach. J Biomech 40(7):1443–1454
Limbert G et al (2013) On the mechanics of bacterial biofilms on non-dissolvable surgical sutures: a laser scanning confocal microscopy-based finite element study. Acta Biomater 9(5):6641–6652
Leyva-Mendivil MF, Lengiewicz J, Limbert G (2017) Skin friction under pressure. The role of micromechanics. Surf Topogr: Metrol Prop 6:014001
Limbert G, Kuhl E (2018) On skin microrelief and the emergence of expression micro-wrinkles. Soft Matter 14(8):1292–1300
Limbert G (2018) Investigating the influence of relative humidity on expression microwrinkles. J Aesthet Nurs 7(4):204–207
Gerhardt LC et al (2008) Influence of epidermal hydration on the friction of human skin against textiles. J R Soc Interface 5(28):1317–1328
Adams MJ, Briscoe BJ, Johnson SA (2007) Friction and lubrication of human skin. Tribol Lett 26(3):239–253
Derler S et al (2009) Friction of human skin against smooth and rough glass as a function of the contact pressure. Tribol Int 42(11–12):1565–1574
Kwiatkowska M et al (2009) Friction and deformation behaviour of human skin. Wear 267(5–8):1264–1273
Wolfram LJ (1983) Friction of skin. J Soc Cosmet Chem 34:465–476
Stupkiewicz S, Lewandowski MJ, Lengiewicz J (2014) Micromechanical analysis of friction anisotropy in rough elastic contacts. Int J Solids Struct 51(23–24):3931–3943
Goldstein B, Sanders J (1998) Skin response to repetitive mechanical stress: a new experimental model in pig. Arch Phys Med Rehabil 79(3):265–272
Budday S, Kuhl E, Hutchinson JW (2015) Period-doubling and period-tripling in growing bilayered systems. Philos Mag(Abingdon) 95(28–30):3208–3224
Cao Y, Hutchinson JW (2012) From wrinkles to creases in elastomers: the instability and imperfection-sensitivity of wrinkling. Proc R Soc A Math Phys Eng Sci 468:94–115
Weickenmeier J, Jabareen M (2014) Elastic–viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient. Int J Numer Methods Biomed Eng 30(11):1238–1262
Li W, Luo XY (2016) An invariant-based damage model for human and animal skins. Ann Biomed Eng 44(10):3109–3122
Buganza Tepole A et al (2011) Growing skin: a computational model for skin expansion in reconstructive surgery. J Mech Phys Solids 59(10):2177–2190
Vermolen FJ, Gefen A, Dunlop JWC (2012) In vitro “wound” healing: experimentally based phenomenological modeling. Adv Eng Mater 14(3):B76–B88
Sherratt JA, Dallon JC (2002) Theoretical models of wound healing: past successes and future challenges. C R Biol 325(5):557–564
Buganza Tepole A (2017) Computational systems mechanobiology of wound healing. Comput Methods Appl Mech Eng 314:46–70
Marsden JE, Hughes TJR (1994) Mathematical foundations of elasticity. Dover, New York, p 556
Holzapfel GA (2000) Nonlinear solid mechanics. A continuum approach for engineering. Wiley, Chichester, p 470
Boehler L (1978) de comportement anisotrope des milieux continus. J Méc 17(2):153–190
Limbert G, Taylor M (2002) On the constitutive modeling of biological soft connective tissues. A general theoretical framework and tensors of elasticity for strongly anisotropic fiber-reinforced composites at finite strain. Int J Solids Struct 39(8):2343–2358
Spencer AJM (1992) Continuum theory of the mechanics of fibre-reinforced composites. Springer, New York
Criscione JC et al (2000) An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J Mech Phys Solids 48(12):2445–2465
Criscione JC, Douglas AS, Hunter WC (2001) Physically based strain invariant set for materials exhibiting transversely isotropic behavior. J Mech Phys Solids 49(4):871–897
Holzapfel GA, Ogden RW (2016) On fiber dispersion models: exclusion of compressed fibers and spurious model comparisons. J Elast 129(1–2):49–68
Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16(1):1–22
Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6):15–35
Li K, Ogden RW, Holzapfel GA (2018) A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues. J R Soc Interface 15(138)
Li K, Ogden RW, Holzapfel GA (2018) Modeling fibrous biological tissues with a general invariant that excludes compressed fibers. J Mech Phys Solids 110:38–53
Alastrué V et al (2009) Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling. J Mech Phys Solids 57(1):178–203
Holzapfel GA et al (2015) Modelling non-symmetric collagen fibre dispersion in arterial walls. J R Soc Interface 12(106)
