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Research Papers

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle

[+] Author and Article Information
Marcos Latorre

Escuela Técnica Superior de Ingeniería
Aeronáutica y del Espacio,
Universidad Politécnica de Madrid,
Plaza Cardenal Cisneros, 3,
Madrid 28040, Spain
e-mail: m.latorre.ferrus@upm.es

Francisco J. Montáns

Escuela Técnica Superior de Ingeniería
Aeronáutica y del Espacio,
Universidad Politécnica de Madrid,
Plaza Cardenal Cisneros, 3,
Madrid 28040, Spain
e-mail: fco.montans@upm.es

1Corresponding author.

Manuscript received April 4, 2017; final manuscript received July 3, 2017; published online August 16, 2017. Assoc. Editor: Jonathan Vande Geest.

J Biomech Eng 139(10), 101007 (Aug 16, 2017) (9 pages) Paper No: BIO-17-1141; doi: 10.1115/1.4037405 History: Received April 04, 2017; Revised July 03, 2017

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.

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References

Figures

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Fig. 1

(a) Stress–strain behavior under instantaneous loads; equilibrated, relaxed response, and isochronic response and (b) relaxation tests

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Fig. 2

(a) Left: predictions for the peak and relaxed behaviors in Fig. 6(a) of Ref. [10]. (b) Right: WYPiWYG strain energy terms for the instantaneous (equilibrated + nonequilibrated) and equilibrated responses.

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Fig. 3

(a) Left: stress relaxation predictions for the experimental data of Fig. 6(b) of Ref. [10] (longitudinal and transverse specimens). (b) Right: stress relaxation predictions using the model in Ref. [10] (redrawn from Fig. 6(b) of Ref. [10]).

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Fig. 4

(a) Left: WYPiWYG hyperelastic predictions for the instantaneous (equilibrated + nonequilibrated) and relaxed (equilibrated) responses of the experiments in Fig. 4(a) of Ref. [10]. (b) Right: WYPiWYG stored energy terms for the instantaneous (equilibrated + nonequilibrated) and relaxed (equilibrated) responses of the experiments in Fig. 4(a) of Ref. [10].

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Fig. 5

Predictions for the relaxation tests performed at different stress levels. Experimental data redrawn from Fig. 4(b) of Ref. [10].

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