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A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue

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Abstract

The mechanical behavior of soft tissue demonstrates a number of complex features including nonlinearity, anisotropy, viscoelasticity, and growth. Characteristic features of the time-dependent and anisotropic behavior are related to the properties of various components of the tissue such as fibrous collagen and elastin networks, large proteins and sugars attached to these networks, and interstitial fluid. Attempts to model the elastic behavior of these tissues based on assumptions about the behavior of the underlying constituents have been reasonably successful, but the essential addition of viscoelasticity to these models has been met with varying success. Here, a new rheological network model is proposed using, as its basis, an orthotropic hyperelastic constitutive model for fibrous tissue and a viscoelastic reptation model for soft materials. The resulting model has been incorporated into numerical and computational models, and is shown to capture the mechanical behavior of soft tissue in various modes of deformation including uniaxial and biaxial tension and simple shear.

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Notes

  1. Note that the use of “network” in this context refers to a combination of springs and dashpots, and not to an interconnected matrix of macromolecules or fibers that forms the basis for several microstructural models for elastomers and soft tissue (Bischoff et al. 2002b; Arruda and Boyce 1993).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Carolina, 300 South Main, Columbia, SC, 29208, USA

    Jeffrey E. Bischoff

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48105, USA

    Ellen M. Arruda & Karl Grosh

Authors
  1. Jeffrey E. Bischoff
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  2. Ellen M. Arruda
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  3. Karl Grosh
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Correspondence to Jeffrey E. Bischoff.

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Bischoff, J.E., Arruda, E.M. & Grosh, K. A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue. Biomech Model Mechanobiol 3, 56–65 (2004). https://doi.org/10.1007/s10237-004-0049-4

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  • DOI: https://doi.org/10.1007/s10237-004-0049-4

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