Springer Online Journal Archives 1860-2000
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Abstract Recently the authors have derived various new types of path independent integrals in which the theoretical limitations of the so-calledJ integral are overcome. First, for elastodynamic crack problems, a path independent integralJ′ which has the physical meaning of energy release rate was derived. Later, more general forms of path independent integralsT * andT were derived, which are valid for any constitutive relation under quasi-static as well as dynamic conditions. This paper presents the theoretical and computational aspects of these integrals, of relevance in non-linear dynamic fracture mechanics. An efficient solution technique is also presented for non-linear dynamic finite element method in which a factorization of the assembled stiffness matrix is done only once throughout the computation for a given mesh pattern. Finite element analyses were carried out for an example problem of a center-cracked plate subject to a uniaxial impact loading. The material behavior was modeled by three different constitutive relations such as linear-elastic, elastic-plastic, elastic-viscoplastic cases. The applicability of theT * integral to non-linear dynamic fracture mechanics was shown with the numerical results.
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