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Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

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Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

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dc.contributor.author Latorre, Marcos es_ES
dc.contributor.author Montáns, Francisco Javier es_ES
dc.date.accessioned 2023-01-23T19:00:26Z
dc.date.available 2023-01-23T19:00:26Z
dc.date.issued 2015-08-02 es_ES
dc.identifier.issn 0178-7675 es_ES
dc.identifier.uri http://hdl.handle.net/10251/191436
dc.description.abstract [EN] In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials. es_ES
dc.description.sponsorship Partial financial support for this work has been given by grant DPI2011-26635 from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of Spain es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Computational Mechanics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Viscoelasticity es_ES
dc.subject Hyperelasticity es_ES
dc.subject Logarithmic Strains es_ES
dc.subject Anisotropy es_ES
dc.subject Biological tissues es_ES
dc.subject Polymers es_ES
dc.title Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00466-015-1184-8 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//DPI2011-26635//Modelado computacional de la termo-elasto-viscoplasticidad en grandes deformaciones/ es_ES
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Latorre, M.; Montáns, FJ. (2015). Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains. Computational Mechanics. 56(3):506-531. https://doi.org/10.1007/s00466-015-1184-8 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00466-015-1184-8 es_ES
dc.description.upvformatpinicio 506 es_ES
dc.description.upvformatpfin 531 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 56 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\466438 es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Cristensen RM (2003) Theory of viscoelasticity. Elsevier, Dover es_ES
dc.description.references Shaw MT, MacKnight WJ (2005) Introduction to polymer viscoelasticity. Wiley-Blackwell, New York es_ES
dc.description.references Argon AS (2013) The physics of deformation and fracture of polymers. Cambridge University Press, Cambridge es_ES
dc.description.references Schapery RA, Sun CT (eds) (2000) Time dependent and nonlinear effects in polymers and composites. American Society for Testing and Materials (ASTM), West Conshohocken es_ES
dc.description.references Gennisson JL, Deffieux T, Macé E, Montaldo G, Fink M, Tanter M (2010) Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging. Ultrasound Med Biol 36(5):789–801 es_ES
dc.description.references Schapery RA (2000) Nonlinear viscoelastic solids. Int J Solids Struct 37(1):359–366 es_ES
dc.description.references Truesdell C, Noll W (2004) The non-linear field theories of mechanics. Springer, Berlin es_ES
dc.description.references Rivlin RS (1965) Nonlinear viscoelastic solids. SIAM Rev 7(3):323–340 es_ES
dc.description.references Fung YC (1993) A first course in continuum mechanics. Prentice-Hall, Upper Saddle River es_ES
dc.description.references Fung YC (1972) Stress–strain-history relations of soft tissues in simple elongation. Biomechanics 7:181–208 es_ES
dc.description.references Sauren AAHJ, Rousseau EPM (1983) A concise sensitivity analysis of the quasi-linear viscoelastic model proposed by Fung. J Biomech Eng 105(1):92–95 es_ES
dc.description.references Rebouah M, Chagnon G (2014) Extension of classical viscoelastic models in large deformation to anisotropy and stress softening. Int J Non-Linear Mech 61:54–64 es_ES
dc.description.references Poon H, Ahmad MF (1998) A material point time integration procedure for anisotropic, thermo rheologically simple, viscoelastic solids. Comput Mech 21(3):236–242 es_ES
dc.description.references Drapaca CS, Sivaloganathan S, Tenti G (2007) Nonlinear constitutive laws in viscoelasticity. Math Mech Solids 12(5):475–501 es_ES
dc.description.references Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York es_ES
dc.description.references Holzapfel GA (2000) Nonlinear solid mechanics. A continuum approach for engineering. Wiley, Chichester es_ES
dc.description.references Peña JA, Martínez MA, Peña E (2011) A formulation to model the nonlinear viscoelastic properties of the vascular tissue. Acta Mech 217(1–2):63–74 es_ES
dc.description.references Peña E, Peña JA, Doblaré M (2008) On modelling nonlinear viscoelastic effects in ligaments. J Biomech 41(12):2659–2666 es_ES
