This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surfac...This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.展开更多
To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditi...To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditions, a new approach to enforcing surfacecontact constraints for the tran- sient nonlinear finite elementproblems, referred to as 'the reduced augmented Lagrangianbi-conjugate gradient method (ALCG)', is developed in this paper.Based on the nonlinear constrained optimization theory and iscompatible with the explicit time integration scheme, this approachcan also be used in implicit scheme naturally.展开更多
文摘This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.
基金State Education Commission Doctoral FoundationNatural Science Foundation of Liaoning Province
文摘To avoid the numerical oscillation of the penalty method andnon-compatibility with ex- plicit operators of conventional Lagrangemultiplier methods used in transient contact problems to en- forcesurface contact conditions, a new approach to enforcing surfacecontact constraints for the tran- sient nonlinear finite elementproblems, referred to as 'the reduced augmented Lagrangianbi-conjugate gradient method (ALCG)', is developed in this paper.Based on the nonlinear constrained optimization theory and iscompatible with the explicit time integration scheme, this approachcan also be used in implicit scheme naturally.
