Mechanical modeling of growth considering domain variationPart II: Volumetric and surface growth involving Eshelby tensors

Journal of the Mechanics and Physics of Solids

Volumn 58, Issue 9, 2010, Pages 1434-1459

  Ganghoffer, Jean Franois ^a  

^a NANCY UNIVERSITÉ   (France)

Author keywords

Configurational mechanics; Curvature tensor; Material surface forces; Surface growth; Volumetric growth

Indexed keywords

CONFIGURATIONAL MECHANICS; CURVATURE TENSORS; MATERIAL SURFACE FORCES; SURFACE GROWTH; VOLUMETRIC GROWTH;

ELASTOHYDRODYNAMICS; STRESSES; SURFACE PROPERTIES; TISSUE;

TENSORS;

EID: 78049280599     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2010.05.003     Document Type: Article

References (72)

1. J.A. Adam The effect of surface curvature on wound healing in bone Appl. Math. Lett. 15 2002 59 62
2. V. Alastrue, M.A. Martinez, and M. Doblar Modelling adaptive volumetric finite growth in patientspecific redisually stressed arteries J. Biomech. 41 2008 1773 1781
3. D. Ambrosi, and F. Mollica On the mechanics of a growing tumor Int. J. Eng. Sci. 40 2002 1297 1316
4. D. Ambrosi, and F. Guana Stress-modulated growth Math. Mech. Solids 12 2007 319 342
5. G.A. Ateshian On the theory of reactive mixtures for modeling biological growth Biomech. Model. Mechanobiol. 6 2007 423 445
6. Bilby, B.A., Gardner, L.R.T., Stroh, A.N., 1957. Continuous distribution of dislocations anf the theory of plasticity. In: Proceedings of the Ninth International Congress of Applied Mechanics, Brussels, 1956, Universit de Bruxelles, pp. 3544.
7. C.J. Chung, and Y.C. Fung Residual stresses in arteries G.W. Schmid-Schnbein, S.L.Y. Woo, B.W. Zweifach, Frontiers in Biomechanics 1986 Springer-Verlag New York 117 129
8. P.R. Couchman, and R.G. Linford Aspects of solid surface therpmodynamics: relationships of the Shuttleworth type J. Electroanal. Chem. 115 1980 143 148
9. S.C. Cowin Tissue growth and remodeling Annu. Rev. Biomed. Eng. 6 2004 77 107
10. S.C. Cowin, and D.H. Hegedus Bone remodeling: theory of adaptive elasticity J. Elasticity 6 3 1976 313 326
11. A. Di Carlo Surface and bulk growth unified P. Steinmann, G.A. Maugin, Mechanics of Material Forces. Advances in Mechanics and Mathematics Vol. 11 2005 Springer
12. DiCarlo, A., Quiligotti, S., 2002. Growth and mass balance. Mech. Res. Comm. 29, 449456. 27
13. A.D. Drozdov Volumetric growth of viscoelastic solids Mech. Solids 25 1990 99 106
14. H.F. El-Nashar, and H.A. Cerdeira A discrete surface growth model for two components Physica A 283 2000 6 10
15. V.M. Entov Mechanical model of scoliosis Mech. Solids 18 1983 199 206
16. M. Epstein, and G.A. Maugin Thermomechanics of volumetric growth in uniform bodies Int. J. Plasticity 16 2000 951 978
17. Y.C. Fung Biomechanics: Motion, Flow, Stress and Growth 1990 Springer New York
18. Y.C. Fung Biomechanics: Material Properties of Living Tissues. 1993 Springer New York
19. J.F. Ganghoffer, and B. Haussy Mechanical modeling of growth considering domain variation. Part I: constitutive framework Int. J. Solids Struct. 42 15 2005 4311 4337
20. Garikipati, K., Narayanan, H., Arruda, E.M., Grosh, K., Calve, A., 2003. Material forces in the context of biotissue remodeling. In: Proceedings of the EUROMECH Colloquium 445 Mechanics of material forces, Kaiserlautern, Germany, 2124 May 2003.