dc.description.references Holzapfel GA (1996) On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures. Int J Numer Methods Engrg 39(22):3903–3926 es_ES
dc.description.references Liefeith D, Kolling S (2007) An Anisotropic Material Model for Finite Rubber Viscoelasticity. LS-Dyna Anwenderforum, Frankenthal es_ES
dc.description.references Haupt P (2002) Continuum mechanics and theory of materials, 2nd edn. Springer, Berlin es_ES
dc.description.references Bergström JS, Boyce MC (1998) Constitutive modeling of the large strain time-dependent behavior of elastomers. J Mech Phys Solids 46(5):931–954 es_ES
dc.description.references Le Tallec P, Rahier C, Kaiss A (1993) Three-dimensional incompressible viscoelasticity in large strains: formulation and numerical approximation. Comput Methods Appl Mech Eng 109:233–258 es_ES
dc.description.references Haupt P, Sedlan K (2001) Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling. Arch Appl Mech 71:89–109 es_ES
dc.description.references Lion A (1996) A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Contin Mech Thermodyn 8(3):153–169 es_ES
dc.description.references Lion A (1998) Thixotropic behaviour of rubber under dynamic loading histories: experiments and theory. J Mech Phys Solids 46(5):895–930 es_ES
dc.description.references Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Methods Appl Mech Eng 60(2):153–173 es_ES
dc.description.references Craiem D, Rojo FJ, Atienza JM, Armentano RL, Guinea GV (2008) Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries. Phys Med Biol 53:4543–4554 es_ES
dc.description.references Kaliske M, Rothert H (1997) Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Comput Mech 19(3):228–239 es_ES
dc.description.references 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):3637–3645 es_ES
dc.description.references Reese S, Govindjee S (1998) A theory of finite viscoelasticity and numerical aspects. Int J Solids Struct 35(26):3455–3482 es_ES
dc.description.references Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12(2):93–99 es_ES
dc.description.references Sidoroff F (1974) Un modèle viscoélastique non linéaire avec configuration intermédiaire. J Mécanique 13(4):679–713 es_ES
dc.description.references Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36(1):1–6 es_ES
dc.description.references Bilby BA, Bullough R, Smith E (1955) Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc R Soc Lond Ser A 231(1185):263–273 es_ES
dc.description.references Herrmann LR, Peterson FE (1968) A numerical procedure for viscoelastic stress analysis. In: Seventh meeting of ICRPG mechanical behavior working group, Orlando, FL, CPIA Publication, vol 177, pp 60–69 es_ES
dc.description.references Taylor RL, Pister KS, Goudreau Gl et al (1970) Thermomechanical analysis of viscoelastic solids. Int J Numer Methods Eng 2(1):45–59 es_ES
dc.description.references Hartmann S (2002) Computation in finite-strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations. Comput Methods Appl Mech Eng 191(13–14):1439–1470 es_ES
dc.description.references Eidel B, Kuhn C (2011) Order reduction in computational inelasticity: why it happens and how to overcome it–The ODE-case of viscoelasticity. Int J Numer Methods Eng 87(11):1046–1073 es_ES
dc.description.references Haslach HW Jr (2005) Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomech Model Mechanobiol 3(3):172–189 es_ES
dc.description.references Pioletti DP, Rakotomanana LR, Benvenuti JF, Leyvraz PF (1998) Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J Biomech 31(8):753–757 es_ES
dc.description.references Merodio J, Goicolea JM (2007) On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics. Mech Res Commun 34(7):561–571 es_ES
dc.description.references Bonet J (2001) Large strain viscoelastic constitutive models. Int J Solids Struct 38(17):2953–2968 es_ES
dc.description.references Peric D, Dettmer W (2003) A computational model for generalized inelastic materials at finite strains combining elastic, viscoelastic and plastic material behaviour. Eng Comput 20(5/6):768–787 es_ES
dc.description.references Nedjar B (2002) Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part I: continuum formulations. Comput Methods Appl Mech Eng 191(15):1541–1562 es_ES
dc.description.references Latorre M, Montáns FJ (2014) On the interpretation of the logarithmic strain tensor in an arbitrary system of representation. Int J Solids Struct 51(7):1507–1515 es_ES
