Gerhard Holzapfel
(TU Graz - Austria)

Computational Modeling of Fiber-Reinforced Solids with Application to Fibrous Soft Tissues


Fibrous soft tissues such as artery walls can be viewed as fiber-reinforced solids assembled by an extrafibrillar matrix, embedded families of collagen fibers and elastic fibers, whereas the active mechanical contribution is due to cells. For arterial walls the matrix can be considered as an isotropic material while the collagen fibers generate the anisotropy of the tissue. In various fibrous soft tissues collagen fibers are not perfectly aligned but are arranged in a rather dispersed structure for which a mean direction can be defined; for a review on microstructural aspects. Remarkably, the dispersed collagen structure depends on the state of disease, for example, for abdominal aortic aneurysms the out-of-plane dispersion of collagen fibers is increased and, consequently, the material and structural parameters change.

A future challenge is to base material models on a multiscale approach so that the macroscopic mechanical tissue response is linked to the microstructural components. After reviewing morphological aspects of fibrous soft tissues in health and disease we briefly present a recent multiscale model of fiber recruitment and damage with a discrete fiber dispersion method. In particular, the model is based on the triangular discretization of a unit sphere with a finite number of elementary areas. A summation of fiber contributions of all elementary areas yields the resultant fiber strain energy. Fiber recruitment, softening and damage are considered. The model was implemented in finite element codes and verified by representative examples.

Finally we briefly discuss challenges ahead, e.g., the cross-linking of collagen fibers has a significant effect on the tissue response within which the fibers are embedded. The number of cross-links increases with age, which is an important factor in the age-related stiffening of arterial walls. Hence, advanced continuum models are needed that take account of information on cross-links at the micro-structure level.



Gerhard A. Holzapfel is Professor of Biomechanics and Head of the Institute of Biomechanics at Graz University of Technology (TUG), Austria, since 2007. He is also Adjunct Professor at the Norwegian University of Science and Technology (NTNU), Trondheim, Norway, and Visiting Professor at the University of Glasgow, Scotland. Until 2013 he was Professor of Biomechanics at the Royal Institute of Technology (KTH) in Stockholm, Sweden, for 9 years (7 years as an Adjunct Professor). After his PhD in Mechanical Engineering in Graz he received an Erwin-Schrödinger Scholarship for foreign countries to be a Visiting Scholar at Stanford University (1993-95). He achieved his Habilitation at TU Vienna in 1996 and received a START-Award in 1997, which is the most prestigious research award in Austria for young scientists. In the following years (1998-2004) he was the Head of a research group on ``Computational Biomechanics'' at TUG. Among several awards and honors in the past years he is listed in ``The World's Most Influential Scientific Minds: 2014'' (Thomas Reuters) and he received the Erwin Schrödinger Prize 2011 from the Austrian Academy of Sciences for his lifetime achievements.

Professor Holzapfel’s research includes experimental and computational biomechanics and mechanobiology with an emphasis on soft biological tissues, the cardiovascular system including blood vessels in health and disease, therapeutic interventions such as balloon angioplasty and stent implantation, second-harmonic imaging microscopy and medical image processing; nonlinear continuum mechanics, constitutive (multi-scale) modeling of solids at finite strains such as cross-linked actin networks, growth and remodeling, nonlinear finite element methods, fracture and material failure. He has authored a graduate textbook entitled ``Nonlinear Solid Mechanics. A Continuum Approach for Engineering'' (John Wiley & Sons), and co-edited seven books. He contributed chapters to 20+ other books, and published 200+ peer-reviewed journal articles. He is the co-founder and co-editor of the International Journal ``Biomechanics and Modeling in Mechanobiology'' (Springer-Verlag, Berlin, Heidelberg).