Modeling Multifield Contact Problems With Semi-Analytical Method

The work in this dissertation aims at modeling complex and multifield contact problems,including magneto-electro-elastic(MEE)contacts and their dynamic loading cases,contacts of functionally graded materials in the presence of surface elastic energy,and fretting contacts involving wear evolution,etc,via a semi-analytical method(SAM),the related theoretical basis and fast solution approaches.Contact model systems are developed to describe the combined influences of multi-physical coupling,surface energy,fretting evolution,material graduation,and dynamic loading on the contact behaviors of material systems,and to study material responses to input energies.The main works are reported as follows:1.The frequency response functions(FRFs)for the magneto-electro-elastic fields in a multiferroic half-space are analytically derived with respect to a unit concentrated normal force,a unit concentrated tangential force,a unit electric charge,and/or a unit magnetic charge,which are then converted into the results of continuous Fourier transforms of the influence coefficients(ICs),followed by the discrete Fourier transforms with a proper aliasing treatment.The conjugate gradient method(CGM)is used to obtain the unknown distributed pressure.Furthermore,the discrete convolution-fast Fourier transform(DC-FFT)algorithm is implemented to calculate the in-plane electric/magnetic potentials and subsurface stresses.The model is implemented to analyze the frictional sliding contact between a half-space and a sphere,and to study the coupled effects of surface electric/magnetic charges and friction on contact behaviors,including pressure,stresses,and electric/magnetic potentials.A sensitivity analysis is conducted to evaluate the influences of friction and material properties on the contact-induced multifield coupling behaviors.A number of case studies are committed,and the results indicate that electric/magnetic charge densities and the friction coefficient strongly influence the contact pressure,stress,and electric potential.2.A surface magneto-electro-elastic model is built to account for the effectsof surface energy on the contact behaviors.The FRFs for the MEE film are analytically derived with surface effects incorporated.Following the method in(1),frictional contact model involving a multiferroic thin film is developed.The proposed model is implemented to analyze the influences of surface MEE,multiferroic film thickness,and friction coefficient on the contact behaviors,including pressure/stresses and electric/magnetic potentials.A sensitivity analysis is conducted to evaluate the influence of surface parameters and their coupling on the contact behaviors.A set of behavior maps for the pressure and electric/magnetic potentials are constructed to reveal the influences of film thickness and material characteristic length,which can be used to determine the appropriateness of the geometry configuration(i.e.film or half-space)and surface behaviors(i.e.with or without considering the surface MEE effects).3.The general solutions to MEE thin films are obtained,incorporating the loading velocity in a dynamic process.Following the method in(1,2),the FRFs and their conversion into ICs for the MEE film are analytically derived.Fast numerical techniques,including the CGM and the DC-FFT,are employed for efficient numerical solutions to the dynamic contact behaviors,including the distributions and variations of contact pressure and electric/magnetic potentials,as well as subsurface stresses.The model is implemented to analyze the influences of loading velocity,film thickness,and sphere radius on the dynamic MEE responses,including pressure/stresses and electric/magnetic potentials.An energy conversion factor is selected to evaluate the performance of MEE energy conversion.Furthermore,a sensitivity analysis is conducted to evaluate the influence of material properties and their coupling on the efficiency of mechanical-electric/magnetic energy conversion.4.The core fundamental solutions to the elastic displacements and stresses for an elastic thin film with respect to the unit applied force are derived,incorporating the surface effects by means of the surface elastic theory.Following the method in(1,2,3),contact model involving a functionally graded elastic thin film is developed to study the combined effects of shear modulus ratio,film thickness,and surface energy on the contact behavior of thin-film materials.A performance map is constructed to reveal the influences of film thickness and material characteristic length,which correlates the geometric configuration(i.e.a film or a half-space)and surface behaviors(i.e.with or without considering the surface effects).5.Based on the SAM introduced above,an efficient fretting contact model for simulating rough surface contact problems involving torsional fretting wear,considering the evolution of surface topograohy with wear cycles,is developed,combined with worn surface updating based on the calculated wear depth using a modified Archard's equation.Torsional fretting wear tests are conducted using a ball-on-flat configuration to obtain the wear coefficient and wear profiles.The worn surface predicted by the numerical model for different loading cases have been compared with the corresponding experimental results,and the numerical results are well agreement with the experimental results.