Sáez P et al (2012) Anisotropic microsphere-based approach to damage in soft fibered tissue. Biomech Model Mechanobiol 11(5):595–608
Ogden RW (2016) Nonlinear continuum mechanics and modelling the elasticity of soft biological tissues with a focus on artery walls. In: Holzapfel GA, Ogden RW (eds) Lecture notes from the summer school “Biomechanics: trends in modeling and simulation, September, 2014, Graz. Springer, Heidelberg
Winitzki S (2003) Uniform approximations for transcendental functions. In: Kumar V et al (eds) Computational science and its applications—ICCSA 2003: Proceedings of international conference, Part I, Montreal, 18–21 May 2003. Springer, pp 780–789
Ogden RW (1984) Non-linear elastic deformations. Ellis Horwood, West Sussex
Jansen LH, 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 117:65–83
Shergold OA, Fleck NA, Radford D (2006) The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. Int J Impact Eng 32(9):1384–1402
Delalleau A et al (2008) A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo. Skin Res Technol 14(2):152–164
Lapeer RJ, Gasson PD, Karri V (2010) Simulating plastic surgery: from human skin tensile tests, through hyperelastic finite element models to real-time haptics. Prog Biophys Mol Biol 103(2–3):208–216
Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66(5):754–771
Ogden RW (1972) Large deformation isotropic elasticity – correlation of theory and experiment for compressible rubberlike solids. Proc R Soc Lond A Math Phys Sci 328(1575):567
Ogden RW (1972) Large deformation isotropic elasticity – correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Sci 326(1567):565
Shergold OA, Fleck NA (2004) Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin. Proc R Soc A Math Phys Eng Sci 460(2050):3037–3058
Lim J et al (2011) Mechanical response of pig skin under dynamic tensile loading. Int J Impact Eng 38(2):130–135
Evans SL, Holt CA (2009) Measuring the mechanical properties of human skin in vivo using digital image correlation and finite element modelling. J Strain Anal Eng Des 44(5):337–345
Flynn C, Taberner A, Nielsen P (2011) Modeling the mechanical response of in vivo human skin under a rich set of deformations. Ann Biomed Eng 39(7):1935–1946
Flynn C et al (2013) Simulating the three-dimensional deformation of in vivo facial skin. J Mech Behav Biomed Mater 28(0):484–494
Flory PJ (1969) Statistical mechanics of chain molecules. Wiley, Chichester
Kuhl E et al (2005) Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. J Mech Phys Solids 53:1552–1573
Kratky O, Porod G (1949) Röntgenuntersuchungen gelöster Fadenmoleküle. Recl Trav Chim Pays-Bas Belg 68:1106–1122
Bischoff JE, Arruda EA, Grosh K (2002) A microstructurally based orthotropic hyperelastic constitutive law. J Appl Mech Trans ASME 69(5):570–579
Bischoff JE, Arruda EM, Grosh K (2004) A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue. Biomech Model Mechanobiol 3(1):56–65
Garikipati K et al (2004) A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J Mech Phys Solids 52(7):1595–1625
Flynn C, McCormack BAO (2008) A simplified model of scar contraction. J Biomech 41(7):1582–1589
Flynn CO, McCormack BAO (2009) A three-layer model of skin and its application in simulating wrinkling. Comput Methods Biomech Biomed Engin 12(2):125–134
Kuhl E, Holzapfel GA (2007) A continuum model for remodeling in living structures. J Mater Sci 42(21):8811–8823
Kuhn W (1936) Beziehungen zwischen Molekühlgrösse, statistischer Molekülgestalt und elastischen Eigenschaften hochpolymerer Stoffe. Kolloid Z 76:258–271
Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic-materials. J Mech Phys Solids 41(2):389–412
Cohen A (1991) A Padé approximant to the inverse Langevin function. Rheol Acta 30(3):270–273
Nguessong AN, Beda T, Peyraut F (2014) A new based error approach to approximate the inverse langevin function. Rheol Acta 53(8):585–591
Jedynak R (2015) Approximation of the inverse Langevin function revisited. Rheol Acta 54(1):29–39
Marchi BC, Arruda EM (2015) An error-minimizing approach to inverse Langevin approximations. Rheol Acta 54(11):887–902
Darabi E, Itskov M (2015) A simple and accurate approximation of the inverse Langevin function. Rheol Acta 54(5):455–459
Bischoff JE, Arruda EM, Grosh K (2000) Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. J Biomech 33(6):645–652
