Dal, Hüsnü
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 continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive model which is additively decomposed into an isotropic part for the ground matrix and an exponential anisotropic part for the two families of collagen fibers embedded in the ground matrix. In addition we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step (solved for the frozen crack phase-field parameter) and a crack evolution step (solved for the frozen deformation map); a history field governed by the failure criterion is successively updated. Subsequently, a conventional Galerkin procedure leads to the weak forms of the governing differential equations for the physical problem. Accordingly, we provide the discrete residual vectors and a corresponding linearization yields the element matrices for the two sub-problems. Finally, we demonstrate the numerical performance of the crack phase-field model by simulating uniaxial extension and simple shear fracture tests performed on specimens obtained from a human aneurysmatic thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.


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...
A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis
Göktepe, Serdar; Parker, Kit; Kuhl, Ellen (2010-08-07)
We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In respo...
An Experimental study of mechanical properties of non enzymatically glycated bovine femur cortical bone
Fındıkoğlu, Gülin; Evis, Zafer; Department of Engineering Sciences (2012)
The aim of this study is to investigate the deterioration in mechanical integrity of the collagen network in bovine bone with aging, which are related to fracture toughness. Age-related changes in collagen molecular structures formed by non-enzymatic glycation were examined and indentation fracture technique was used as a method for measuring the microstructural toughness of cortical bone. Microcrack propagation characteristics of bone for fragility were also studied. Young and old group of bovine cortical ...
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. (2018-04-01)
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 va...
A Diffusive crack model for fiber reinforced polymer composites
Aksu Denli, Funda; Dal, Hüsnü; Department of Mechanical Engineering (2020)
Recently, classical fracture mechanics approaches based on Griffith type sharp crack topologies have left the stage to diffusive crack approaches or the so called phase field models. Crack initiation and propagation is based on the variational principles for energy minimization leading to symmetric set of algebraic equations. In this thesis, which is the first attempt to model failure of engineered composites using an anisotropic crack phase–field approach, Fiber Reinforced Polymer (FRP) specific anisotropi...
Citation Formats
O. GÜLTEKİN, H. Dal, and G. A. HOLZAPFEL, “A PHASE FIELD APPROACH TO MODEL FRACTURE OF ARTERIAL WALLS,” 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40829.