21. Ganghoffer, J.F. On Eshelby tensors in the context of the thermodynamics of open systems. Application to volumetric growth. Int. J. Eng. Sci., in press.
22. K. Garikipati, E.M. Arruda, K. Grosh, H. Narayanan, and S. Calve A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics J. Mech. Phys. Solids 52 2004 1595 1625
23. K. Garikipati. The kinematics of biological growth Appl. Mech. Rev. 62 3 2009 030801 10.1115/1.3090829
24. D. Gross, S. Kolling, R. Mueller, and I. Schmidt Configurational forces and their application in solid mechanics Eur. J. Mech. A/Solids 22 2003 669 692
25. M.E. Gurtin Multiphase thermomechanics with interfacial structure. Part 1 Arch. Rat. Mech. Anal. 104 1988 185 221
26. M.E. Gurtin, and A. Struthers Multiphase thermomechanics with interfacial structure. Part 3 Arch. Rat. Mech. Anal. 112 1990 97 160
27. M.E. Gurtin On the nature of configurational forces Arch. Rat. Mech. Anal. 131 1995 67 100
28. M.E. Gurtin Configurational forces as Basic Concepts of Continuum Physics 2000 Springer New York
29. B. Haussy, and J.F. Ganghoffer Instability analysis in pressurized transversely isotropic Saint-VenantKirchhoff and neo-Hookean cylindrical thick shells Arch. Appl. Mech. 2005 1 18
30. G. Himpel, K. Kuhl, A. Menzel, and P. Steinamnn Computational modelling of isotropic multiplicative growth CMES 8 2 2005 119 134
31. F.H. Hsu The influences of mechanical loads on the form of a growing elastic body J. Biomech. 1 1968 303 311
32. Z. Huang The equilibrium equations and constitutive equations of the growing deformable body in the framework of continuum theory Int. J. Non-linear Mech. 39 2004 951 962
33. J.D. Humphrey Continuum biomechanics of soft biological tissues Proc. R. Soc. London A 459 2003 3 46
34. J.D. Humphrey, and K.R. Rajagopal Math. Methods Mod. Appl. Sci. 12 3 2002 407 430
35. D.A. Kessler, and H. Levine Pattern selection in three dimensional dendritic growth Acta Metall. 36 10 1988 2693 2706
36. Klarbring, A., Olsson, T., Stalhand, J., 2006. Theory of residual stresses with application to an arterial geometry. In: Proceedings of the 35th Solid Mechanics Conference, Krakow, Poland, 04-08/09/2006.
37. S.M. Klisch, S.S. Chen, R.L. Sah, and A. Hoger A growth mixture theory for cartilage with application to growth-related experiments on cartllage explants J. Biomech. Eng. Trans. ASME 125 2003 169 179
38. E. Kuhl, and P. Steinmann Material forces in open system mechanics Comput. Methods Appl. Mech. Eng. 193 2004 2357 2381
39. J.S. Langer Instabilities and pattern formation in crystal growth Rev. Mod. Phys. 52 1980 1 28
40. E.H. Lee Elastic-plastic deformation at finite strains J. Appl. Mech. 36 1969 1 6
41. P.H. Leo, and R.F. Sekerka The effect of surface stress o,n crystalmelt and crystalcrystal equilibrium Acat Metall. 37 12 1989 3119 3138
42. R.G. Linford Surface thermodynamics of solids Solid State Surf. Sci. 2 1973 1 152
43. V.A. Lubarda, and A. Hoger On the mechanics of solids with a growing mass Int. J. Solids Struct. 39 2002 4627 4664
44. G.A. Maugin Material Inhomogeneities in Elasticity 1993 Chapman et al. London
45. G.A. Maugin Thermomechanics of inhomogeneousheterogeneous systems: application to the irreversible progress of two- and three dimensional defects ARI 50 1997 41 56
46. G.A. Maugin On shock waves and phase-transition fronts in continua ARI 50 1998 141 150
