living matter lab


winter 12 - me337 - mechanics of growth


me 337 - mechanics of growth 12

ellen kuhl, alexander zollner
office hours thu 11-12:30, durand 217
course announcement

winter 2012
tue thu 09:30-10:45


in contrast to traditional engineering structures living structures show the fascinating ability to grow and adapt their form, shape and microstructure to a given mechanical environment. this course addresses the phenomenon of growth on a theoretical and computational level and applies the resulting theories to classical biomechanical problems like bone remodeling, hip replacement, wound healing, atherosclerosis or in stent restenosis. this course will illustrate how classical engineering concepts like continuum mechanics, thermodynamics or finite element modeling have to be rephrased in the context of growth. having attended this course, you will be able to develop your own problem-specific finite element based numerical solution techniques and interpret the results of biomechanical simulations with the ultimate goal of improving your understanding of the complex interplay between form and function.

journal club

mechanics of growth on imechanica

class papers

pang h, shiwalkar ap, madormo cm, taylor re, andriacchi tp, kuhl e. computational modeling of bone density profiles in response to gait: a subject-specific approach. biomech model mechanobio, 2012;doi:10.1007/s10237-011-0318-y. (download)

buganza tepole a, ploch cj, wong j, gosain ak, kuhl e. growing skin - a computational model for skin expansion in reconstructive surgery. j mech phys solids, 2011;59:2177-2190. (download)

taylor re, zheng ch, jackson pr, doll jc, chen jc, holzbaur krs, besier t, kuhl e. the phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players. comp meth biomech biomed eng, 2009;12:83-93. (download)


  • 30 % homework - 3 homework assignments, 10% each
  • 30 % midterm - closed book, closed notes, one single page cheat sheet
  • 20 % final project oral presentations - graded by the class
  • 20 % final project essay - graded by instructor


day date topic slides homework
tue jan 10 motivation - everything grows! s01
thu jan 12 basics maths - notation and tensors s02 h01
tue jan 17 basic kinematics - large deformation and growth s03
thu jan 19 kinematics - growing hearts s04
tue jan 24 guest lecture - growing skin s05
thu jan 26 guest lecture - growing leaflets s06
tue jan 31 basic balance equations - closed and open systems s07
thu feb 02 basic constitutive equations - growing tumors s08 h02
tue feb 07 volume growth - finite elements for growth s09
thu feb 09 volume growth - growing arteries s10
tue feb 14 volume growth - growing skin s11
thu feb 16 volume growth - growing hearts s12
tue feb 21 basic constitutive equations - growing bones s13
thu feb 23 density growth - finite elements for growth s14 h03
tue feb 28 density growth - growing bones s15
thu mar 01 everything grows! - midterm summary s16
tue mar 06 midterm
thu mar 08 remodeling - remodeling arteries and tendons s18
tue mar 13 class project - discussion, presentation, evaluation s19
thu mar 15 class project - discussion, presentation, evaluation
thu mar 15 written part of final projects due

final project

ASME SBC 2011.jpg

buganza a, wong j, kuhl e. computational modeling of mechanically driven skin growth due to different expander geometries, farmington, pennsylvania, 2011

matlab files

finally... here's the matlab code for growth

additional reading

(1) taylor re, zheng c, jackson rp, doll jc, chen jc, holzbaur krs, besier t, kuhl e. the phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players, comp meth biomech biomed eng, 2009;12:83-93.
(2) taber l. biomechanics of growth, remodeling, and morphogenesis, appl mech rew 48, 487-545, 1995
(3) jacobs cr, levenston me, beaupre gs, simo jc, carter dr. numerical instabilities in bone remodeling simulations: the advantages of a node-based finite element approach, j biomechanics 28, 449-459, 1995
(4) kuhl e, menzel a, steinmann p. computational modeling of growth - a critical review, a classification and two new consistent approaches, computational mechanics 32, 71-88, 2003
(5) rodriguez ek, hoger a, mc culloch a. stress-dependent finite growth in soft elastic tissues, j biomechanics 27, 455-467, 1994
(6) kuhl e, maas r, himpel g, menzel a. computational modeling of arterial wall growth - attempts towards patient-specific simulations based on computer tomography, biomech model mechanobio 6, 321-331, 2007
(7) zöllner am, buganza tepole A, kuhl e. on the biomechanics and mechanobiology of growing skin. j theor bio 297, 166-175 , 2012