Contents |
mechanics of growth
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me 337 - mechanics of growth 10 ellen kuhl, manuel rausch fall 2010, tue thu 11:00-12:15, 420-040 |
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.
class papers
papers from your final projects, now accepted for publication!
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, accepted for publication. 2011. (download)
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, accepted for publication. 2011. (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)
grading
- 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
syllabus
| day | date | topic | slides | homework | |
|---|---|---|---|---|---|
| tue | sep | 21 | motivation - everything grows! | s01 | |
| thu | sep | 23 | basics maths - notation and tensors | s02 | h01 |
| tue | sep | 28 | guest lecture: class project - growing tennis player arms | s03 | |
| thu | sep | 30 | guided reading - no class | s04 | |
| tue | oct | 05 | basics kinematics - large deformation and growth | s05 | |
| thu | oct | 07 | guest lecture: growing arteries | s06 | |
| tue | oct | 12 | basic balance equations - closed and open systems | s07 | growing giant |
| thu | oct | 14 | basic constitutive equations - growing tumors | s08 | h02 |
| tue | oct | 19 | volume growth - finite elements for growth | s09 | |
| thu | oct | 21 | volume growth - growing arteries | s10 | |
| tue | oct | 26 | volume growth - growing skin | s11 | |
| thu | oct | 28 | volume growth - growing hearts | s12 | |
| tue | nov | 02 | basic constitutive equations - growing bones | s13 | growing astronaut h03 |
| thu | nov | 04 | density growth - finite elements for growth | s14 | |
| tue | nov | 09 | density growth - growing bones | s15 | |
| thu | nov | 11 | everything grows! - midterm summary | s16 | |
| tue | nov | 16 | midterm | ||
| thu | nov | 18 | remodeling - remodeling arteries and tendons | s18 | |
| tue | nov | 30 | class project - discussion, presentation, evaluation | s19 | |
| thu | dec | 02 | class project - discussion, presentation, evaluation | ||
| thu | dec | 02 | written part of final projects due | - |
final project
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 nonlinear finite element code for density growth in hard and volume growth in soft tissues!
me337_matlab.tar.gz ... the one where u got it all
or... if you prefer to look @all the individual files
nlin_fem.m ... the one and only
extr_dof.m ... the one which extracts element information from the global
field
assm_sys.m ... the one with the strange big A operator
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
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
quads_2d.m ... the one with the 2d quadrillateral element
tetra_3d.m ... the one with the 3d tetrahedral element
brick_3d.m ... the one with the 3d brick element
cnst_den.m ... the one with the constitutive equations for density growth
cnst_vol.m ... the one with the constitutive equations for volume growth
updt_den.m ... the one with yet another newton iteration to calculate the dnsity
updt_vol.m ... the one with yet another newton iteration to calculate the volume
ex_tube1.m ... the one with the tube under tension
ex_tube2.m ... the one with the tube under compression
ex_tube3.m ... the one with the tube stented
ex_beams.m ... the one with the beam
ex_humr1.m ... the one with the coards 3d humerus
ex_humr2.m ... the one with the fine 3d humerus
ex_femur.m ... the one with the 2d femur
ex_frame.m ... the one with the topology optimization
ex_cylin.m ... the one with the idealized humerus of trabecular bone
ex_tubed.m ... the one with the idealized humerus of cortical bone
ex_bimat.m ... the one with the idealized humerus of cortical and trabecular bone
ex_punch.m ... the one with the 3d punch
ex_block.m ... the one with the3d block
ex_unity.m ... the one with the two 2d elements
mesh_sqr.m ... the one which meshes a square domain
in_humer.m ... the one which reads 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 which reads 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_den.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) 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