Dunn MG, Silver FH, Swann DA (1985) Mechanical analysis of hypertrophic scar tissue: structural basis for apparent increased rigidity. J Invest Dermatol 84(1):9–13
Belkoff SM, Haut RC (1991) A structural model used to evaluate the changing microstructure of maturing rat skin. J Biomech 24(8):711–720
Gunner CW, Hutton WC, Burlin TE (1979) The mechanical properties of skin in vivo—a portable hand-held extensometer. Br J Dermatol 100(2):161–163
Meijer R, Douven LFA, Oomens CWJ (1999) Characterisation of anisotropic and non-linear behaviour of human skin in vivo. Comput Methods Biomech Biomed Eng 2(1):13–27
Jor JWY et al (2011) Estimating material parameters of a structurally based constitutive relation for skin mechanics. Biomech Model Mechanobiol 10(5):767–778
Flynn C, McCormack BAO (2008) Finite element modelling of forearm skin wrinkling. Skin Res Technol 14(3):261–269
Flynn CO, McCormack BAO (2010) Simulating the wrinkling and aging of skin with a multi-layer finite element model. J Biomech 43(3):442–448
Limbert G, Middleton J (2005) A polyconvex anisotropic strain energy function. Application to soft tissue mechanics. In: ASME summer bioengineering conference, Vail
Itskov M, Ehret AE, Mavrilas D (2006) A polyconvex anisotropic strain-energy function for soft collagenous tissues. Biomech Model Mechanobiol 5(1):17–26
Itskov M, Aksel N (2004) A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. Int J Solids Struct 41(14):3833–3848
Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48
Tonge TK, Voo LM, Nguyen TD (2013) Full-field bulge test for planar anisotropic tissues: Part II – A thin shell method for determining material parameters and comparison of two distributed fiber modeling approaches. Acta Biomater 9(4):5926–5942
Buganza Tepole A, Gosain AK, Kuhl E (2014) Computational modeling of skin: using stress profiles as predictor for tissue necrosis in reconstructive surgery. Comput Struct 143:32–39
Flynn C, Rubin MB, Nielsen P (2011) A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles. Int J Numer Methods Biomed Eng 27(11):1793–1811
Ankersen J et al (1999) Puncture resistance and tensile strength of skin simulants. Proc Inst Mech Eng Part H J Eng Med 213(H6):493–501
Flynn C, Rubin MB (2012) An anisotropic discrete fibre model based on a generalised strain invariant with application to soft biological tissues. Int J Eng Sci 60:66–76
Limbert G (2011) A mesostructurally-based anisotropic continuum model for biological soft tissues—decoupled invariant formulation. J Mech Behav Biomed Mater 4(8):1637–1657
Bischoff JE, Arruda EM, Grosh K (2002) Finite element simulations of orthotropic hyperelasticity. Finite Elem Anal Des 38(10):983–998
Lu J, Zhang L (2005) Physically motivated invariant formulation for transversely isotropic hyperelasticity. Int J Solids Struct 42(23):6015–6031
Korelc J, Šolinc U, Wriggers P (2010) An improved EAS brick element for finite deformation. Comput Mech 46(4):641–659
Gautieri A et al (2011) Hierarchical structure and nanomechanics of collagen microfibrils from the atomic scale up. Nano Lett 11:757–766
Sun YL et al (2002) Direct quantification of the flexibility of type I collagen monomer. Biochem Biophys Res Commun 295(2):382–386
Groves RB et al (2013) An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J Mech Behav Biomed Mater 18(0):167–180
Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128
Yang W et al (2015) On the tear resistance of skin. Nat Commun 6:6649
Sherman VR, Yang W, Meyers MA (2015) The materials science of collagen. J Mech Behav Biomed Mater 52:22–50
Sherman VR et al (2017) Structural characterization and viscoelastic constitutive modeling of skin. Acta Biomater 53:460–469
Wang S et al (2012) Mechanics of epidermal electronics. J Appl Mech 79(3):031022–031022
Barbenel JC, Evans JH (1973) The time-dependent mechanical properties of skin. J Invest Dermatol 69(3):165–172
Pereira JM, Mansour JM, Davis BR (1990) Analysis of shear-wave propagation in skin – application to an experimental procedure. J Biomech 23(8):745–751
Pereira JM, Mansour JM, Davis BR (1991) Dynamic measurement of the viscoelastic properties of skin. J Biomech 24(2):157–162
Lanir Y (1979) The rheological behavior of the skin: experimental results and a structural model. Biorheology 16:191–202
