zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Configurational forces and the basic laws for crack propagation. (English) Zbl 1054.74508
Summary: This paper develops a framework for dynamical fracture, concentrating on the derivation of basic field equations that describe the motion of the crack tip in two space dimensions. The theory is based on the notion of configurational forces in conjunction with a mechanical version of the second law.

74A45Theories of fracture and damage
74A15Thermodynamics (mechanics of deformable solids)
Full Text: DOI
[1] Atkinson, C.; Eshelby, J. D.: The flow of energy into the tip of a moving crack. Int. J. Frac. 4, 3-8 (1968)
[2] Eshelby, J. D.: The force on an elastic singularity. Phil. trans. Roy. soc. Lond. 244, 87-112 (1951) · Zbl 0043.44102
[3] Eshelby, J. D.: The continuum theory of lattice defects. Progress in solid state physics 3, 79-144 (1956)
[4] Eshelby, J. D.: The elastic energy-momentum tensor. J. elasticity 5, 321-335 (1975) · Zbl 0323.73011
[5] Freund, L. B.: Energy flux into the tip of an extending crack in an elastic solid. J. elasticity 2, 341-349 (1972)
[6] Freund, L. B.: Dynamic fracture mechanics. (1990) · Zbl 0712.73072
[7] Gurtin, M. E.: The nature of configurational forces. Arch. rat. Mech. anal. 131, 67-100 (1995) · Zbl 0836.73002
[8] Gurtin, M. E.; Struthers, A.: Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation. Arch. rat. Mech. anal. 112, 97-160 (1990) · Zbl 0723.73018
[9] Gurtin, M. E.; Yatomi, C.: On the energy release rate in elastodynamic crack propagation. Arch. rat. Mech. anal. 74, 231-247 (1980) · Zbl 0485.73079
[10] Hutchinson, J. W.: Plastic stress and strain fields at a crack tip. J. mech. Phys. solids 16, 337-347 (1968)
[11] Kostrov, B. V.; Nikitin, L. V.: Some general problems of mechanics of brittle fracture. Arch. mech. Stos. 22, 749-775 (1970) · Zbl 0232.73110
[12] Lam, P. S.; Freund, L. B.: Analysis of dynamic growth of a tensile crack in an elastic-plastic material. J. mech. Phys. solids 33, 153-167 (1985)
[13] Maugin, G. A.: Material inhomogeneities in elasticity. (1993) · Zbl 0797.73001
[14] Podio-Guidugli, P.: Inertia and invariance. Ann. mat. Pura appl. (IV) 171 (1996) · Zbl 0949.74003
[15] Rice, J. R.: Mathematical analysis in the mechanics of fracture. Fracture 2, 191-311 (1968) · Zbl 0214.51802
[16] Rice, J. R.; Rosengren, G. F.: Plane strain deformation near a crack tip in a power law hardening material. J. mech. Phys. solids 16, 1-12 (1968) · Zbl 0166.20703
[17] 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, 443-460 (1984)
[18] Truesdell, C. A.; Noll, W.: The non-linear field theories of mechanics. Handbuch der physik /3 (1965) · Zbl 0779.73004
[19] Willis, J. R.: Equations of motion for propagating cracks. The mechanics and physics of fracture, 57-67 (1975)
[20] Zehnder, A. T.; Rosakis, A. J.: Dynamic fracture initiation and propagation in 4340 steel under impact loading. Int. J. Fracture 43, 271-285 (1990)