Dynamic propagation problem on Dugdale model of mode III interface crack

Abstract

By the theory of complex functions, the dynamic propagation problem on Dugdale model of mode 111 interface crack for nonlinear characters of materials was studied. The general expressions of analytical solutions are obtained by the methods of self-similar functions. The problems dealt with can be easily transformed into Riemann-Hilbert problems and their closed solutions are attained rather simply by this approach. After those solutions were utilized by superposition theorem, the solutions of arbitrarily complex problems could be obtained.

Asymmetrical dynamic propagation problems on mode III interface crack

“…Under the conditions of sufficing Eq. (13), as long as self-similar function m(τ ) fulfils boundary conditions of concrete problems, equation of motion and interfacial connective term need not be reconsidered [5][6][7][8][9]15] .…”

“…(9), sequential conditions of an interface between two different materials can be rewritten as follows [5][6][7][8][9]15] :…”

“…The shear stresses are equivalent on the plane y = 0, −∞ < x < ∞, but the directions are opposite. Outside of the crack, the displacement along the interface holds continuum [5][6][7][8][9]15] .…”

“…In order to depict universality, the relationship C (1) 55 /ρ (1) < C (2) 55 /ρ (2) assumed exists. When the two media are identical, the solutions obtained must be transformed into corresponding solutions of sole medium problem [5][6][7][8][9]15] . There result…”

“…On account of the complexity in mathematics, researches on dynamics problems are not adequate deep [4−9] . Some researchers investigated interfacial edge crack and nonhomogeneous propagation interface crack problems, but most only attained the numerical solution [10−13] , a few obtained analytical solution [14,15] . Consequently, it is necessary to study asymmetrical dynamic propagation problems.…”