ABSTRACT of the Doctoral Thesis

Multi-Scale Modeling and Simulation of Metallic Foams

by Thomas Daxner (2002)

The subjects of the present thesis are metallic foams, which have entered the stage of practical application, their most important mechanical properties being high energy absorption capacity as well as high specific strength and stiffness. Metallic foams consist of a solid skeleton formed by struts and/or cell walls and a high volume fraction of voids, making them highly inhomogeneous materials. Their heterogeneity leads to thermomechanical responses, that are markedly different from those of bulk solids, and gives rise to material properties that have made cellular materials attractive for many engineering applications. It also presents an obvious target for modeling studies aimed at gaining an improved understanding of the mechanical behavior of cellular materials and of structures made of them.

In the present thesis, simulations of the mechanical responses of cellular metals are carried out at different length scales. In micromechanical approaches, their inhomogeneous structure is accounted for at the level of individual cells, cell walls, struts, and vertices. At this length scale, discrete geometrical models of the cellular microstructure are examined with the Finite Element method in combination with unit cell approaches, providing information on the local deformation and load transfer behavior. The micromechanical behavior is correlated to the mechanical behavior at the structural level, for example, in the form of overall yield surfaces or the effective behavior under multiaxial loading conditions. Advantageous and detrimental topologies and values of microgeometrical parameters are identified for supporting materials design and development.

At the macromechanical level, that is, the level of samples and components that are two or three orders of magnitude larger than the typical size of individual cells, only the overall thermomechanical behavior is accounted for. Constitutive models for metallic foams, which are implemented in the Finite Element code \ABAQUS, are evaluated with regard to their performance in simulating impact tests related to passenger protection in motor vehicles. Among other results, the investigation shows the existence of optimum crash-absorption behavior, described by high energy absorption capability at a low peak force, for a well-defined foam-specific apparent density.

At the same macroscopic level, an algorithm for the optimization of foam density distributions in components made of or containing metallic foam is presented along with examples of structures that are improved with regard to strength or stiffness. The implementation of the algorithm as a material law, which is self-adapting in analogy to living tissue (bone), yields distinct speed benefits in comparison to existing methods.

In addition, questions involving the spatial variations or gradients of cell sizes and shapes within a given sample or structure are studied at length scales that are intermediate between microscale and macroscale. A section of the present thesis is devoted to the influence of mesoscopic inhomogeneities on the mechanical behavior of bodies made of metallic foams under crush and crash loads.

revised 020801 (hjb)