Methodology For Quasi-static Compression And Impact Responses Of Multi-layered Cushioning Structures And Its Applications

Foam and honeycomb materials are commonly used in automobile, aeronautics, astronautics, helmet industries to absorb kinetic energy created by the external shock because of their lightweight and good cushioning properties. Multi-layered cushioning structures are stacked by different cushioning materials or identical monolayer panels to improve the energy absorption ability of sandwich structure that is available in engineering applications. It will require a large mount of experimental data to capture the cushioning properties because cushioning materials exhibit exceptionally nonlinear behaviors and also depend on many factors, such as environment temperature, compressive strain rates and structural parameters, so it is meaningful to explore suitable methods for predicting compressive responses of the multi-layered cushioning structure on the basis of constitutive relationship of single layer cushioning materials. The several types of multilayer cushioning structure are investigated by using virtual parameter method proposed in this paper and explicit finite element method as follows:(1) Virtual parameter method was proposed for determining quasi-static compresive responses of multi-layered cushioning structure. The mass or damping parameter were added to the interface between the different layers to consider the inertia force or damping force to modify the system equations of motion from nonlinear algebraic equations to a set of ordinary differential equations so that the Runge-Kutta method can be applied to obtain the numerical solution of the system responses. The rationale of the method was shown both analytically and numerically by assessing the reliability of the virtual mass and damping method. The virtual mass method illustrates the corresponding vibration frequencies approches infinitity and vibration amplitudes approach zero when the virtual mass is close to zero. The virtual damping method demonstrates the derivative term is almost negligible as the virtual damping decreases to some certain value. It can be concluded that the response of the composite cushioning system remains almost unchanged as long as the virtual parameter is smaller than a certain value.(2) A differential-algebraic system was transformed into original differential equations by virtual mass method to obtain impact resonses of multi-layered foam cushioning structure. Similarly, the deduction processes show the vibration frequency created by virtual mass tends to infinity and vibration amplitude approximates to zero as virtual mass involved comes near zero. The virtual mass method was also utilized to investigate drop impact responses of span beam supported at two ends of the rigid body under the cushioning effect of the multi-layered foam structure. The numerical results suggest the effect of virtual mass on the displacements and stresses histories of the beam is negligible if virtual mass reduces to be a certain value as well.(3) Corrugated paperboard exhibtes strong nonlinear mechanical propereties due to the fact that nominal stress of monolayer board drops with increasing strain caused by buckling of corrugated core defore densification occurs. The virtual mass method and virtual damping method were applied to compute the compressive behaviors of multi-layered corrugated sandwich plates, and the analysis process indicates the virtual inertia forces and virtual damping forces play small perturbation to lead to progressive buckling for multilayer cushioning structures. The results show that the number of peak points on stress-strain curves is equivalent to the number of structural layers of corrugated board, which is validated against experimental data.(4) The constitutive relationship of EPS was fitted as a function of density of EPS, compressive strain rate, and strain based on the experimental stress-strain data, and constitutive relation for honeycomb material was given related to cell length, cell thickness, the yield strength of material from which the honeycomb structure is made, strain rate and strain on the basis of empirical formula. The dynamic equation of two-layered composite cushinong structure made of foam and honeycomb under uniaxial loading conditions was established on the basis of the two constitutive laws mentioned above, then the impact response was analyzed by adopting virtual mass method and optimization design is obtained. The explicit finite element modeling of head-EPS-aluminum honeycomb composite cushioning structure was built to explore the response of the head transmitted from the EPS and honeycomb materials under multiaxial loading conditions. The response surface methodology was applied to determine optimization specific energy absorbing as a function of height of foam, height of honeycomb, and cell length of honeycomb, and the second-order polynomial function is utilized to solve the maximum specific energy absorbing during optimization process. It is found that EPS-honeycomb structure has more excellent energy absorbing capacity than traditional EPS cushioning system. Virtual mass and damping parameters have negligible effect on the uniaxial quasi-static compression and impact responses when an appropriate virtual parameter is selected for analyzing compressive responses of multi-layered cushioning structure, which is easily captured by Runge-Kutta method. For the case of multi-layered corrugated paperboard, the virtual inertia forces generated by mass and damping inserted between the layers cause layers to reach the buckling state in chronological order. The virtual mass and virtual damping can be extended to the multi-layered honeycomb or lattice structures to capture layer-wise collapse mechanism. Finite element method provides effective way for optimization design of multi-layered cushioning structure subjected to multiaxial compressive loading sceneros.