Hamiltonian analysis applied to the dynamic crack growth and arrest in a Double Cantilever Beam
The paper deals with the dynamic crack growth and arrest in an elastic DCB specimen,idealized by a Bernoulli-Euler beam.The surface energy of the material is 1 2Γ and the initial crack is blunted with the energy 2Γ0>2Γ1.The crack is then pushed ahead while the loading is frozen,the crack velocity and arrest length depending on the ratio 1 R = Γ0/Γ1.The analytical approach used to investigate the beam behaviour and the crack growth,is based on the Hamiltons principle of stationary action,considering an approximate equation of motion,based on a N modes decomposition of the beam deflection.This process leads to a set of N second order differential equations where the unknowns are the mode amplitudes and their derivatives,coupled to a single equation exhibiting the current crack length l(t),velocity l&(t) and acceleration &l&(t).The results concerning the crack kinematics,particularly the arrest length,are in good accordance with those obtained by a Finite Element Model associated to a cohesive zone model.The method is then applied to a material with heterogeneous fracture properties,in particular with a distribution of small brittle flaws perturbating the crack kinematics.This method allows a large range of configurations with a low computational time.
Crack arrest Hamiltonian Lagrange equations Double Cantilever Beam pops-in
Gilles DEBRUYNE Radhi ABDELMOULA
LaMSID-EDF-CEA,1 avenue du Gal de Gaulle 92141 Clamart,France Paris XIII University,LSPM,Avenue J.B.Clément 93430 Villetaneuse,France
国际会议
北京
英文
1-10
2013-06-16（万方平台首次上网日期，不代表论文的发表时间）