On the finite motions generated by a mode I propagating crack. (English) Zbl 1005.74055

Tarantino, Angelo Marcello

J. Elasticity 57, No. 2, 85-103 (1999).

Summary: We investigate the motion field surrounding a rapidly propagating crack loaded symmetrically about the crack plane. The problem is formulated within the framework of finite elastodynamics for thin slabs composed of compressible hyperelastic material. Writing the equations of motion together with initial and internal boundary conditions (in a coordinate system that translates with the moving crack tip), we perform an asymptotic local analysis of a traction-free straight crack that suddenly grows at constant velocity. Moreover, asymptotic Piola-Kirchhoff and Cauchy stress fields are computed, and we discuss the order of singularity of dynamic stresses.

MSC:

74R10	Brittle fracture
74H35	Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74B20	Nonlinear elasticity
74H10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics

Keywords:

mode I propagating crack; asymptotic Piola-Kirchhoff stress fields; asymptotic Cauchy stress field; finite elastodynamics; compressible hyperelastic material; asymptotic local analysis; traction-free straight crack; singularity of dynamic stresses