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[http://biomechanics.stanford.edu/me337/matlab_ex01.m matlab_ex01.m] small matlab file to get used to tensor notation | [http://biomechanics.stanford.edu/me337/matlab_ex01.m matlab_ex01.m] small matlab file to get used to tensor notation | ||
| − | [http://biomechanics.stanford.edu/me337/assm_sys.m assm_sys.m] assembly of global system of equations | + | [http://biomechanics.stanford.edu/me337/assm_sys.m assm_sys.m] assembly of global system of equations <br> |
| − | [http://biomechanics.stanford.edu/me337/cnst_grw.m .cnst_grw.m] constitutive equations of growth | + | [http://biomechanics.stanford.edu/me337/cnst_grw.m .cnst_grw.m] constitutive equations of growth <br> |
| − | [http://biomechanics.stanford.edu/me337/element1.m element1.m] element residual and tangent | + | [http://biomechanics.stanford.edu/me337/element1.m element1.m] element residual and tangent <br> |
| − | [http://biomechanics.stanford.edu/me337/ex_frame.m ex_frame.m] example frame structure | + | [http://biomechanics.stanford.edu/me337/ex_frame.m ex_frame.m] example frame structure <br> |
| − | [http://biomechanics.stanford.edu/me337/ex_unity.m ex_unite.m] example two elements | + | [http://biomechanics.stanford.edu/me337/ex_unity.m ex_unite.m] example two elements <br> |
| − | [http://biomechanics.stanford.edu/me337/extr_dof.m extr_dof.m] extract element information from global field | + | [http://biomechanics.stanford.edu/me337/extr_dof.m extr_dof.m] extract element information from global field <br> |
| − | [http://biomechanics.stanford.edu/me337/mesh_sqr.m mesh_sqr.m] mesh square domain | + | [http://biomechanics.stanford.edu/me337/mesh_sqr.m mesh_sqr.m] mesh square domain <br> |
| − | [http://biomechanics.stanford.edu/me337/nlin_fem.m nlin_fem.m] main program | + | [http://biomechanics.stanford.edu/me337/nlin_fem.m nlin_fem.m] main program <br> |
| − | [http://biomechanics.stanford.edu/me337/num2strd.m num2strd.m] format string | + | [http://biomechanics.stanford.edu/me337/num2strd.m num2strd.m] format string <br> |
| − | [http://biomechanics.stanford.edu/me337/plot_int.m plot_int.m] plot internal variables on spatial/deformed configuration | + | [http://biomechanics.stanford.edu/me337/plot_int.m plot_int.m] plot internal variables on spatial/deformed configuration <br> |
| − | [http://biomechanics.stanford.edu/me337/plot_mat.m plot_mat.m] plot material/undeformed configuration | + | [http://biomechanics.stanford.edu/me337/plot_mat.m plot_mat.m] plot material/undeformed configuration <br> |
| − | [http://biomechanics.stanford.edu/me337/res_norm.m res_norm.m] calculate norm of residual | + | [http://biomechanics.stanford.edu/me337/res_norm.m res_norm.m] calculate norm of residual <br> |
| − | [http://biomechanics.stanford.edu/me337/solve_nr.m solve_nr.m] solve system of equations with given boundary conditions | + | [http://biomechanics.stanford.edu/me337/solve_nr.m solve_nr.m] solve system of equations with given boundary conditions <br> |
| − | [http://biomechanics.stanford.edu/me337upd_dens.m upd_dens.m] calculate current density based on local newton iteration | + | [http://biomechanics.stanford.edu/me337upd_dens.m upd_dens.m] calculate current density based on local newton iteration <br> |
==additional reading== | ==additional reading== | ||
Revision as of 11:25, 3 May 2007
Contents |
teaching in general
teaching_philososphy
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
| day | date | topic | slides | homework | |
|---|---|---|---|---|---|
| tue | apr | 03 | introduction - different forms of growth | s01 | h01 wiki growth |
| thu | apr | 05 | rep tensor calculus - tensor algebra | s02 | |
| tue | apr | 10 | rep tensor calculus - tensor analysis | s03 | h02 tensors |
| thu | apr | 12 | kinematic equations | s04 | |
| tue | apr | 17 | balance equations – closed systems | s05 | |
| thu | apr | 19 | balance equations – open systems | s06 | example rocket propulsion |
| tue | apr | 24 | constitutive equations – density growth | s07 | example astronaut |
| thu | apr | 26 | constitutive equations – volume growth | s08 | example tumor growth |
| tue | mai | 01 | finite element method – density growth theory | s09 | |
| thu | mai | 03 | finite element method – density growth matlab | s10 | matlab density |
| tue | mai | 08 | examples – bone remodeling | example bone | |
| thu | mai | 10 | finite element method – density growth alternative | ||
| tue | mai | 15 | finite element method – density growth discussion | take-home assign | |
| thu | mai | 17 | example – hip replacement, wound healing | ||
| tue | mai | 22 | kinematic equations – volume growth | ||
| thu | mai | 24 | balance equations – volume growth | galileo problem | |
| tue | mai | 29 | finite element method - volume growth theory | wiki growth | |
| thu | mai | 31 | finite element method – volume growth matlab | ||
| tue | jun | 05 | example – atherosclerosis, in stent restenosis | ||
| thu | jun | 07 | wiki session – vote on articles |
matlab
matlab_ex01.m small matlab file to get used to tensor notation
assm_sys.m assembly of global system of equations
.cnst_grw.m constitutive equations of growth
element1.m element residual and tangent
ex_frame.m example frame structure
ex_unite.m example two elements
extr_dof.m extract element information from global field
mesh_sqr.m mesh square domain
nlin_fem.m main program
num2strd.m format string
plot_int.m plot internal variables on spatial/deformed configuration
plot_mat.m plot material/undeformed configuration
res_norm.m calculate norm of residual
solve_nr.m solve system of equations with given boundary conditions
upd_dens.m calculate current density based on local newton iteration
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