A theory of mechanical behavior of elastic media with growing damage and other changes in structure. (English) Zbl 0704.73073

Summary: Strain energy-like potentials are used to model the mechanical behavior of linear and nonlinear elastic media with changing structure, such as micro- and macrocrack growth in monolithic and composite materials. Theory and experiment show that the applied work for processes in which changes in structure occur is in certain cases independent of some of the deformation history. Consequences of this limited path-independence are investigated, and various relationships for stable mechanical response are derived. For example, it is shown that work is at a minimum during stable changes in structure, which should be useful for developing approximate solutions by variational methods. Some final remarks indicate how the theory may be extended to include thermal, viscoelastic and fatigue effects.


74R99 Fracture and damage
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74E30 Composite and mixture properties
74A15 Thermodynamics in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
Full Text: DOI


[1] Broek, D., ()
[2] Budiansky, B., J. appl. mech., 26, 259, (1959)
[3] Budiansky, B.; Hutchinson, J.W.; Lambropoulos, J.C., Int. J. solids struct., 19, 337, (1983)
[4] Chaboche, J.L., J. appl. mech., 55, 59, (1988)
[5] Charalambides, P.G.; McMeeking, R.M., (), 189
[6] Coleman, B.D.; Gurtin, M.E., J. chem. phys., 47, 597, (1967)
[7] Drucker, D.C., (), 487
[8] Dwight, H.B., ()
[9] Evans, A.G.; Fu, Y., Acta metall., 33, 1525, (1985)
[10] Fu, Y., Ph.D. thesis, (1983), Lawrence Berkeley Laboratory, Univ. of Calif Berkeley
[11] Greenberg, M.D., ()
[12] Kinlock, A.J.; Young, R.J., ()
[13] Lamborn, M.J.; Schapery, R.A., (), 991
[14] Malvern, L.E., ()
[15] Onat, E.T.; Leckie, F.A., J. appl. mech., 55, 1, (1988)
[16] Reddy, J.N.; Rasmussen, M.L., ()
[17] Reifsnider, K.L., Damage in composite materials, () · Zbl 0703.73009
[18] Rice, J.R., J. appl. mech., 37, 728, (1970)
[19] Rice, J.R., J. mech. phys. solids, 19, 433, (1971) · Zbl 0235.73002
[20] Rice, J.R., (), 23
[21] Roberts, A.D.; Thomas, A.G., Wear, 33, 45, (1975)
[22] Schapery, R.A., J. appl. phys., 35, 1451, (1964)
[23] Schapery, R.A., (), 5
[24] Schapery, R.A., (), Book No. H00228
[25] Schapery, R.A., Int. J. fracture, 25, 195, (1984)
[26] Schapery, R.A., Polymer engng sci., 27, 63, (1987)
[27] Schapery, R.A., ()
[28] Schapery, R.A.; Jordan, W.M.; Goetz, D.P., (), 543
[29] Weitsman, Y., (), 161
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