The micromechanics of fluid-solid interactions during growth in porous soft biological tissue

Biomechanics and Modeling in Mechanobiology

Volumn 8, Issue 3, 2009, Pages 167-181

  Narayanan, H ^a   Arruda, E M ^a   Grosh, K ^a   Garikipati, K ^a  

^a University of Michigan   (United States)

Author keywords

Homogenisation; Mixture theory; Operator splitting

Indexed keywords

MECHANICS; MECHANISMS; MIXTURES; TRANSPORT PROPERTIES;

BIOLOGICAL GROWTH; FLUID PHASIS; FLUID SOLID INTERACTION; FLUID TRANSPORT; FLUID-PHASE; HOMOGENIZATION; MIXTURE THEORY; OPERATOR-SPLITTING; SOFT BIOLOGICAL TISSUE; SOFT TISSUE;

TISSUE;

COLLAGEN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; FINITE ELEMENT ANALYSIS; GROWTH, DEVELOPMENT AND AGING; METABOLISM; MICROFLUIDICS; ORGAN SIZE; POROSITY; STANDARD; TENDON; TIME;

ANIMALS; BIOMECHANICS; COLLAGEN; FINITE ELEMENT ANALYSIS; MICROFLUIDICS; MODELS, BIOLOGICAL; ORGAN SIZE; POROSITY; REFERENCE STANDARDS; TENDONS; TIME FACTORS;

EID: 67349281679     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-008-0126-1     Document Type: Article

References (32)

1. Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2002) Molecular biology of the cell. Garland Science, Oxford
2. D Ambrosi F Mollica 2002 On the mechanics of a growing tumor Int J Eng Sci 40 1297 1316 (Pubitemid 34715668)
3. F Armero 1999 Formulation and finite element implementation of a multiplicative model of coupled poro-pplasticity at finite strains under fully-saturated conditions Comp Methods Appl Mech Eng 171 205 241
4. JE Bischoff EM Arruda K Grosh 2002 A microstructurally based orthotropic hyperelastic constitutive law J Appl Mech 69 570 579
5. JE Bischoff EM Arruda K Grosh 2002 Orthotropic elasticity in terms of an arbitrary molecular chain model J Appl Mech 69 198 201 (Pubitemid 35202568)
6. Brennen CE (1995) Cavitation and bubble dynamics. Oxford University Press, New York
7. Bromberg S, Dill KA (2002) Molecular driving forces: statistical thermodynamics in chemistry and biology. Garland, Oxford
8. A Brooks T Hughes 1982 Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comp Methods Appl Mech Eng 32 199 259 (Pubitemid 13490980)
9. S Calve R Dennis P Kosnik K Baar K Grosh E Arruda 2004 Engineering of functional tendon Tissue Eng 10 755 761 (Pubitemid 38880393)
10. SC Cowin DH Hegedus 1976 Bone remodeling I: a theory of adaptive elasticity J Elast 6 313 325
11. M Epstein GA Maugin 2000 Thermomechanics of volumetric growth in uniform bodies Int J Plast 16 951 978
12. Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edn. Springer, New York
13. K Garikipati VS Rao 2001 Recent advances in models for thermal oxidation of silicon J Comput Phys 174 138 170
14. K Garikipati EM Arruda K Grosh H Narayanan S Calve 2004 A continuum treatment of growth in biological tissue: mass transport coupled with mechanics J Mech Phys Solids 52 1595 1625
15. K Garikipati JE Olberding H Narayanan EM Arruda K Grosh S Calve 2006 Biological remodelling: stationary energy, configurational change, internal variables and dissipation J Mech Phys Solids 57 1493 1515
16. S Han SJ Gemmell KG Helmer P Grigg JW Wellen AH Hoffman CH Sotak 2000 Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport J Magn Reson 144 217 227
17. T Hughes L Franca M Mallet 1987 A new finite element formulation for computational fluid dynamics: VII. Convergence analysis of the generalized SUPG formulation for linear time-dependent multidimensional advective-diffusive systems Comp Methods Appl Mech Eng 63 1 97 112 (Pubitemid 17638984)
18. JD Humphrey Rajagopal 2002 A constrained mixture model for growth and remodeling of soft tissues Math Methods Mod Appl Sci 12 3 407 430
19. SM Klisch TJ van Dyke A Hoger 2001 A theory of volumetric growth for compressible elastic biological materials Math Mech Solids 6 551 575
20. O Kratky G Porod 1949 Röntgenuntersuchungen gelöster Fadenmoleküle Recl Trav Chim 68 1106 1122
21. E Kuhl K Garikipati E Arruda K Grosh 2005 Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network J Mech Phys Solids (UK) 53 7 1552 1573
22. EH Lee 1969 Elastic-plastic deformation at finite strains J Appl Mech 36 1 6
23. Milton GW (2002) Theory of composites. Cambridge University Press, London
24. Nordin M, Lorenz T, Campello M (2001) Biomechanics of tendons and ligaments. In: Nordin M, Frankel VH (eds) Basic biomechanics of the musculoskeletal system. Lippincott Williams and Wilkins, New York, pp 102-125
25. VS Rao TJR Hughes K Garikipati 2000 On modelling thermal oxidation of silicon ii: Numerical aspects Int J Numer Methods Eng 47 1/3 359 378
26. EK Rodriguez A Hoger AD McCullough 1994 Stress-dependent finite growth in soft elastic tissues J Biomech 27 455 467 (Pubitemid 24102058)
27. BG Sengers CWJ Oomens FPT Baaijens 2004 An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering J BioMech Eng 126 82 91 (Pubitemid 38649195)
28. JC Simo RL Taylor KS Pister 1985 Variational and projection methods for the volume constraint in finite deformation elasto-plasticity Comp Methods Appl Mech Eng 51 177 208
29. LA Taber JD Humphrey 2001 Stress-modulated growth, residual stress and vascular heterogeneity J BioMech Eng 123 528 535 (Pubitemid 34016544)
30. Taylor RL (1999) FEAP-a finite element analysis program. University of California at Berkeley, Berkeley
31. T Tezduyar S Sathe 2003 Stabilization parameters in SUPG and PSPG formulations J Comput Appl Mech 4 71 88
32. Truesdell C, Noll W (1965) The non-linear field theories (Handbuch der Physik, band III). Springer, Berlin