Wu JZ et al (2006) Estimation of the viscous properties of skin and subcutaneous tissue in uniaxial stress relaxation tests. Biomed Mater Eng 16(1):53–66
Khatyr F et al (2004) Model of the viscoelastic behaviour of skin in vivo and study of anisotropy. Skin Res Technol 10(2):96–103
Boyer G et al (2009) Dynamic indentation on human skin in vivo: ageing effects. Skin Res Technol 15(1):55–67
Boyer G et al (2007) In vivo characterization of viscoelastic properties of human skin using dynamic micro-indentation. Annu Int Conf IEEE Eng Med Biol Soc 1–16:4584–4587
Goh KL, Listrat A, Béchet D (2014) Hierarchical mechanics of connective tissues: integrating insights from nano to macroscopic studies. J Biomed Nanotechnol 10(10):2464–2507
Redaelli A et al (2003) Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons—a computational study from molecular to microstructural level. J Biomech 36(10):1555–1569
Kearney SP et al (2015) Dynamic viscoelastic models of human skin using optical elastography. Phys Med Biol 60(17):6975–6990
Lokshin O, Lanir Y (2009) Viscoelasticity and preconditioning of rat skin under uniaxial stretch: microstructural constitutive characterization. J Biomech Eng 131(3):031009–031010
Lokshin O, Lanir Y (2009) Micro and macro rheology of planar tissues. Biomaterials 30(17):3118–3127
Fung YC (1973) Biorheology of soft tissues. Biorheology 10:139–155
Ehret A (2011) Generalised concepts for constitutive modelling of soft biological tissues. PhD Thesis RWTH Aachen University, pp 1–230
Balbi V, Shearer T, Parnell WJ (2018) A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation. Proc R Soc A Math Phys Eng Sci 474(2217):20180231
Bischoff J (2006) Reduced parameter formulation for incorporating fiber level viscoelasticity into tissue level biomechanical models. Ann Biomed Eng 34(7):1164–1172
Pioletti DP et al (1998) Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J Biomech 31(8):753–757
Coleman BD, Noll W (1961) Foundations of linear viscoelasticity. Rev Mod Phys 3(2):239–249
Limbert G (2004) Development of an advanced computational model for the simulation of damage to human skin. Welsh Development Agency (Technology and Innovation Division) – FIRST Numerics, Cardiff, pp 1–95
Limbert G, Middleton J (2004) A transversely isotropic viscohyperelastic material: application to the modelling of biological soft connective tissues. Int J Solids Struct 41(15):4237–4260
Limbert G, Middleton J (2005) An anisotropic viscohyperelastic constitutive model of the posterior cruciate ligament suitable for high loading-rate situations. In: IUTAM symposium on impact biomechanics: from fundamental insights to applications. Dublin
Limbert G, Middleton J (2006) A constitutive model of the posterior cruciate ligament. Med Eng Phys 28(2):99–113
Reese S, Govindjee S (1998) A theory of finite viscoelasticity and numerical aspects. Int J Solids Struct 35:3455–3482
Lubarda VA (2004) Constitutive theories based on the multiplicative decomposition of deformation gradient: thermoelasticity, elastoplasticity and biomechanics. Appl Mech Rev 57:95–108
Vassoler JM, Reips L, Fancello EA (2012) A variational framework for fiber-reinforced viscoelastic soft tissues. Int J Numer Methods Eng 89(13):1691–1706
Nguyen TD, Jones RE, Boyce BL (2007) Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites. Int J Solids Struct 44(25–26):8366–8389
Nedjar B (2007) An anisotropic viscoelastic fibre–matrix model at finite strains: continuum formulation and computational aspects. Comput Meth Appl Mech Eng 196(9–12):1745–1756
Flynn C, Rubin MB (2014) An anisotropic discrete fiber model with dissipation for soft biological tissues. Mech Mater 68:217–227
Hollenstein M, Jabareen M, Rubin MB (2013) Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration. Comput Mech 52(3):649–667
Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput Methods Appl Mech Eng 190(34):4379–4403
Pena E et al (2007) An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects. Int J Solids Struct 44(3–4):760–778
Pena E et al (2008) On finite-strain damage of viscoelastic-fibred materials. Application to soft biological tissues. Int J Numer Methods Eng 74(7):1198–1218
Ehret AE, Itskov M, Weinhold GW (2009) A micromechanically motivated model for the viscoelastic behaviour of soft biological tissues at large strains. Nuovo Cimento Della Societa Italiana Di Fisica C-Geophysics and Space Physics 32(1):73–80
