Modeling of foams for impact simulations

Abstract: Stimulated by the strong drive in the automotive industry to reduce energy consumption,and, linked to that, the need to reduce weight, this thesis concerns modeling of foams forimpact simulations. To start with, a continuum hyperelasto-viscoplastic model is developedwithin the framework of Theory of Porous Media. Special attention is put on thevolumetric hardening behavior that foams show under large compressive deformation. Thefoam is represented as a mixture between solid phase material and pore phase material;these are in this context polymer or metal and gas, respectively. Depending primarily onthe stiffness of the solid material and the loading rate, the influence of the gas phase maybe significant and it may therefore be included in the model. Additionally, the gas flowthrough the solid skeleton of open-cell foams is modeled based on the mass balance forthe mixture. A coupled system of equations is obtained for which a staggered solutionstrategy is used. The staggered method makes the coupled analysis possible in standardfinite element software. Two models are thereby developed; a single-phase model for thesolid skeleton, disregarding the gas response, and a two-phase model, including also the gasresponse. Both have been implemented in the commercial finite element code LS-DYNA.Numerical examples are included to verify and validate the modeling.The second half of this thesis is dedicated to the modeling of thin porous structures,like thin foam layers in a reinforcing component in the body of a car. The thickness of thefoam may be close to the size of the largest pores in the microstructure. In that situation,the scale of variations of deformation may not be well separated from the scale of themicrostructure, whereby conventional continuum models may not be a good representationof the foam layer. This issue is addressed by explicitly including the microstructurethrough a representative volume element (RVE) and obtaining its response by means ofhomogenization. To represent the structure on the macroscopic scale, two different shellmodels are developed. Each integration point of the shell will include an RVE, and asubscale boundary value problem will be solved for those points in the structure where ahigh resolution is desired, normally where steep gradient of deformation occur. This willresult in a nested multiscale computational scheme. Numerical examples to illustrate thedeveloped models are included.