Phase-field models for the failure of anisotropic continua

Date

2017-03-10

Author

Dal, Hüsnü
Aksu Denli, Funda
Holzapfel, Gerhard

Metadata

Show full item record

Item Usage Stats

174
views

0
downloads

This study presents a phase-field approach for an anisotropic continuum to model fracture of biological tissues and fibre-reinforced composites. 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 anisotropic crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive models for single and multiple families of 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 and a crack evolution step. Various anisotropic failure criteria are studied. Our preliminary investigations suggest that the novel energy based anisotropic failure criteria presented is superior to stress based criteria existing in the literature. Representative numerical examples are devised for crack initiation and propagation in CFRP composites and rupture in 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.

URI

https://www.tu-ilmenau.de/fileadmin/media/analysis/trunk/170304_BoA_GAMM_2017.pdf
https://hdl.handle.net/11511/87256

Conference Name

88th Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 6-10, 2017

Collections

Department of Mechanical Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

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...
Harmonic Motion Microwave Doppler Imaging: A Simulation Study Using a Simple Breast Model Top, Can Baris; Gençer, Nevzat Güneri (2014-02-01) A hybrid method for tissue imaging using dielectric and elastic properties is proposed and investigated with simple bi-layered breast model. In this method, local harmonic motion is generated in the tissue using a focused ultrasound probe. A narrow-band microwave signal is transmitted to the tissue. The Doppler component of the scattered signal, which depends on the dielectric and elastic properties of the vibrating region, is sensed. A plane-wave spectrum technique is used together with reciprocity theorem...
Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method Ciğeroğlu, Ender (Elsevier BV, 2014-11-01) Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion...
Coordinate transformation aided finite element method for contour detection of breast tumors in microwave imaging ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2018-10-01) A coordinate transformation based finite element method is presented for detecting contours of breast cancer tissues in the context of microwave imaging. The geometry and location of a single or multiple cancerous tumors inside a breast tissue are identified by constructing an inverse problem based on the genetic optimization algorithm. The expensive forward solution phase during repeated cost function evaluations is accelerated by placing a transformation medium inside the finite element mesh. This allows ...
Free standing layer-by-layer films of polyethyleneimine and poly(l-lysine) for potential use in corneal stroma engineering Altay, Gizem; Hasırcı, Vasıf Nejat; Khademhosseini, Ali; Department of Biomedical Engineering (2011) In this study we fabricated free standing multilayer films of polyelectrolyte complexes for potential use in tissue engineering of corneal stroma by using the layer-by-layer (LbL) approach. In the formation of these LbL films negatively charged, photocrosslinkable (methacrylated) hyaluronic acid (MA-HA) was used along with polycations polyethyleneimine (PEI) and poly(L-lysine) (PLL). Type I collagen (Col) was blended in with PLL for improving the water absorption and cell attachment properties of the films....

Citation Formats

H. Dal, F. Aksu Denli, and G. Holzapfel, “Phase-field models for the failure of anisotropic continua,” presented at the 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 6-10, 2017, Weimar, Germany, 2017, Accessed: 00, 2021. [Online]. Available: https://www.tu-ilmenau.de/fileadmin/media/analysis/trunk/170304_BoA_GAMM_2017.pdf.