## METHODOLOGY

Aluminium square tubes have been widely adopted for energy absorption by different industrial applications because of its availability and low cost. Many engineering systems including automobile crashbox are designed with aluminium alloys due to their strength to weight ratio, The use of aluminium for crash energy absorption is based on its inherent properties hence the need to understand its behavior and performance under conditions prevalent in practical application.

In this chapter, numerical investigation of the effect of lateral inertia on aluminium square tube extrusions under axial impact were performed by modelling the tubes and simulating properties and loading conditions using the nonlinear explicit finite element code LS DYNA.

The main objective of this investigation is to

Understand how the plastic deformation of the extrusion is affected by lateral inertia.

Compare and validate numerical simulation with existing experimental and theoretical predictions.

Compare the static and dynamic behavior of the tubes.

## LS DYNA

Advancements in the scope of research related to impact analysis, crashworthiness and also improvements in computational power has led to the development of different software packages for high fidelity simulations for analysis of a wide range of parameters that influence the behavior of structures.

Commonly used are ABAQUS, ANSYS and LS DYNA.

LS DYNA is a multipurpose finite element software package developed by Livermore software technology corporation (LSTC), used extensively for implicit and explicit nonlinear transient dynamic finite element analysis. LS DYNAs characteristic elaborate contact algorithm, material library and wide option for element formulation makes it well suited for automotive crashworthiness and occupant safety simulations.

## Pre-Processing

The LS DYNA package is equipped with LS PREPOST which is an inbuilt graphical pre-processor for modelling and definition of parameters. Another option is to prepare an input file using a text editor in ASCII format or using any other third-party software available for pre-processing.

In this investigation, the LS PREPOST option was used for preprocessing input commands. This is because of the ease of maneuver and integration with the LS DYNA solver.

## Model Formulation

The models used for this investigation were based on the configuration of the test rig installed at the Norwegian university of science and technology used for impact test. Langseth and Hopperstad (1998) used this set up for dynamic and static experimental test and subsequent validation of numerical simulations.

## Element Formulation

The tube was modelled using the Belytschko-Lin-Tsay shell element with nine integration points through the thickness due to nonlinearity of the material property. The element size 5X5 was used with reference to Krauss and Laananen (1994), whose work suggested that the element size 5X5 is enough to produce optimum results for an extrusion with no initiator. A smaller element size as suggested by Langseth et al., (1999), who used a 3X3 element size in the numerical analysis, would give a more accurate result but will need more CPU run time. The striker or impactor was modelled as a rigid element. The total number of elements was 3464.

## Geometry

The tubes geometry used for this research was based on the dimensions of the crashbox of a Toyota yaris saloon car. The finite element model of the car as obtained from NHTSA archive had a crashbox measuring 220mm in length and thickness of 2.5mm. (Fig 3.1). The cross section of the tube measures 50mm X 90mm. Initial geometrical imperfections were modelled as a trigger having an amplitude of 3mm. The impactor was modelled to have a cross section of 150mm X 150 mm and a varying height based on the mass intended.

## Material Model

LS DYNA is equipped with a robust library of material models that reflect the properties and behavior of different materials. Commonly used in the simulation of the response of energy absorbing materials include the plastic kinematic model, MAT_3 (Wang, et al., 2005, Mamalis et al., 2003c), the piecewise linear plasticity model, MAT_24 (Mamalis et al., 2003b, Meguid at al., 2004b) and the anisotropic plasticity model, MAT_103 (Fyllingen et al., 2007).The aluminium alloy was modelled as an elasto-plastic material. MAT_024 (piecewise linear plasticity) keyword was used to model the AA6060 alloy of temper T4 because an arbitrary stress strain curve and an arbitrary strain rate dependency can be defined. The Johnson cook and Cowper Symmonds constitutive models were less preferred because aluminium is considered to be strain rate insensitive. Based on the material model proposed by Berstad et al., (1994), Isotropic constitutive model was used because tensile test in three directions have been performed on the alloy and results show that the AA6060 alloy can be considered as almost isotropic. Aluminium has a nonlinear stress-strain curve, from literature the uniaxial true stress-strain behaviour of the material was fitted into the five parameter model:

?=?_o+?_(i=1)^2?R_i +?_(i=1)^2?X_i +?_v

### R_i=?Q_i [1-exp?(-C_i ?_p )]

### X_i=(1-?)Q_i [1-exp?(-C_i ?_p )]

Where ?_o represents the proportionality limit or the yield stress, ?_p=?-?_o/E (?_pis the effective plastic strain, ? is the total strain and E is the youngs modulus). The plastic strain was found by subtracting the elastic part from the total strain.

The parameter, ?, determines the relationship between the kinematic and isotropic hardening. ?_v is the viscous stress and is neglected since aluminium alloys are recognized as almost strain rate insensitive. C_i, govern the rate of change of isotropic and kinematic hardening, Q_i is the asymptotic values. This is because the hardening property is an important factor necessary to properly define the response of the aluminium tubes. For aluminium AA6060, the hardening parameter ? was found to be 0.7. Hence the material tested shows 70% isotropic hardening and 30% kinematic hardening.

The stress strain curve applied to the material model was derived from the true stress and strain values.

## Boundary Conditions

The lower end of the tube was given translational and rotational restraint in all directions to simulate the clamped condition. The impacting mass was constrained in all directions except in the axial direction. This is to prevent unwanted oscillations during contact.

## Contact Definition

The contact between the rigid block and the tube was modelled using the Automatic node to Surface option with a coefficient of friction of 0.25. The contact between the lobes during deformation was modelled with a single surface contact algorithm without friction.