# Modeling of foams for impact simulations

[Doktorsavhandling]

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 for impact simulations. To start with, a continuum hyperelasto-viscoplastic model is developed within the framework of Theory of Porous Media. Special attention is put on the volumetric hardening behavior that foams show under large compressive deformation. The foam 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 on the stiffness of the solid material and the loading rate, the influence of the gas phase may be significant and it may therefore be included in the model. Additionally, the gas flow through the solid skeleton of open-cell foams is modeled based on the mass balance for the mixture. A coupled system of equations is obtained for which a staggered solution strategy is used. The staggered method makes the coupled analysis possible in standard finite element software. Two models are thereby developed; a single-phase model for the solid skeleton, disregarding the gas response, and a two-phase model, including also the gas response. 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 the foam 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 the microstructure, whereby conventional continuum models may not be a good representation of the foam layer. This issue is addressed by explicitly including the microstructure through a representative volume element (RVE) and obtaining its response by means of homogenization. To represent the structure on the macroscopic scale, two different shell models are developed. Each integration point of the shell will include an RVE, and a subscale boundary value problem will be solved for those points in the structure where a high resolution is desired, normally where steep gradient of deformation occur. This will result in a nested multiscale computational scheme. Numerical examples to illustrate the developed models are included.

**Nyckelord: **Foams, Constitutive modeling, Theory of Porous Media, Computational Homogenization, Multiscale Analysis, Shell theory.

Denna post skapades 2008-09-30. Senast ändrad 2013-09-25.

CPL Pubid: 74604