Application of Papkovich-Neuber General Solution for Crack Problems in Strain Gradient Elasticity

In this paper, we use the Papkovich-Neuber potentials to derive the variant of general solution for the plain problems of strain gradient elasticity theory (SGET) in bounded domains. General solution contains complete sets of functions satisfying 2D Laplace equations and modified Helmholtz equations, including the polynomial and modified Bessel functions of integer and fractional orders with corresponding angular periodicity. It is shown that proposed form of general solution allows to derive the known SGET asymptotic solutions for the crack-tip fields.

Automated summary

In this paper, the authors use the Papkovich-Neuber potentials to derive a variant of the general solution for plain problems in strain gradient elasticity theory (SGET) in bounded domains. The general solution consists of complete sets of functions satisfying 2D Laplace equations and modified Helmholtz equations, including polynomial and modified Bessel functions of integer and fractional orders with angular periodicity. The proposed form of the general solution allows for the derivation of known SGET asymptotic solutions for crack-tip fields.