Microstructural randomness versus representative volume element in thermomechanics

Journal of Applied Mechanics, Transactions ASME

Volumn 69, Issue 1, 2002, Pages 25-35

  Ostoja Starzewski, Martin ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BRITTLE FRACTURE; ELASTICITY; FREE ENERGY; MATHEMATICAL TRANSFORMATIONS; MICROSTRUCTURE; RANDOM PROCESSES;

THERMOMECHANICS;

CONTINUUM MECHANICS;

EID: 0036395220     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1410366     Document Type: Article

References (45)

1. Maugin, G.A., 1999, The Thermomechanics of Nonlinear Irreversible Behaviors - An Introduction, World Scientific, Singapura.
2. Ziegler, H., 1963, "Some Extremum Principles in Irreversible Thermodynamics With Applications to Continuum Mechanics," Progress in Solid Mechanics, Vol. 42, North-Holland, Amsterdam, pp. 91-191.
3. Muschik, W., and Fang, J., 1989, "Statistical Foundations of Non-equilibrium Contact Quantities. Bridging Phenomenological and Statistical Nonequilibrium Thermodynamics," Acta Phys. Hung., 66, pp. 39-57.
4. Lemaitre, J., and Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK.
5. Maugin, G.A., 1992, The Thermomechanics of Plasticity and Fracture, Cambridge University Press, Cambridge, UK.
6. Mei, C.C., Auriault, J.-L., and Ng, C.-O., 1996, "Some Applications of the Homogenization Theory," Adv. Appl. Mech., 32, pp. 277-348.
7. Dvorak, G.J., 1997, "Thermomechanics of Heterogeneous Media," J. Therm. Stresses, 20, pp. 799-817.
8. Drugan, W.J., and Willis, J.R., 1996, "A Micromechanics-Based Nonlocal Constitutive Equation and Estimates of Representative Volume Element Size for Elastic Composites," J. Mech. Phys. Solids, 44, pp. 497-524.
9. Gusev, A.A., 1997, "Representative Volume Element Size for Elastic Composites: A Numerical Study," J. Mech. Phys. Solids, 45, No. 9, pp. 1449-1459.
10. Jiang, M., Ostoja-Starzewski, M., and Jasiuk, I., 2001, "Scale-Dependent Bounds on Effective Elastoplastic Response of Random Composites," J. Mech. Phys. Solids, 49, No. 3, pp. 655-673.
11. Bažant, Z.P., and Planas, J., 1998, Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton, FL.
12. Chudnovsky, A., 1977, The Principles of Statistical Theory of the Long Time Strength, Novosibirsk (in Russian).
13. Krajcinovic, D., 1996, Damage Mechanics, North-Holland, Amsterdam.
14. Krajcinovic, D., 1997, "Essential Structure of the Damage Mechanics Theories," Theor. Appl. Mech., T. Tatsumi, E. Watanabe, and T. Kambe, eds., Elsevier Science, Amsterdam, pp. 411-426.
15. Hill, R., 1963, "Elastic Properties of Reinforced Solids: Some Theoretical Principles," J. Mech. Phys. Solids, 11, pp. 357-372.
16. Hazanov, S., and Huet, C., 1994, "Order Relationships for Boundary Conditions Effect in Heterogeneous Bodies Smaller Than the Representative Volume," J. Mech. Phys. Solids, 41, pp. 1995-2011.
17. Ziegler, H., 1983, An Introduction to Thermomechanics, North-Holland, Amsterdam.
18. Ziegler, H., and Wehrli, C., 1987, "The Derivation of Constitutive Relations From Free Energy and the Dissipation Functions," Adv. Appl. Mech., 25, Academic Press, New York, pp. 183-238.
19. Germain, P., Nguyen, Quoc Son, and Suquet, P., 1983, "Continuum Thermodynamics," ASME J. Appl. Mech., 50, pp. 1010-1020.
20. Beran, M.J., 1974, "Application of Statistical Theories for the Determination of Thermal, Electrical, and Magnetic Properties of Heterogeneous Materials," Mechanics of Composite Materials, Vol. 2, G.P. Sendeckyj, ed., Academic Press, San Diego, CA, pp. 209-249.
21. Nemat-Nasser, S., and Hori, M., 1993, Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, Amsterdam.
