Multiscale Modeling in Continuum Mechanics and Structured Deformations
Suggested readings
J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Analysis 63, 337–403, 1977.
B. Bourdin, G. Francfort, J.J. Marigo, Numerical experiments in revisited brittle fracture, Journal of Mechanics and Physics of Solids, 48, 797–826, 2000.
R. Choksi, G. Del Piero, I. Fonseca, D.R. Owen, Structured deformations as energy minimizers in models of fracture and hysteresis, Math. & Mech. of Solids 4, 321–356, 1999.
P. Ciarlet, Mathematical Elasticity, Vol.1, North-Holland, 1998.
G. Del Piero, D.R. Owen, Structured deformations, Lecture Notes, Gruppo Naz: Fisica Matematica (GNFM) Ravello 1997, Quaderni Ist. Naz. di Alta Matematica (INDAM) n.58, 2000.
L. Deseri, D.R. Owen, Active slip-band separation and the energetics of slip in single crystals, Int. J. Plasticity 16, 1411–1418, 2000.
M.E. Gurtin, An introduction to Continuum Mechanics, Academic Press, 1981.
G. Francfort, J.J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46, 1319–1342, 1998.
D.R. Owen, R. Paroni, Second-order structured deformations, Arch. Rational Mech. Analysis 155, 215–235, 2000.
M. Silhavy, The mechanics and thermodynamics of continuous media, Springer, Berlin 1997 (Chapters I and II).
M. Silhavy, On isotropic rank-one convex functions, Proc. Roy. Soc. Edinburgh 129a, 1081–1105, 1999.
H. Stumpf, K.C. Le, Variational principles of nonlinear fracture mechanics, Acta Mechanica 83, 25–37, 1990