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Variational Constituive Models for Soft Biological Tissues

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Book cover Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 49))

Abstract

Biological soft tissues are heterogeneous composite materials made of cells and molecules of the extracellular matrix. These tissues are frequently classified into four basic categories: muscle, epithelial, nervous and connective, each one with its own mechanical and functional properties. Their mechanical response to external forces (excluding those mechanisms associated with time scales typical of tissue remodeling), are characterized by anisotropy, high nonlinearity, strain rate dependency, permanent deformation and eventually, damage. Despite a wide set of constitutive models that have already been proposed in the specialized literature to represent the macroscopic behavior of these materials, this work focuses attention on a particular group, coined as variational in the sense that the incremental internal variable updates are found as minimizers of a pseudo strain-energy potential, called Incremental Potential evaluated at each time-step. General cases of models for viscoelastic, viscoplastic and fiber reinforced soft materials are discussed with the aid of numerical examples exploring the features of the corresponding approach.

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References

  1. Junqueira, L.C., Carneiro, J.: Histologia Basica, 10th edn. Guanabara Koogan S.A, Rio de Janeiro (2004)

    Google Scholar 

  2. Fung, Y.: Biomechanics—Mechanical Properties of Living Tissues. Springer, New York (1993)

    Google Scholar 

  3. Shergold, O.A., Fleck, N.A., Radford, D.: The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates. Int. J. Impact Eng. 32, 1384–1402 (2006)

    Article  Google Scholar 

  4. Giles, J.M., Black, A.E., Bischoff, J.E.: Anomalous rate dependence of the preconditioned response of soft tissue during load controlled deformation. J. Biomech. 40, 777–785 (2007)

    Article  Google Scholar 

  5. Munõz, M.J., Bea, J.A., Rodríguez, J.F., Ochoa, I., Grasa, J., Pérez Del Palomar, A., Zaragoza, P., Osta, R., Doblaré, M.: An experimental study of the mouse skin behaviour: damage and inelastic aspects. J. Biomech. 41(1), 93–99 (2008)

    Article  Google Scholar 

  6. Miller, K.: Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. J. Biomech. 32(5), 531537 (1999)

    Article  Google Scholar 

  7. Limbert, G., Taylor, M., Middleton, J.: Three-dimensional finite element modelling of the human ACL: simulation of passive knee flexion with a stressed and stress-free ACL. J. Biomech. 11(41), 1723–1731 (2004)

    Article  Google Scholar 

  8. Holzapfel, G.A., Weizscker, H.W.: Biomechanical behavior of the arterial wall and its numerical characterization. Comput. Biol. Med. 28(4), 37792 (1998)

    Article  Google Scholar 

  9. Lanir, Y.: Constitutive equations for fibrous connective tissues. J. Biomech. 16(1), 1–12 (1983)

    Article  Google Scholar 

  10. Pioletti, D.P., Rakotomanana, L.R.: Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J. Biomech. 31(8), 753–757 (1998)

    Article  Google Scholar 

  11. Pioletti, D.P., Rakotomanana, L.R.: Non-linear viscoelastic laws for soft biological tissues. Eur. J. Mech. A/Solids 19, 749–759 (2000)

    Article  MATH  Google Scholar 

  12. Limbert, G., Taylor, M.: On the constitutive modeling of biological soft connective tissues: a general theoretical framework and explicit forms of the tensors of elasticity for strongly anisotropic continuum fiber-reinforced composites at finite strain. Int. J. Solids Struct. 39(8), 2343–2358 (2002)

    Article  MATH  Google Scholar 

  13. El Sayed, T., Mota, A., Fraternali, F., Ortiz, M.: A variational constitutive model for soft biological tissues. J. Biomech. 41, 1458–1466 (2008)

    Article  Google Scholar 

  14. Ehret, A.E., Itskov, M.: Modeling of anisotropic softening phenomena: application to soft biological tissues. Int. J. Plast. 25(5), 901–919 (2009)

    Article  MATH  Google Scholar 

  15. Ortiz, M., Stainier, L.: The variational formulation of viscoplastic constitutive updates. Comput. Methods Appl. Mech. Eng. 171(31), 419–444 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Radovitzky, R., Ortiz, M.: Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng. 172, 203–240 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fancello, E., Ponthot, J.P., Stainier, L.: A variational formulation of constitutive models and updates in nonlinear finite viscoelasticity. Int. J. Numer. Methods Eng. 65(13), 1831–1864 (2006)

    Article  MATH  Google Scholar 

  18. Fancello, E.A., Vigneron, L., Ponthot, J., Stainier, L.: A viscoelastic formulation for finite strains: application to brain soft tissues. In: XXVII CILAMCE—Iberian Latin American Congress on Computational Methods in Engineering (2006)

    Google Scholar 

  19. Fancello, E., Vassoler, J., Stainier, L.: Comput. Methods Appl. Mech. Eng. A variational constitutive update algorithm for a set of isotropic hyperelastic viscoplastic material models 197, 4132–4148 (2008)

    Google Scholar 

  20. Vassoler, J.M., Reips, L., Fancello, E.A.: A variational framework for fiber-reinforced viscoelastic soft tissues. Int. J. Numer. Methods Eng. 89(13), 16911706 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, New York (2000)

    Google Scholar 

  22. Neto, E.D.S., Peric, D., Owen, D.R.J.: Computational Methods for Plasticity. Wiley, Chichester (2008)

    Google Scholar 

  23. Anand, L., Weber, G.: Finite deformations constitutive equations and a time integration procedure for isotropic hyperelastic-viscoplastic solids. Comput. Methods Appl. Mech. Eng. 79(14), 173–202 (1990)

    MATH  Google Scholar 

  24. Holzapfel, G., Gasser, T.C.: A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput. Methods Appl. Mech. Eng. 190(21), 4379–4403 (2001)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil

    Jakson Manfredini Vassoler

  2. Department of Mechanical Engineering, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil

    Eduardo Alberto Fancello

Authors
  1. Jakson Manfredini Vassoler
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  2. Eduardo Alberto Fancello
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Correspondence to Jakson Manfredini Vassoler .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Santa Catarina State Uni. - UDESC, Joinville, Santa Catarina, Brazil

    Pablo Andrés Muñoz-Rojas

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Vassoler, J.M., Fancello, E.A. (2016). Variational Constituive Models for Soft Biological Tissues. In: Muñoz-Rojas, P. (eds) Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials. Advanced Structured Materials, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-04265-7_4

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  • DOI: https://doi.org/10.1007/978-3-319-04265-7_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04264-0

  • Online ISBN: 978-3-319-04265-7

  • eBook Packages: EngineeringEngineering (R0)

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