Indentation Law Research Articles

LOW-VELOCITY IMPACT RESPONSE OF COMPOSITE LAMINATES WITH A DELAMINATION

The impact response behavior of composite laminates with a delamination is investigated, using the finite-element method based on the Mindlin plate theory. To evaluate the impact force acting on the composite laminates from a rigid ball, an indentation law incorporating the Newton-Raphi:on method is employed. The Newmark time integration algorithm is adopted to solve the motion of the rigid ball. To deal with the dynamic contact between two delaminated layers effectively, the classical Lagrange multiplier technique is modified by combining with a special time integration algorithm. The proposed method can overcome the two principal deficiencies of the classical Lagrange multiplier method efficiently. Numerical results provide much of the information for understanding the impact phenomenon of composite laminates with a delamination.

Response of Plate and Shell Structures due to Low Velocity Impact

The dynamic response of isotropic and laminated composite plate and shell structures under low velocity impact have been investigated using nine-node degenerated shell elements with assumed shear and membrane strain fields to model the target. The effects of large displacement and change in thickness have been included during the formulation process of the shell element. The incremental form of governing equations is formulated based on the Updated Lagrangian approach where the effects of geometric nonlinearities as well as permanent deformation of target are accounted for. Both the Hertzian contact law and experimental indentation law are incorporated into the finite element program to establish the contact force history. Numerical examples on isotropic and composite laminated plate and shell structures under low velocity impact are presented.

Combined effects of shear deformation and permanent indentation on the impact response of elastic plates

The dynamic response of a shear-deformable elastic plate to the impact of a mass causing permanent indentation has been considered. Experimental data form the basis of the indentation law and an elastic recovery is assumed when the striking mass leaves the plate. The contact force and the plate center displacement time histories as well as the energy absorbed during impact have been calculated. These results have been compared for elastic impacts with and without shear deformation effects.

Smooth indentation of an initially stressed orthotropic beam

The contact behavior between a smooth rigid cylinder and a simply supported orthotropic beam under uniaxial initial stresses is studied. The displacements are computed by superposing Mindlin plate solution with the solution obtained from Biot's theory of incremental deformation. Finite Fourier transforms are used in solving the equations. A point matching technique is used to compute the contact stresses and the amount of indentation for a given contact length. The effects of orthotropy and initial stresses on the contact stress distribution are investigated. An indentation law is established from the numerical results.