An uncoupled directional damage model for fibred biological soft tissues. Formulation and computational aspects

Abstract

SUMMARYIn this paper we present a fully three-dimensional finite-strain damage model for fibrous soft tissue. Continuum damage mechanics is used to describe the softening behaviour of soft tissues under large deformation. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. We considered the internal variables associated to damage to correspond to separated contributions of the matrix and fibres. In order to show clearly the performance of the constitutive model, we present 3D simulations of the behaviour of the human medial collateral ligament and of a coronary artery. Results show that the model is able to capture the typical stress-strain behaviour observed in fibrous soft tissues and seems to confirm the soundness of the proposed formulation.

Creating a model of diseased artery damage and failure from healthy porcine aorta

“…The alterations in mechanical and failure properties were assessed via uniaxial tension testing. A constitutive model composed of the Gasser-Ogden-Holzapfel model, for elastic response, and a continuum damage model, for the failure, was also employed to provide a further basis for comparison [1,2]. For the concentrations used here it was found that: collagenase treated samples showed decreased fracture stress in the axial direction only; elastase treated samples showed increased fracture stress in the circumferential direction only; and glutaraldehyde samples showed no change in either direction.…”

Anisotropic microsphere-based approach to damage in soft fibered tissue

“…The adopted damage model uses the concept of internal variables, which provides a general description of materials involving irreversible effects and, therefore, must fulfill the Clausius-Planck inequality. We refer, e.g., to Holzapfel (2000) or Calvo et al (2007), where this damage formulation is adopted. In its material form and without thermal effects, it can be expressed as D = −Ψ + P :Ḟ ≥ 0 where D is the internal dissipation anḋ (•) is the material time derivative.…”

“…Moreover, we will restrict ourselves to damage on the anisotropic contribution of the isochoric part. We refer to Holzapfel (2000) and Calvo et al (2007) for the damage formulation of the isotropic part. Using the previous split form of the free energy, we postulate therefore…”

“…The thermodynamic force f i is conjugated to the internal variable D i , so the process could be controled by f i instead of D i (see e.g. Simo (1987);Calvo et al (2007)). The damage evolution equations are given in the strain space; therefore, the free energy is given just byλ i .…”

“…Damage in soft biological tissue is produced by the progressive failure or softening of either the matrix or the fibers. In this context, some authors have proposed continuum damage models for only one component of the material (fibers or matrix), applied to transversally anisotropic soft tissues following the approach of Simo (1987) (Natali et al, 2005;Balzani et al, 2006;Calvo et al, 2007;Ehret and Itskov, 2009;Peña and Doblaré, 2009), or that of Göktepe and Miehe (2005) and Dal and Kaliske (2009) in connection the microsphere framework for failure of rubber-like materials. Other models for the failure of fibrils (see e.g Buehler (2008); Tang et al (2010)) use molecular simulations to provides a more detailed insight into the failure process of collagen fibrils, which is basically due to the rupture of the cross-links between the tropocollagen molecules that compose the fibril.…”