French Work on Fracture

Miannay, D.

doi:10.1016/b978-0-08-028691-4.50014-6

Cited by 1 publication

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“…The problem of singularities in the theory of elasticity and in fracture mechanics is widely discussed in the related scientific literature [1][2][3]. The singularity of solutions for stresses at the crack tip in the linear theory of elasticity excludes the use of traditional criteria for the strength of bodies with stress concentration.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the formally obtained singular solutions contradict not only the physical meaning, but also the postulates of the theory of elasticity. Such paradoxes still require an explanation [3]. Gradient elasticity allows one to describe size effects [4], and provides regularization of singular solutions of differential equations of elasticity theory [5,6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Approach to Non-Singular Plane Cracks Theory in Gradient Elasticity

Lurie

Volkov-Bogorodsky

Vasiliev

2019

MCA

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A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the function on the right side of the Helmholtz equation is a singular classical solution. An assertion is proved that allows us to propose a new solution for displacements and stresses at the crack tip through the vector harmonic potential, which determines by the Papkovich–Neuber representation. One of the goals of this work is a definition of a new representation of the solution of the plane problem of the theory of elasticity through the complex-valued harmonic potentials included in the Papkovich–Neuber relations represented in a symmetric form, which is convenient for applications. It is shown here that this new representation of the solution for the mechanics of cracks can be written through one harmonic complex-valued potential. The explicit potential value is found by comparing the new solution with the classical representation of the singular solution at the crack tip constructed using the complex potentials of Kolosov–Muskhelishvili. A generalized solution of the singular problem of fracture mechanics is reduced to a non-singular stress concentration problem, which allows one to implement a new concept of non-singular fracture mechanics, where the scale parameter along with ultimate stresses determines the fracture criterion and is determined by experiments.

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Section: Introductionmentioning

confidence: 99%