A Mechanical Model of Cellular Solids for Energy Absorption

Abstract

Cellular materials, also known as foams, have a variety of applications in the field of packaging, and shock mitigation in the case of crash of vehicles, due to their ability to protect goods by absorbing energy in the case of impact while reducing the transmitted loads. To properly design energy absorption devices and systems such as bumpers, road barriers, helmets, sole paddings, packages, etc. it is necessary to use precisely predictive models of cellular materials, in order to select the most suitable foam for the considered application. The model must describe the stress-strain behavior, at least uniaxial compression, but also sometimes the tension and multiaxial loading, then energy absorption characteristics is evaluated. Moreover, it must take into account affecting factors like the strain-rate. Secondarily, modeling the influence of the density heavily helps designer in selecting the best solution in terms of minimum weight per given energy to dissipate. In previous works, the authors present more than one model able to describe the quasistatic stress-strain behavior of several cellular materials. The current paper presents a very general model able to describe, with properly identified parameters, the mechanical characteristics of a much larger variety of cellular materials including metal foams, foam mechanical properties (like, e.g., the dependence on density), and takes into account the influence of strain-rate. Among the considered materials are the Foaminal 1 aluminum foam and the APM 1 hybrid foam. The model is fitted to experimental tests with parameters identified based on past experimental data from the authors themselves. Tests include quasi-static, dynamic, and impact tests at different loading speed and impact energy. It is shown that the proposed model is fundamentally suitable for most materials, virtually any foamed material, and it is an outstandingly useful tool for designers in the mentioned areas.

Characterization of Energy Absorption and Strain Rate Sensitivity of a Novel Elastomeric Polyurea Foam

“…In contrast, higher energy absorption and higher strength are characteristics of closed‐cell foams but at reduced efficiency due to the higher density. [ 3–9 ] Therefore, a foam with a hierarchical structure composed of regions of open‐cell and others of closed‐cell is optimal for improving the impact‐mitigation ability of structures to absorb the impact energy. [ 10,11 ] Nonetheless, regardless of the cell structure, the foam padding is required to lower the amplitude of the incoming force while broadening the peak of the force‐time history, hence allowing the body to respond with inducing injury naturally.…”

A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads

“…where ε is the compressive strain, σ LEO is the compressive stress of the LEO model, and the oscillation fitting parameter ω is the only additional parameter compared to the Avalle model. [7] The fitting parameters are: σ p as the plateau stress, σ s as the linearhardening slope in the plateau region, σ d as the Rusch densification parameter, n as the Rusch densification exponent, and m as the linear-plateau transition parameter.…”

“…where m, n, r, and s are fitting parameters. Avalle [7] updated the model to better capture plateau stresses apparent in the mechanical response as…”

“…Gibson and Ashby [ 5,6 ] described the three regions of compressive stress–strain curve as elastic, plateau, and densification, and proposed scaling relationships for both elastic modulus and yield stress versus relative density of cellular solids based on an analytical model. Avalle [ 7 ] updated Rusch's model to include a term to describe the plateau region beyond yielding. Recently, a statistical constitutive model based on a distributed collapse of individual cells has been proposed to capture the stress‐collapse post‐yield, which is typical of these stochastic cellular materials.…”

Tunable Energy Absorbing Property of Bilayer Amorphous Glass Foam via Dry Powder Printing

“…These concepts often consist of soft materials, such as hydrogels, and require external stimuli, such as magnetic field, mechanical stress, and temperature, to activate the tunable mechanical properties. Cellular structured materials are greatly used for energy absorbing applications [11][12][13][14]. Several research studies showed that graded cellular structures enabled gradual collapse leading to more energy absorption and this is beneficial for protecting payloads from dynamic loads [15][16][17][18].…”