dc.description.references Eterovic AL, Bathe KJ (1990) A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures. Int J Numer Methods Eng 30(6):1099–1114 es_ES
dc.description.references Simo JC (1992) Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput Methods Appl Mech Eng 99(1):61–112 es_ES
dc.description.references Caminero MA, Montáns FJ, Bathe KJ (2011) Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures. Comput Struct 89(11):826–843 es_ES
dc.description.references Montáns FJ, Benítez JM, Caminero MA (2012) A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution. Mech Res Commun 43:50–56 es_ES
dc.description.references Papadopoulos P, Lu J (2001) On the formulation and numerical solution of problems in anisotropic finite plasticity. Comput Meth Appl Mech Eng 190(37):4889–4910 es_ES
dc.description.references Miehe C, Apel N, Lambrecht M (2002) Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials. Comput Meth Appl Mech Eng 191(47):5383–5425 es_ES
dc.description.references Vogel F, Göktepe S, Steinmann P, Kuhl E (2014) Modeling and simulation of viscous electro-active polymers. Eur J Mech 48:112–128 es_ES
dc.description.references Holmes DW, Loughran JG (2010) Numerical aspects associated with the implementation of a finite strain, elasto-viscoelastic-viscoplastic constitutive theory in principal stretches. Int J Numer Methods Eng 83(3):366–402 es_ES
dc.description.references Holzapfel GA, Gasser TC, Stadler M (2002) A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. Eur J Mech 21(3):441–463 es_ES
dc.description.references 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):8366–8389 es_ES
dc.description.references Nedjar B (2007) An anisotropic viscoelastic fibre-matrix model at finite strains: continuum formulation and computational aspects. Comput Methods Appl Mech Eng 196(9):1745–1756 es_ES
dc.description.references Latorre M, Montáns FJ (2013) Extension of the Sussman-Bathe spline-based hyperelastic model to incompressible transversely isotropic materials. Comput Struct 122:13–26 es_ES
dc.description.references Latorre M, Montáns FJ (2014) What-you-prescribe-is-what-you-get orthotropic hyperelasticity. Comput Mech 53(6):1279–1298 es_ES
dc.description.references Latorre M, Montáns FJ (2015) Material-symmetries congruency in transversely isotropic and orthotropic hyperelastic materials. Eur J Mech 53:99–106 es_ES
dc.description.references Miñano M, Montáns FJ (2015) A new approach to modeling isotropic damage for Mullins effect in hyperelastic materials. Int J Solids Struct 67–68:272–282 es_ES
dc.description.references Montáns FJ, Bathe KJ (2005) Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spin. Int J Numer Methods Eng 63(2):159–196 es_ES
dc.description.references Montáns FJ, Bathe KJ (2007) Towards a model for large strain anisotropic elasto-plasticity. Computational plasticity. Springer, New York, pp 13–36 es_ES
dc.description.references Bathe KJ (2014) Finite element procedures, 2nd edn. Klaus-Jurgen Bathe, Berlin es_ES
dc.description.references Weber G, Anand L (1990) Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Comput Methods Appl Mech Eng 79(2):173–202 es_ES
dc.description.references Hartmann S, Quint KJ, Arnold M (2008) On plastic incompressibility within time-adaptive finite elements combined with projection techniques. Comput Methods Appl Mech Eng 198:178–193 es_ES
dc.description.references Simo JC, Miehe C (1992) Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Comput Methods Appl Mech Eng 98(1):41–104 es_ES
dc.description.references Sansour C, Bocko J (2003) On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law. Int J Numer Methods Eng 58(14):2131–2160 es_ES
dc.description.references 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 es_ES
dc.description.references Sussman T, Bathe KJ (2009) A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension-compression test data. Commun Numer Methods Eng 25:53–63 es_ES
dc.description.references Sussman T, Bathe KJ (1987) A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput Struct 26:357–409 es_ES
dc.description.references Ogden RW (1997) Nonlinear elastic deformations. Dover, New York es_ES
dc.description.references Kim DN, Montáns FJ, Bathe KJ (2009) Insight into a model for large strain anisotropic elasto-plasticity. Comput Mech 44(5):651–668 es_ES
dc.subject.ods 03.- Garantizar una vida saludable y promover el bienestar para todos y todas en todas las edades es_ES


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