47. G.A. Maugin On the universality of the thermomechanics of forces driving singular sets Arch. Appl. Mech. 69 1999 1 15
48. G.A. Maugin, and C. Trimarco The dynamics of configurational forces at phase-transition fronts Meccanica 30 1995 605 619
49. A. Menzel, and P. Steinmann On configurational forces in multiplicative elastoplasticity Int. J. Solids Struct. 44 2007 4442 4471
50. R.D. Mindlin Second gradient of strain and surface-tension in linear elasticity Int. J. Solids Struct. 1 1965 417 438
51. A.N. Norris The energy of a growing elastic surface Int. J. Solids Struct. 35 36 1998 5237 5252
52. H. Narayanan, E.M. Arruda, K. Grosh, and K. Garikipati The micromechanics of fluidsolid interactions during growth in porous soft biological tissue Biomech. Model. Mechanobiol. 8 2009 167 181
53. W. Noll Materially uniform simple bodies with inhomogeneities Arch. Rat. Mech. Anal. 27 1967 1 32
54. T. Olsson, and A. Klarbring Residual stresses in soft tissues as a consequence of growth and remodeling: application to an arterial geometry Eur. J. Mech. A/Solids 27 2008 959 974
55. P.J. Olver Application of Lie Groups to Differential Equations. 1989 Springer-Verlag
56. H. Petryk, and Z. Mroz Time derivatives of integrals and functionals defined on varying volume and surface domains Arch. Mech. 38 56 1986 697 724
57. K.R. Rajagopal Multiple natural configurations in continuum mechanics Rep. Inst. Comput. Appl. Mech. 1995 6
58. K.R. Rajagopal, and A.R. Srinivasa Mechanics of the inelastic behavior of materials. Part I: Theoretical underpinnings Int. J. Plasticity 14 1998 945 967
59. J. Rodriguez, J.M. Giocolea, and F. Gabakdon A volumetric model of growth or arterial walls with arbitrary geometry and loads J. Biomech. 40 2007 961 971
60. E.K. Rodriguez, A. Hoger, and A.D. McCullogh Stress-dependent finite growth in soft elastic tissues J. Biomech. 27 4 1994 455 467
61. Skalak, R., 1981. Growth as a finite displacement field. In: Carlsson, D.E., Shield, R.T. (Eds.), Proceedings of the IUTAM Symposium on Finite Elasticity. Martinus Nijhoff, The Hague, pp. 347355.
62. R. Skalak, G. Dasgupta, and M. Moss Analytical description of growth J. Theoret. Biol. 94 1982 555 577
63. R. Skalak, A. Tozeren, R.P. Zarda, and S. Chien Strain energy function of red blood cell membranes Biophys. J. 13 1973 245 264
64. R. Skalak, D.A. Farrow, and A. Hoger Kinematics of surface growth J. Math. Biol. 35 1997 869 907
65. A.A. Stein The deformation of a rod of growing biological material under longitudinal compression J. Appl. Math. Mech. 59 1995 139 146
66. L. Taber Biomechanics of growth, remodeling and morphogenesis Appl. Mech. Rev. 48 1995 487 545
67. L.A. Taber, and J.D. Humphrey Stress-modulated growth, residual stress and vascular heterogeneity J. Biomech. Eng. 123 2001 528 535
68. C. Truesdell, and R.A. Toupin The classical field theories S. Flgge, Handbuch der Physik, vol. III (1) 1960 Springer Berlin 226 793
69. K. Takamizawa, and T. Matsuda Kinematics for bodies undergoins residual stress and its applications to the left ventricle J. Appl. Mech. 57 1990 321 329
70. Thompson, D.W., 1992. On Growth and Form. Dover reprint of 1942. 2nd ed.
71. R.F. Xiao Computer simulation of surface growth J. Crystal Growth 174 1997 531 538
72. C.Y. Wang, and J.B. Bassingthwaighte Biological growth of a surface Math. Biosci. 142 1997 91 106