Compact closed form solution of the incremental plane states in a pre-stressed elastic composite with an elliptical hole

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 95; no. 2; pp. 193 - 199
• Main Authors: Craciun, E. M., Barbu, Luminita
• Format: Journal Article
• Language: English
• Published: Weinheim Blackwell Publishing Ltd 01.02.2015; Wiley Subscription Services, Inc
• Subjects: complex potentials; Conformal mapping; conformal mapping technique; Displacement; Elliptic hole; Exact solutions; Fracture mechanics; Mathematical analysis; plane state; pre-stressed composite material; Representations; Riemann-Hilbert problem; Shear; Stresses
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201300125

We consider an unbounded, homogeneous, pre‐stressed orthotropic elastic composite containing an elliptical hole and subject to uniform remote tensile and uniform remote tangential shear loads (Mode I and respectively Mode II of fracture). Using the conformal mapping technique and the representation of the stress and displacement fields by complex potentials, we determine the solution of the problem in a compact and elementary form. When the smaller semiaxis of the elliptical hole tends to zero, i.e. the hole becomes a crack, the potentials obtained reduce to a form similar to that of the crack problem, obtained by solving the corresponding Riemann‐Hilbert problem. The authors consider an unbounded, homogeneous, pre‐stressed orthotropic elastic composite containing an elliptical hole and subject to uniform remote tensile and uniform remote tangential shear loads (Mode I and respectively Mode II of fracture). Using the conformal mapping technique and the representation of the stress and displacement fields by complex potentials, they determine the solution of the problem in a compact and elementary form.