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  • 1.
    Kroon, Martin
    Royal Institute of Technology (KTH).
    A constitutive framework for modelling thin incompressible viscoelastic materials under plane stress in the finite strain regime2011In: Mechanics of time-dependant materials, ISSN 1385-2000, E-ISSN 1573-2738, Vol. 15, no 4, p. 389-406Article in journal (Refereed)
    Abstract [en]

    Rubbers and soft biological tissues may undergo large deformations and are also viscoelastic. The formulation of constitutive models for these materials poses special challenges. In several applications, especially in biomechanics, these materials are also relatively thin, implying that in-plane stresses dominate and that plane stress may therefore be assumed. In the present paper, a constitutive model for viscoelastic materials in the finite strain regime and under the assumption of plane stress is proposed. It is assumed that the relaxation behaviour in the direction of plane stress can be treated separately, which makes it possible to formulate evolution laws for the plastic strains on explicit form at the same time as incompressibility is fulfilled. Experimental results from biomechanics (dynamic inflation of dog aorta) and rubber mechanics (biaxial stretching of rubber sheets) were used to assess the proposed model. The assessment clearly indicates that the model is fully able to predict the experimental outcome for these types of material.

  • 2.
    Kroon, Martin
    Royal Institute of Technology KTH.
    Assessment of three possible criteria for remodelling of collagen gels and collagenous tissues2010In: Presented at ASME Summer Bioengineering Conference, 16-19 June, 2010, ASME Press, 2010, p. 775-776Conference paper (Refereed)
    Abstract [en]

    Collagenous tissues are living structures, in which new material may be added and the structural organisation may change over time. The maintenance of the collagen matrix is accomplished by fibre-producing cells, such as fibroblasts. During maintenance, the extracellular matrix (ECM) influences the development, shape, migration, proliferation, survival, and function of the cells. The mobility of the fibroblasts and their ability to contract the ECM are important properties for a proper maintenance of the ECM [1,2]. The purpose of the present paper is to shed some more light on the interaction between the ECM and the fibre-producing cells. The fibroblasts remodel the collagen gel by reorienting the individual collagen fibres. This reorientation of fibres is described by an evolution law, which depends on a continuum mechanics entity. Three possible choices are assessed: reorientation towards increasing Cauchy stress, increasing elastic stretch, and increasing current stiffness of the material. The model is compared with experimental results, and the three different criteria are evaluated in terms of the predicted distribution of collagen fibres after remodeling and resulting stress-strain relations. Experimental results from tissue equivalents in the form of collagen gels are used when assessing the three criteria [3]. We consider a network of collagen fibres, where the fibres are embedded in a matrix fluid. The collagen fabric and the surrounding fluid are assumed to be the only load-carrying constituents in the material. Embedded in and attached to the collagen fabric is also a population of fibroblasts. The collagen fabric is composed of collagen fibres, which in turn are bundles of collagen fibrils. The deformation of a line element in the matrix is described by the deformation gradient F(X) = ∂x/∂X, which is decomposed according to F = FelFlfFr, see Fig. 1. The fibroblasts’ remodelling of the collagen fabric results in a new matrix configuration Ωr. This deformation of the matrix is described by Fr. The configuration Ωr does not necessarily fulfill equilibrium, and the deformation gradient Flf takes the matrix to the state Ωlf, that fulfils global equilibrium with no external loads applied. Finally, if external loads are applied to the material, the configuration Ωel is attained, and this deformation is described by the deformation gradient Fel.

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