Fracture paths from front kinetics: Relaxation and rate independence

Archive for Rational Mechanics and Analysis

Volumn 193, Issue 3, 2009, Pages 539-583

  Larsen, C J ^a   Ortiz, M ^b   Richardson, C L ^a  

^a Life Science and Bioengineering Center   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350648376     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-009-0216-y     Document Type: Article

References (12)

1. Ambrosio L.: A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B (7) 3(4), 857-881 (1989).
2. Ambrosio L., Fusco N., Pallara D.: Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000).
3. Coleman B.D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13, 167-179 (1963).
4. Dal Maso G., Francfort G.A., Toader R.: Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176(2), 165-225 (2005).
5. Evans L.C., Gariepy R.F.: Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992).
6. Francfort G.A., Larsen C.J.: Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure Appl. Math. 56(10), 1465-1500 (2003).
7. Francfort G.A., Marigo J.-J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319-1342 (1998).
8. Mielke, A.: Evolution in rate-independent systems (ch. 6). Handbook of Differential Equations, Evolutionary Equations, vol. 2 (Eds. Dafermos C.M. and Feireisl E.). Elsevier B.V., Amsterdam, 461-559, 2005.
9. Mielke, A., Ortiz, M.: A class of minimum principles for characterizing the trajectories of dissipative systems. ESAIM Control Optim. Calc. Var. (2007, in press).
10. Paris P., Erdogan F.: A critical analysis of crack propagation laws. Trans. ASME 85, 528-534 (1963).
11. Rosakis A.J., Duffy J., Freund L.B.: The determination of dynamic fracture toughness of aisi 4340 steel by the shadow spot method. J. Mech. Phys. Solids 32(4), 443-460 (1984).
12. Yoffe E.H.: The moving griffith crack. Phil. Mag. 42, 739-750 (1951).