Heiko Topol

Heiko Topol

Visiting Assistant Professor of Mathematical Sciences

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Heiko Topol joined Carnegie Mellon University in Qatar as a postdoctoral research associate in cooperation with Michigan State University. In 2016, he moved to Qatar University's Center for Advanced Materials as an assistant research professor, returning to CMU-Q in 2017.

Topol has previously worked at Beijing Jiaotong University in China and RWTH Aachen University's Institute of General Mechanics. 


  • Diploma, Mechanical Engineering, Ruhr University Bochum, Bochum, Germany
  • Doctor of Engineering Science, RWTH Aachen University, Aachen, Germany

Research Description

My research covers different areas of applied mathematics and mechanics:

  • My biomechanics research deals with the mathematical modeling of soft tissues. Biological soft tissues are complex structures, which are composed of multiple components with different functions and properties. In the framework of my research I consider tissue models that consist of a mixture of a ground substance matrix and embedded collagenous fibers. 
  • When the length of the propagating wave is comparable to the characteristic size of the heterogeneities, reflections and refractions at the component interfaces lead to dispersion and attenuation of the waves, and different approaches allow to determine the frequency band structure (attenuation curves and dispersion curves) of the material.
  • The asymptotic homogenization method is a well-established tool to determine the effective properties  of heterogeneous materials. The developed models consider classical approaches which imply that the mechanical properties of the original heterogeneous medium can be approximated by a homogeneous modeling medium with the same homogenized or effective properties.
  • Due to different factors the mechanical behavior of the different constituents in a composite depends on time. Examples for such a time-dependent behavior are the viscoelastic nature of polymers, changes in the material properties due to environmental conditions (material degradation due to chemical reactions, moisture, …), and changes in the interface/interphase properties between the different constituents. A work combines analytical and numerical approaches in order to study the local stress distribution in composites for pulled-out fibers.
  • Axial bulging propagation and swelling. 

Research Keywords

Continuum mechanics, homogenization, wave propagation, biomechanics, composites, numerical methods ( finite element methods, finite difference methods, …), heat transfer


I. V. Andrianov, V. V. Danishevskyy, H. Topol,
Local stress distribution in composites for pulled-out fibers with axially varying bonding,
Acta Mech. (manuscript accepted in January 2020),
DOI: 10.1007/s00707-020-02634-6

K. Gou, H. Topol, H. Demirkoparan, T. J. Pence:
Stress-swelling finite element modeling of cervical response with homeostatic collagen fiber distributions,
J. Biomech. Eng. (published online in Dec. 2019),
DOI: 10.1115/1.4045810

H. Topol, H. Demirkoparan, T. J. Pence:
Morphoelastic fiber remodeling in pressurized thick-walled cylinders with application to soft tissue collagenous tubes, 
Eur. J. Mech. A/Solids 77: 103800 (2019),
DOI: 10.1016/j.euromechsol.2019.103800

H. Topol, K. Gou, H. Demirkoparan, T. J. Pence:
Hyperelastic modeling of the combined effects of tissue swelling and deformation-related collagen renewal in fibrous soft tissue
Biomech. Model Mechanobiol. (online) (2018),
DOI: 10.1007/s10237-018-1043-6

V. Zamani, T. J. Pence, H. Demirkoparan, H. Topol:
Hyperelastic Models for the Swelling of Soft Material Plugs in Confined Spaces,
Int. J. Nonlin. Mech. (in press) (2018),
DOI: 10.1016/j.ijnonlinmec.2018.04.010

I. V. Andrianov, V. V. Danishevskyy, H. Topol,  A. S. Luyt,
Shear wave propagation in layered composites with degraded matrices at locations of imperfect bonding,
Wave Motion 78, 9-31 (2018),
DOI: 10.1016/j.wavemoti.2017.12.007

I. V. Andrianov, H. Topol, V. V. Danishevskyy:
Asymptotic Analysis of Heat Transfer in Composite Materials with Nonlinear Thermal Properties
Int. J. Heat Mass Tran. 111:736-754 (2017),
DOI: 10.1016/j.ijheatmasstransfer.2017.03.124

H. Topol, H. Demirkoparan, T. J. Pence, A. Wineman:
Time-Evolving Collagen-Like Structural Fibers in Soft Tissues: Biaxial Loading and Spherical Inflation
Mech. Time-Depend. Mat. 21: 1-29 (2017),
DOI: 10.1007/s11043-016-9315-y

