Compatibility and the genesis of residual stress by volumetric growth

Journal of Mathematical Biology

Volumn 34, Issue 8, 1996, Pages 889-914

  Skalak, Richard ^a,c   Zargaryan, Stephen ^a,b   Jain, Rakesh K ^a,b   Netti, Paolo A ^a,b   Hoger, Anne ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

^c MASSACHUSETTS GENERAL HOSPITAL   (United States)

Author keywords

Compatibility; Growth strain; Residual stress

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; COMPARATIVE STUDY; ELASTICITY; GROWTH; HUMAN; MATHEMATICS; NEOPLASM; PATHOLOGY; PATHOPHYSIOLOGY; PHYSIOLOGY; PRESSURE;

ANIMALS; BIOMECHANICS; ELASTICITY; GROWTH; HUMANS; MATHEMATICS; MODELS, BIOLOGICAL; NEOPLASMS; PRESSURE;

EID: 0029679856     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/BF01834825     Document Type: Article

References (30)

1. Blume, J. A. 1989, Compatibility conditions for a left Cauchy-Green strain field. J. Elasticity 21: 271-308
2. Boley, B. A. and Weiner, J. H. 1960, Theory of Thermal Stresses, Wiley and Sons, New York
3. Boucher, Y., Baxter, L. T. and Jain, R. K. 1990, Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: Implications for therapy. Cancer Res. 50: 4478-4484
4. Boucher, Y. and Jain, R. K. 1992, Microvascular pressure in the principal driving force for interstitial hypertension in solid tumors: Implications for vascular collapse. Cancer Res. 52: 5110-5114
5. Cesaro, E. 1906, Sulle formole del Volterra, fundamentali nella teoria delle distorisioni elastische. Rend. Napoli (3a), vol. 12, 311-321
6. Cowin, S. 1993, Bone stress adaptation models. J. Biomechanical Engineering 115: 528-533
7. Fredrickson, A. G. 1964, Principles and Applications of Rheology. Prentice-Hall, Englewood Cliffs, NJ
8. Fung, Y. C. 1965, Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ
9. Fung, Y. C. 1990, Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag, New York
10. Gairola, B. K. D. 1979, Nonlinear elastic problems. In: Dislocations in Solids, vol. 1, the Elastic Theory, F. R. N. Nabarro (ed.), North-Holland Pub. Co., Amsterdam, pp. 223-342
11. Green, A. E. and Adkins, J. E. 1960, Large Elastic Deformations and Non-Linear Continuum Mechanics. Clarendon Press, Oxford
12. Gurtin, M. E. 1972, The Linear Theory of Elasticity, In: Mechanics of Solids, vol. 2, C. Truesdell (Ed.) Springer-Verlag, pp. 1-295
13. Hirth, J. P. and Lothe, J. 1981, Theory of Dislocations, 2nd Edition, John Wiley and Sons, New York
14. Hoger, A. and Carlson, D. E. 1984, On the derivative of the square root of a tensor and Guo's rate theorems, J. of Elasticity, 14: 329-336
15. Hoger, A. 1986, On the determination of residual stress in an elastic body, J. of Elasticity, 16: 303-324
16. Hoger, A. 1993, The constitutive equation for finite deformations of a transversely isotropic hyperelastic material with residual stress, J. of Elasticity, 33: 107-118
17. Jain, R. K. and Baxter, L. T. 1988, Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: Significance of intersitial pressure. Cancer Res. 48: 7022-7032
18. Jain, R. K. 1994, Barriers to drug delivery in solid tumors. Scientific American 271: 58-65
19. Kondo, K. 1955, Geometry of Deformations and Stresses. In: Unifying Study of the Basic Problems in engineering Sciences by Means of Geometry, vol. I. K. Kondo (Ed.). Gakujustu Bunken Fukyu-Kai, Tokyo, pp. 1-17
20. Kosevich, A. M. 1979, Crystal dislocations and the theory of elasticity. In: Dislocations in Solids, vol. 1, The Elastic Theory, F. R. N. Nabarro (Ed.), North-Holland Pub. Co. Amsterdam, pp. 33-141
21. Love, A. E. H. 1927, A Treatise on the Mathematical Theory of Elasticity. Cambridge Univ. Press, Cambridge
22. Nabarro, F. R. N. 1967, Theory of Crystal Dislocations. Clarendon Press, Oxford
23. Netti, P. A., Roberge, S., Boucher, Y., Baxter, L. T. and Jain, R. K. 1995, Intersitial hypertension coupled with high vascular permeability can impair tumor blood flow, in preparation
24. Rodriguez, E. K., Hoger, A. and McCulloch, A. D. 1994, Stress-dependent finite growth in soft elastic tissue, Journal of Biomechanics, 27: 455-467
25. Roesler, H. 1987, The history of some fundamental concepts in bone biomechanics. J. Biomechanics 20: 1025-1034
26. Shield, R. T. 1973, The rotation associated with large strains. SIAM J. Appl. Math. 25: 483-191
27. Silk, W. K. and Erickson, R. O. 1979, Kinematics of plant growth. J. Theor. Biology 76: 481-501
28. Skalak, R. 1981, Growth as a finite displacement field. In: Proceedings of the IUTAM Symposium on Finite Elasticity. D. E. Carlson and R. T. Shield (Eds.) Martinus Nijhoff, The Hague, pp. 347-355
29. Synge, J. L. and Schild, A. 1949, Tensor Calculus. Univ. of Toronto Press, Toronto
30. Thompson, D'Arcy W. 1969, On Growth and Form. 2nd Edn. Cambridge Univ. Press, Cambridge