Numerical aspects of anisotropic failure in soft biological tissues favor energy-based criteria: A rate-dependent anisotropic crack phase-field model

Gueltekin, Osman
Dal, Hüsnü
Holzapfel, Gerhard A.
A deeper understanding to predict fracture in soft biological tissues is of crucial importance to better guide and improve medical monitoring, planning of surgical interventions and risk assessment of diseases such as aortic dissection, aneurysms, atherosclerosis and tears in tendons and ligaments. In our previous contribution (Gultekin et al., 2016) we have addressed the rupture of aortic tissue by applying a holistic geometrical approach to fracture, namely the crack phase-field approach emanating from variational fracture mechanics and gradient damage theories. In the present study, the crack phase-field model is extended to capture anisotropic fracture using an anisotropic volume-specific crack surface function. In addition, the model is equipped with a rate-dependent formulation of the phase-field evolution. The continuum framework captures anisotropy, is thermodynamically consistent and based on finite strains. The resulting Euler-Lagrange equations are solved by an operator-splitting algorithm on the temporal side which is ensued by a Galerkin-type weak formulation on the spatial side. On the constitutive level, an invariant-based anisotropic material model accommodates the nonlinear elastic response of both the ground matrix and the collagenous components. Subsequently, the basis of extant anisotropic failure criteria are presented with an emphasis on energy-based, Tsai-Wu, Hill, and principal stress criteria. The predictions of the various failure criteria on the crack initiation, and the related crack propagation are studied using representative numerical examples, i.e. a homogeneous problem subjected to uniaxial and planar biaxial deformations is established to demonstrate the corresponding failure surfaces whereas uniaxial extension and peel tests of an anisotropic (hypothetical) tissue deal with the crack propagation with reference to the mentioned failure criteria. Results favor the energy-based criterion as a better candidate to reflect a stable and physically meaningful crack growth, particularly in complex three-dimensional geometries with a highly anisotropic texture at finite strains.


GUELTEKIN, O.; Dal, Hüsnü; HOLZAPFEL, G. A. (2017-09-07)
The estimation of rupture in fibrous soft tissues has emerged as a central task in medical monitoring and risk assessment of diseases such as aortic dissection and aneurysms. In an attempt to address the challenges we have established a computational framework within the context of crack phase-field modeling and proposed an energy-based anisotropic failure criterion based on the distinction of isotropic and anisotropic material responses. Numerically we compare that criterion with other anisotropic failure ...
Phase-field approach to model fracture in human aorta
Gültekin, Osman; Holzapfel, Gerhard A.; Dal, Hüsnü (null; 2019-08-23)
Over the last decades the supra-physiological and pathological aspects of arterial tissues have become a prominent research topic in computational biomechanics in terms of constitutive modeling considering damage and fracture [1]. The current study presents a variational approach to the fracture of human arterial walls, featuring a thermodynamically consistent, gradient-type, diffusive crack phase-field approach. A power balance renders the Euler-Lagrange equations of the multi-field problem, i.e. the defor...
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Gültekin, Osman; Hager, Sandra Priska; Dal, Hüsnü; Holzapfel, Gerhard A. (Springer Science and Business Media LLC, 2019-5-15)
This study analyzes the lethal clinical condition of aortic dissections from a numerical point of view. On the basis of previous contributions by Gultekin et al. (Comput Methods Appl Mech Eng 312:542-566, 2016 and 331:23-52, 2018), we apply a holistic geometrical approach to fracture, namely the crack phase-field, which inherits the intrinsic features of gradient damage and variational fracture mechanics. The continuum framework captures anisotropy, is thermodynamically consistent and is based on finite str...
GÜLTEKİN, Osman; Dal, Hüsnü; HOLZAPFEL, Gerhard A (2016-06-10)
This study uses a recently developed phase-field approach to model fracture of arterial walls with an emphasis on aortic tissues. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal with the con...
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Citation Formats
O. Gueltekin, H. Dal, and G. A. Holzapfel, “Numerical aspects of anisotropic failure in soft biological tissues favor energy-based criteria: A rate-dependent anisotropic crack phase-field model,” COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, pp. 23–52, 2018, Accessed: 00, 2020. [Online]. Available: