teaching in general

teaching_philosophy
lecture notes continnum mechanics - linear (download)
lecture notes finite element method - linear (download)
lecture notes finite element method - nonlinear (download)

current courses

me 337 - mechanics of growth
tue thu 3:15-4:30
mc cullough 126

goals

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.

syllabus

matlab files

voila!... just to get used to tensor notation and matlab
matlab_ex01.m ... the one with all the tensors

finally... here's the matlab nonlinear finite element code for density growth in bone!
matlab_bone.tar.gz ... the one where u got it all

or... if you prefer to look @all the individual files
i've tried to put comments to most of the variables, send me an email if you want moooore ;-)

assm_sys.m ... the one with the strange big A operator
cnst_grw.m ... the one with the constitutive equations for growth
quads2d.m ... the one with the 2d quadrillateral element
tetra_3d.m ... the one with the 3d tetrahedral element
ex_humer.m ... the one with the example of the 3d humerus
ex_femur.m ... the one with the example of the 2d femur
ex_punch.m ... the one with the example of a 3d punch
ex_block.m ... the one with the example of a 3d block
ex_frame.m ... the one with the example of the 2d frame structure
ex_unity.m ... the one with the example of two 2d elements
extr_dof.m ... the one which extracts element information from the global field
mesh_sqr.m ... the one which meshes a square domain
nlin_fem.m ... the one and only
num_grid.m ... the other one from bex (thanx!)
plot_int.m ... the one to plot internal variables on the spatial/deformed configuration
plot_mat.m ... the one to plot the material/undeformed configuration
res_norm.m ... the one which tells you how far you are away from your ultimate goal
solve_nr.m ... the one with the solution to all problems
upd_dens.m ... the one with yet another newton iteration to calculate the density
in_humer.m ... the one from bex to read the humerus input
data_humr1_elm.dat ... the coarse one with the humerus elements
data_humr1_nod.dat ... the coarse one with the humerus coordinates
data_humr2_elm.dat ... the fine one with the humerus elements
data_humr2_nod.dat ... the fine one with the humerus coordinates
in_femur.m ... the one from bex to read the femur input
data_femur_elm.dat ... the one with all the femur elements
data_femur_nod.dat ... the one with all the femur coordinates

bone example

for those of you who are interested in calculating the bone example from the literature (2) and (3), bex converted the bone file (you're awesome! thanx!) and now you could all run the bone with matlab! just download the gzipped archive above, unpack it, call the main file nlin_fem and type step,,50 to run 50 time steps to allow for density redistribution. you should then obtain the figure on the left... just throw me an email if it doesn't work! ... and yes, i know... the code's slow... so go'n get a cup of coffee... or try to re-code cnst_grw.m in terms of either spatial or material stresses & tangents by using voigt's matrix notation and speed up quads_2d.m by using the traditional old-fashioned b-operator, it's maybe ugly in the code but a loaaad faster!

additional reading

don't feel forced to read all of this! it's just additional information that some of you might want to look at!

(1) taber l: biomechanics of growth, remodeling, and morphogenesis, appl mech rew 48, 487-545, 1995

(2) 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

(3) 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

(4) rodriguez ek, hoger a, mc culloch a: stress-dependent finite growth in soft elastic tissues, j biomechanics 27, 455-467, 1994

(5) 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 mechanobiol, available online first, DOI 10.1007/s10237-006-0062-x

class project - tennisplayers

here's the current state of the tennis player arm density project: bex generated a finite element mesh from the humerus surface data that she got from the simbios people (cool!) - sorry ryan, this seems to be a male player ;-( you can all now download the matlab files from above and just change the input line from the femur to the humerus. the figure on the left has been generated by just applying three load steps, so far it's been just tension in the y-direction. it would be great if you could figure out how to add torsion and bending the way chun hua and nathan have identified it from the literature and explained it in class. i'm currently working on the brick elements for your benchmark solution of the cylinder and also on the volume growth part.

here's the literature you found

p01 p02 p03 p04 rebecca taylor
p05 p06 p07 p08 p09 p10 p11 p12 p13 p14 chun hua zheng
p15 nathaniel benz
p16 p17 p18 p19 p20 p21 julia chen
p22 joey doll
p23 amir shamloo