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

• DOI: 10.3390/mca24040093
• Publication Date: 2019-10-28T08:44:31Z
• Authors: Sergey A. Lurie; Dmitriy B. Volkov...; Valery V. Vasiliev
• Keywords: Elasticity; Helmholtz equation; Singular solution; Representation; Helmholtz free energy

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