22. Jeulin, D., and Ostoja-Starzewski, M., eds., 2001, Mechanics of Random and Multiscale Microstructures (CISM Courses and Lectures), Springer-Verlag, New York, in press.
23. Stoyan, D., Kendall, W.S., and Mecke, J., 1987, Stochastic Geometry and its Applications, J. Wiley and Sons, New York.
24. Dempsey, J.P., 2000, "Research Trends in Ice Mechanics," Int. J. Solids Struct., 37, No. 1-2.
25. Rytov, S.M., Kravtsov, Yu.A., and Tatarskii, V.I., 1989, Principles of Statistical Radiophysics, Vol. 3, Springer-Verlag, Berlin.
26. Huet, C., 1990, "Application of Variational Concepts to Size Effects in Elastic Heterogeneous Bodies," J. Mech. Phys. Solids, 38, pp. 813-841.
27. Sab, K., 1992, "On the Homogenization and the Simulation of Random Materials," Eur. J. Mech. A/Solids, 11, pp. 585-607.
28. Ostoja-Starzewski, M., 1994, "Micromechanics as a Basis of Continuum Random Fields," Appl. Mech. Rev., 47, (No. 1, Part 2), pp. S221-S230.
29. Ostoja-Starzewski, M., 1998, "Random Field Models of Heterogeneous Materials," Int. J. Solids Struct., 35, No. 19, pp. 2429-2455.
30. Ostoja-Starzewski, M., 1999, "Scale Effects in Materials With Random Distributions of Needles and Cracks," Mech. Mater., 31, No. 12, pp. 883-893.
31. Ostoja-Starzewski, M., 1999, "Microstructural Disorder, Mesoscale Finite Elements, and Macroscopic Response," Proc. R. Soc. London, Ser. A, A455, pp. 3189-3199.
32. Hazanov, S., 1998, "Hill Condition and Overall Properties of Composites," Arch. Appl. Mech., 66, pp. 385-394.
33. Hazanov, S., 1999, "On Apparent Properties of Nonlinear Heterogeneous Bodies Smaller Than the Representative Volume," Acta Mech., 134, pp. 123-134.
34. Huet, C., 1999, "Coupled Size and Boundary-Condition Effects in Viscoelastic Heterogeneous Composite Bodies," Mech. Mater., 31, No. 12, pp. 787-829.
35. Hazanov, S., and Amieur, M., 1995, "On Overall Properties of Elastic Heterogeneous Bodies Smaller Than the Representative Volume," Int. J. Eng. Sci., 33, No. 9, pp. 1289-1301.
36. Ostoja-Starzewski, M., 1990, "A Generalization of Thermodynamic Orthogonality to Random Media," J. Appl. Math. Phys., 41, pp. 701-712.
37. Ziegler, H., 1968, "A Possible Generalization of Onsager's Theory," IUTAM Symp. Irreversible Aspects of Continuum Mechanics, H. Parkus and L.I. Sedov, eds., Springer-Verlag, New York, pp. 411-424.
38. Ashby, M.F., and Jones, D.R.H., 1986, Engineering Materials, Vol. 2, Pergamon Press, Oxford.
39. Ostoja-Starzewski, M., Sheng, P.Y., and Jasiuk, I., 1997, "Damage Patterns and Constitutive Response of Random Matrix-Inclusion Composites," Eng. Fract. Mech., 58, Nos. 5 and 6, pp. 581-606.
40. Alzebdeh, K., Al-Ostaz, A., Jasiuk, I., and Ostoja-Starzewski, M., 1998, "Fracture of Random Matrix-Inclusion Composites: Scale Effects and Statistics," Int. J. Solids Struct., 35, No. 19, pp. 2537-2566.
41. Hermann, H.J., and Roux, S., eds., 1990, Statistical Models for Fracture of Disordered Media, Elsevier, Amsterdam.
42. Ostoja-Starzewski, M., Jasiuk, I., Wang, W., and Alzebdeh, K. 1996, "Composites With Functionally Graded Interfaces: Meso-continuum Concept and Effective Properties," Acta Mater., 44, No. 5, pp. 2057-2066.
43. Zbib, H., and Aifantis, E.C., 1989, "A Gradient Dependent Flow Theory of Plasticity: Application to Metal and Soil Instabilities," Appl. Mech. Rev., (Mechanics Pan-America 1989, C.R. Steele, A.W. Leissa, and M.R.M. Crespo da Silva, eds.), 42, No. 11, Part 2, pp. S295-S304.
44. Lacy, T.E., McDowell, D.L., and Talreja, R., 1999, "Gradient Concepts for Evolution of Damage," Mech. Mater., 31, No. 12, pp. 831-860.
45. Ostoja-Starzewski, M., and Trȩbicki, J., 1999, "On the Growth and Decay of Acceleration Waves in Random Media," Proc. R. Soc. London, Ser. A, A455, pp. 2577-2614.