Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites

To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.

A TWO-LEVEL MULTISCALE DECONVOLUTION METHOD FOR THE LARGE EDDY SIMULATION OF TURBULENT FLOWS

This report presents a novel continuous deconvolution method which is used to solve the closure problem in Large Eddy Simulation (LES for short) leading to a new LES model. In the deconvolution method described herein the flow velocities u are approximated by their average ũ on a fine intermediate length scale γ and then, by means of an exact extrapolation formula, expressed in terms of the averaged flow ū on the length scale α, which we seek to resolve. We prove existence, uniqueness and regularity of the weak solution w(α, γ) of the resulting LES models as well as energy estimates of the weak solution that are uniform in the intermediate length scale γ of the deconvolution procedure. We show also that the modeling error ‖ū - w(α, γ)‖ is driven only by the deconvolution error ‖u - ũ‖ and is independent of the resolved scale α.

NUMERICAL METHODS FOR THE THREE-DIMENSIONAL TWO-BODY PROBLEM IN THE ACTION-AT-A-DISTANCE ELECTRODYNAMICS

We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses Stürmer's extrapolation formula and assumes that a step of integration can be taken as a step of light ladder, which limits its use to shallow energies. The second method is an improvement of pre-existing iterative schemes, designed for stronger convergence and can be used at high-energies.