A Mechanical Model of Cellular Solids for Energy Absorption


Safety is a high priority in industry. Safety devices such as helmets, road barriers, bumpers, and packages must have the ability to effectively absorb and dissipate energy during impacts to minimize the extent of damage and ensure human and materials safety. This calls for accurate modeling of materials used in the design and fabrication of energy absorption devices and systems. Presently, virtual modeling is highly used in improving product quality before manufacturing. It helps in reducing the number of prototypes, marketing time as well as development costs.

Cellular materials otherwise known as foams exhibit high energy absorption and dissipation capability thus explain their intensive use in applications requiring high shock mitigation such as product packaging. Foams are generally derived from materials by producing cellular structures with voids enclosed by cells. The foams can, however, be designed to adapt to specific applications with a suitable combination of the base material, cellular structure, and density. To this end, accurate predictive models of cellular materials are highly desirable for selecting suitable foam for desired applications. Consequently, the models should describe the stress-strain behavior by taking into account both the compression, tension and multiaxial loading that helps in evaluating the energy absorption characteristics.

Recently, Professor Massimiliano Avalle from University of Genoa together with Professor Giovanni Belingardi from Politecnico di Torino developed a new model to describe the mechanical stress-strain behavior and strain rate sensitivity of material foams. The objective was to fit almost all foam materials in uniaxial loading conditions by considering the factors affecting the density and strain rate. Their work is currently published in the journal Advanced Engineering Materials.

Before the current work, the authors initially presented several models to describe the quasi-static stress-strain behavior of different cellular materials. However, the current work presents a more general model approach with the key areas of concern being: proper parameter identification, evaluation of the mechanical characteristics of a variety of cellular materials and analysis of the influence of strain rate. Among the different cellular materials, foaminal aluminum foam and APM hybrid foam were considered in this study. Eventually, the feasibility of the new model was validated through experimental tests using parameters that were identified in the previous experimental data. The dynamic, impact and quasi-static tests were carried out at different impact energy and loading speeds.

The newly developed model effectively represented the plateau, elastic-plastic transitions and the density of various foam under different testing conditions. It also allowed modeling of the influence of density and strain rate. For instance, a correlation coefficient greater than 95% was obtained indicating the accuracy of the experimental curves. Additionally, the authors noted that the model can equally be used to virtually describe the structural behavior of all-metal foams.

In summary, the Avalle-Belingardi study presented an important new mechanical model for investigating the energy absorption ability of cellular materials. Overall, the model describes the stress-strain behavior specifically the uniaxial compression, which is the main stress mode, as well as the influence of other factors such as the base material properties and strain-rate. The results provide a useful tool for designing energy absorption devices and systems based on metal foams by selecting the most appropriate foam material for a particular application.

About the author

Giovanni Belingardi was born in Torino in 1951, he got his Master degree in Mechanical Engineering at the Politecnico di Torino in 1975.

From 1995 he is full Professor in the Mechanical Engineering Dept of the Politecnico di Torino.

His present research activity is mainly devoted to structural design and experimental testing in automotive engineering, with particular attention to lightweight design of the car body and to passive safety of vehicle occupants and pedestrians.

He is author of more than 320 papers published in international scientific journals and in proceedings of national and international conferences.

He has recently been and at present is the scientific coordinator of the Operative Units of the Mechanical and Aerospace Engineering Department for a number of projects of the framework programs of the European Union, of the National and Regional Governments. Research cooperation with industrial partners has been effective as well.

In 2016 he has been appointed as the scientific responsible of the Interdepartmental Center [email protected] that is fully dedicated to the sustainable mobility and vehicle of the future.

He is the responsible for International cooperation of Politecnico di Torino within the frame of the Automotive Engineering, with particular attention toward Canada, US, Brazil, Poland and Serbia.

About the author

Massimiliano Avalle is full Professor of Machine Design at the University of Genoa, Italy. He got his Phd from Politecnico di Torino, where he has been Associate Professor until 2016.

He has mainly worked in the field of the passive safety of vehicles in the perspective of the improvement of crashworthiness of car structures, the energy absorption of structural components, and the passenger protection. Some valuable contributions in this field have been in stochastic simulations, the use of adhesive and hybrid joining in crash components, the development of the generic car models for crash, the safety of lightweight electric vehicles. More recently he was involved in the protection of vulnerable users introducing the measurement of rotational accelerations to improve the evaluation of the damage to the head during impact, lightweight bonnets pedestrian friendly, and parametric simulations of the leg impact with the use of human body models.

In parallel his research activities were in the modeling of non-conventional materials (like plastics, cellular materials and composites) especially from the point of view of the strain-rate effects and the energy absorption.



Avalle, M., & Belingardi, G. (2018). A Mechanical Model of Cellular Solids for Energy Absorption. Advanced Engineering Materials, 21(4), 1800457.

Go To Advanced Engineering Materials

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