In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstru...In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstructure of the closed-cell aluminum foam. Effective parameters including foam density and the velocity of impactor on foam dynamic behavior are investigated. In order to show the validity and accuracy of results, some static experiments and low-velocity impact tests have been conducted. Results in dicate a remarkable agree me nt between the simulation and experimental data. Moreover, the results show that by increasing the density of foam samples, the highest difference between numerical and experimenidi results for peak stress and absorbed energy are 35.9% and 6.9%, respectively, which is related to the highest density. For impact velocities ranging from 3.1 to 4.2 m/s, the maximum discrepancy in peak stress and absorbed energy occur at an inipact velocity of 3.1 m/s in which corresponding errors are 33.3% and 6.6%, respectively. For the impact velocity of 40 m/s, the highest increase in peak stress and absorbed energy are 667.9% and 370.3% associated with the density of 0.5 and 0.3 g/cm^3, respectively.展开更多
The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency sh...The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency should be accounted for in the mechanical behaviors of nanoscale structures. In the current investigation, the influence of free surface energy on the nonlinear primary resonance of silicon nanoshells under soft harmonic external excitation is studied. In order to obtain more accurate results,the interaction between the first, third, and fifth symmetric vibration modes with the main oscillation mode is taken into consideration. Through the implementation of the Gurtin-Murdoch theory of elasticity into the classical shell theory, a size-dependent shell model is developed incorporating the effect of surface free energy. With the aid of the variational approach, the governing differential equations of motion including both of the cubic and quadratic nonlinearities are derived. Thereafter, the multi-time-scale method is used to achieve an analytical solution for the nonlinear size-dependent problem. The frequency-response and amplitude-response of the soft harmonic excited nanoshells are presented corresponding to different values of shell thickness and surface elastic constants as well as various vibration mode interactions. It is depicted that through consideration of the interaction between the higher symmetric vibration modes and the main oscillation mode, the hardening response of nanoshell changes to the softening one. This pattern is observed corresponding to both of the positive and negative values of the surface elastic constants and the surface residual stress.展开更多
The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic press...The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.展开更多
文摘In the present work, the response of closed-cell aluminum foams under low-velocity impact has been studied numerically and experimentally. Computerized tomography is employed to access three-dimensional (3D) microstructure of the closed-cell aluminum foam. Effective parameters including foam density and the velocity of impactor on foam dynamic behavior are investigated. In order to show the validity and accuracy of results, some static experiments and low-velocity impact tests have been conducted. Results in dicate a remarkable agree me nt between the simulation and experimental data. Moreover, the results show that by increasing the density of foam samples, the highest difference between numerical and experimenidi results for peak stress and absorbed energy are 35.9% and 6.9%, respectively, which is related to the highest density. For impact velocities ranging from 3.1 to 4.2 m/s, the maximum discrepancy in peak stress and absorbed energy occur at an inipact velocity of 3.1 m/s in which corresponding errors are 33.3% and 6.6%, respectively. For the impact velocity of 40 m/s, the highest increase in peak stress and absorbed energy are 667.9% and 370.3% associated with the density of 0.5 and 0.3 g/cm^3, respectively.
文摘The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency should be accounted for in the mechanical behaviors of nanoscale structures. In the current investigation, the influence of free surface energy on the nonlinear primary resonance of silicon nanoshells under soft harmonic external excitation is studied. In order to obtain more accurate results,the interaction between the first, third, and fifth symmetric vibration modes with the main oscillation mode is taken into consideration. Through the implementation of the Gurtin-Murdoch theory of elasticity into the classical shell theory, a size-dependent shell model is developed incorporating the effect of surface free energy. With the aid of the variational approach, the governing differential equations of motion including both of the cubic and quadratic nonlinearities are derived. Thereafter, the multi-time-scale method is used to achieve an analytical solution for the nonlinear size-dependent problem. The frequency-response and amplitude-response of the soft harmonic excited nanoshells are presented corresponding to different values of shell thickness and surface elastic constants as well as various vibration mode interactions. It is depicted that through consideration of the interaction between the higher symmetric vibration modes and the main oscillation mode, the hardening response of nanoshell changes to the softening one. This pattern is observed corresponding to both of the positive and negative values of the surface elastic constants and the surface residual stress.
文摘The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects.To this end, Gurtin-Murdoch elasticity theory is implemented into the irst-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large delections in the postbuckling domain and initial geometric imperfection. Finally, an eficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.