I. V. Andrianov, V. V. Danishevskyy, H. Topol, G. A. Rogerson:
Propagation of Floquet-Bloch shear waves in viscoelastic composites: analysis and comparison of interface/interphase models for imperfect bonding
Acta Mech. 228: 1177-1196 (2017),
DOI: 10.1007/s00707-016-1765-4

H. Topol and H. Demirkoparan: 
Evolution of mechanical properties in tissues undergoing deformation-related fiber remodeling processes
Proc. Appl. Math. Mech. 15: 113-114 (2015),
DOI: 10.1002/pamm.201510047

H. Topol, H. Demirkoparan, T. J. Pence, A. Wineman: 
Uniaxial load analysis under stretch-dependent fiber remodeling applicable to collagenous tissue
J. Eng. Math. 95: 325-345 (2015),
DOI: 10.1007/s10665-014-9771-9

H. Topol and H. Demirkoparan: 
Evolution of the fiber density in biological tissues
Proc. Appl. Math. Mech. 14: 103-104 (2014),
DOI: 10.1002/pamm.201410039

H. Topol, H. Demirkoparan, T. J. Pence, A. Wineman: 
A theory for deformation dependent evolution of continuous fiber distribution applicable to biological tissue remodeling,
IMA J. Appl. Math. 79: 947-977 (2014),
DOI: 10.1093/imamat/hxu027

I.V. Andrianov, V.I. Bolshakov, Y. Kirichek, H. Topol: 
Periodical solutions of certain strongly nonlinear wave equations,
AIP Conf. Proc. 1389: 442-44 (2011),
DOI: 10.1063/1.3636758

I.V. Andrianov, V.V. Danishevs'kyy, H. Topol, D. Weichert:
Nonlinear elastic waves in a 1D layered composite material: some numerical results,
AIP Conf. Proc. 1389: 438-441 (2011),
DOI: 10.1063/1.3638045

I.V. Andrianov, V.V. Danishevs'kyy, H. Topol, D. Weichert: 
Homogenization of a 1D nonlinear dynamical problem for periodic composites
ZAMM – Z. Angew. Math. Meth. 91: 523-534 (2011),
DOI: 10.1002/zamm.201000176

I.V. Andrianov and H. Topol: 
Asymptotic analysis and synthesis in mechanics of solids and nonlinear dynamics

I.V. Andrianov, V.V. Danishevs'kyy, H. Topol, D. Weichert:
Approximate approach for nonlinear deformation and failure of fibre composites,
AIP Conf. Proc. 1281: 825-828 (2010),
DOI: 10.1063/1.3498613

I.V. Andrianov, V.V. Danishevs'kyy, H. Topol, D. Weichert:
Nonlinear dynamic properties of layered composite material, 
AIP Conf. Proc. 1281: 821-824 (2010),
DOI: 10.1063/1.3498612

I.V. Andrianov, V.V. Danishevs'kyy, H. Topol, D. Weichert:
Shear wave dispersion in viscoelastic composite with elastic parallelepiped inclusions,
AIP Conf. Proc. 1168: 848-851 (2009),
DOI: 10.1063/1.3241611

I.V. Andrianov, H. Topol, D. Weichert:
Load transfer in fibre-reinforced composites with viscoelastic matrix: an analytical study,
Arch. Appl. Mech. 79: 999-1007 (2009),
DOI: 10.1007/s00419-008-0265-y

Courses Taught

Ruhr University Bochum – Institute of Mechanics:

  • mechanics of materials (2004-2006)
  • dynamics (2004-2006)

RWTH Aachen University – Institute of General Mechanics:

  • statics (2007-2012)
  • mechanics of materials (2007-2012)
  • dynamics (2007-2012)

Beijing Jiaotong University:

  • mechanics of materials (course for international students, 2012)

Carnegie Mellon University in Qatar

  • 21-120: differential and integral calculus (Fall 2020)
  • 21-256: multivariate analysis (Fall 2020)

Academic Projects

  • “New mathematical models for the large strain swelling response of biological tissues:
    applications to edema, inflammation, and pregnancy" (QNRF NPRP8-2424-1-477)
  • Research on composites (QUUG-CAM-CAM-15/16-3)
  • “New mathematical models for the large strain swelling response of biological tissues"
    (QNRF NPRP 4-1138-1-178)