Weight functions of a crack in a two-dimensional micropolar solid

作者：Antipov Y A^*

来源：Quarterly Journal of Mechanics and Applied Mathematics, 2012, 65(2): 239-271.

DOI：10.1093/qjmam/hbr029

Two models for a crack in an unbounded two-dimensional micropolar solid are analysed. The first one concerns plane-strain deformation, while the second problem assumes the conditions of antiplane-strain loading. In both cases, one of three modes is uncoupled, while the other two are coupled. For a semi-infinite crack, the models reduce to a scalar and an order-2 vector Riemann-Hilbert problems with a Hermitian matrix coefficient. In the plane-strain case, the problem is solved exactly, and the weight functions are derived by quadratures. In the antiplane-strain case, the matrix coefficient cannot be factorized by the methods available in the literature. For a finite antiplane-strain crack, an approximate solution is obtained by the method of orthogonal polynomials. The weight functions are found in a series form through the solution of an infinite system of linear algebraic equations. In both cases, the plane-strain and antiplane-strain micropolar theory, it is shown that if a certain micropolar parameter (the same for both theories) tends to zero, then the solution and the weight functions tend to those of classical elasticity. Numerical results for the weight functions are reported.

• 出版日期2012-5