| Summary: | A failure analysis procedure based on the elastic-plastic finite element analysis of the
higher order beam is presented to predict the mode II and III failure of impulsively loaded
ductile clamped beams.
The variational equation of motion of the problem is first obtained by using the principle
of virtual work and the Total Lagrangian Approach together with the kinematics of the
higher order beam theory and the nonlinear strain-displacement relation. The Finite
Element Method is employed to discretize the beam spatially initiating the numerical
solution procedure. The constitutive model considers elastic-plastic isotropic strain
hardening by von Mises yield criterion and associated flow rule and strain rate sensitivity
by Cowper-Symonds relationship. Equations of motion are integrated by central
difference method in the time domain.
Based on the finite element simulation, two failure criteria are proposed. In the
interaction failure criteria, contributions from tensile tearing and transverse shearing to the
damage of the beam are considered by including tensile strain ratio and shear stress ratio in
the criteria. Both linear and quadratic models are investigated. The beam is modelled as
an elastic-plastic beam with a plastic hinge at each support to calculate the total strain at
the support. The shear stress comes either from the wall reaction obtained from
equilibrium or directly from the finite element analysis of the higher order beam theory. In
the sectional plastic work density criterion, the beam is assumed not to fail until the
sectional plastic work density exceeds the critical value. Post failure analysis is also
included to take account of the residual energy of the beam at failure. Numerical simulations have been carried out for the experiments of blast loaded beams.
Comparison with the experimental results suggests the quadratic interaction criteria is
suitable for this type of analysis. === Applied Science, Faculty of === Civil Engineering, Department of === Graduate
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