Gasser TC, Forsell C (2011) The numerical implementation of invariant-based viscoelastic formulations at finite strains. An anisotropic model for the passive myocardium. Comput Methods Appl Mech Eng 200(49-52):3637–3645
Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Methods Appl Mech Eng 60:153–173
Muñoz MJ et al (2008) An experimental study of the mouse skin behaviour: damage and inelastic aspects. J Biomech 41(1):93–99
Edsberg LE et al (1999) Mechanical characteristics of human skin subjected to static versus cyclic normal presures. J Rehabil Res Dev 36(2):133–141
Ehret AE, Itskov M (2009) Modeling of anisotropic softening phenomena: application to soft biological tissues. Int J Plast 25:901–919
Ehret AE et al (2011) Porcine dermis in uniaxial cyclic loading: sample preparation, experimental results and modeling. J Mech Mater Struct 6(7–8):1125–1135
Volokh KY (2007) Prediciton of arterial failure based on a microstructural bi-layer fiber-matrix model with softening. In: Proceeding of the ASME summer bioengineering conference – 2007, pp 129–130
Volokh KY (2011) Modeling failure of soft anisotropic materials with application to arteries. J Mech Behav Biomed Mater 4(8):1582–1594
Volokh KY (2014) On irreversibility and dissipation in hyperelasticity with softening. J Appl Mech Trans ASME 81(7):074501
Mazza E et al (2005) Nonlinear elastic-viscoplastic constitutive equations for aging facial tissues. Biomech Model Mechanobiol 4(2–3):178–189
Mazza E et al (2007) Simulation of the aging face. J Biomech Eng Trans ASME 129(4):619–623
Rubin MB, Bodner SR (2002) A three-dimensional nonlinear model for dissipative response of soft tissue. Int J Solids Struct 39(19):5081–5099
Mihai LA, Woolley TE, Goriely A (2018) Stochastic isotropic hyperelastic materials: constitutive calibration and model selection. Proc R Soc A Math Phys Eng Sci 474(2211):201708
Lee T et al (2018) Propagation of material behavior uncertainty in a nonlinear finite element model of reconstructive surgery. Biomech Model Mechanobiol b(6):1857–1873
Azencott C-A et al (2017) The inconvenience of data of convenience: computational research beyond post-mortem analyses. Nat Methods 14:937
Buehler MJ (2006) Large-scale hierarchical molecular modeling of nanostructured biological materials. J Comput Theor Nanosci 3(5):603–623
Rim JE, Pinsky PM, van Osdol WW (2009) Multiscale modeling framework of transdermal drug delivery. Ann Biomed Eng 37(6):1217–1229
Bancelin S et al (2015) Ex vivo multiscale quantitation of skin biomechanics in wild-type and genetically-modified mice using multiphoton microscopy. Sci Rep 5:17635
Liu W, Röckner M (2015) Stochastic partial differential equations: an introduction, 1st edn. Springer, New York, p 272
Kamiński M (2007) Generalized perturbation-based stochastic finite element method in elastostatics. Comput Struct 85(10):586–594
Kirchdoerfer T, Ortiz M (2016) Data-driven computational mechanics. Comput Methods Appl Mech Eng 304:81–101
Oishi A, Yagawa G (2017) Computational mechanics enhanced by deep learning. Comput Methods Appl Mech Eng 327:327–351
Barber D (2012) Bayesian reasoning and machine learning. Cambridge University Press, Cambridge, p 697
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Ethics declarations
The author would like to gratefully acknowledge the financial support he has received over the last few years to support research on skin biophysics and applications from the Royal Society, The Royal Academy of Engineering, The British High Commission in South Africa, EPSRC, Procter & Gamble, L’Oréal, Roche and the US Air Force. He would also like to thank Dr. Anton Page of the Biomedical Imaging Unit at the University of Southampton and Mr. Sandy Monteith of Gatan UK for respectively preparing the skin sample for serial block-face imaging and for organising the electron microscopy acquisition at Gatan USA in San Diego.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Limbert, G. (2019). Constitutive Modelling of Skin Mechanics. In: Limbert, G. (eds) Skin Biophysics. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-13279-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-13279-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13278-1
Online ISBN: 978-3-030-13279-8
eBook Packages: EngineeringEngineering (R0)