Keywords: finite element, inverse modelling, timber, punched metal plate, nail plate, double-sided, fastener, connector.

This paper describes how the finite element method (FEM) has been used in conjunction with an inverse modelling technique [1,2] to simulate the behaviour of European whitewood timber joints hydraulically fastened using a prototype punched metal plate fastener with projections/teeth on both sides. Product development of new punched metal plate fasteners is usually largely empirical, based only on physical testing of joints made using different nail plate geometric configurations. With several prototypes and their refinements usually necessary from concept to production, development costs are significant as new tooling is often required for each configuration. The proposed approach has potential to reduce development costs for new fasteners by substitution of prototypes with numerical models.

The objective is to construct a 3-D numerical model that simulates closely the observed experimental behaviour. Material properties needed to make that possible are difficult to determine directly because of constrained access, plasticity and damage of the joint constituent elements. On the other hand, inverse modelling involves calibrating model parameters using measured values and is, therefore, very suitable for the task. The target then is to search for material constants that yield the minimum error norm, i.e. the distance between the measured and computed process parameters. Measured data is obtained from tests conducted to current European standard methods [3]. Computed data is derived from FEM assuming timber to be an orthotropic material with isotropic yielding surfaces defined by Hill's potential function and an associate flow rule. ABAQUS/Standard software [4] is used for the modelling.

For the test specimens, the observed joint failure modes include timber crushing under fastener bearing and fastener tooth bending about the root. This makes modelling of timber in compression and fastener tooth in bending critical aspects of the numerical model. In literature, several constitutive models for timber behaviour in compression have been proposed but none is universally accepted [5]. With each of the models having shortcomings of its own, a simple linear-perfectly plastic model is, therefore, adopted in this study. The reference elastic properties of the timber used are those for Norway spruce obtained from [6]. Reference properties for the steel fastener are derived from standard tension tests.

From the experimental work, three characteristics are identified as necessary to fully define joint behaviour up to ultimate load. These are (1) the joint foundation modulus, (2) the capacity per tooth and (3) the ultimate/secant modulus. To match experimental behaviour, the model stiffness was iteratively modified by scaling of the elastic moduli and the model capacity by scaling of the yield strength. The joint model was constructed progressively from timber and tooth behaviour calibrated separately, through single tooth joint model calibration, culminating in the modelling of a one-eighth joint model. The interface between nail plate and timber is modelled using Coulomb friction contact [4]. This aspect imposed huge demands on the computing effort. Good agreement with test results is achieved.

1

K.M. Zhao and J.K. Lee, "Inverse estimation of material properties for sheet metals", Communications in Numerical Methods in Eng'g, Vol 20, 2004. doi:10.1002/cnm.479

2

X.Q. Peng and J. Cao, "Numerical determination of mechanical elastic constants of textile composites", Proceedings of the 15th Technical Conference of the American Society for Composites, Texas, U.S.A., 2000.

3

T. Zhou, "Towards Optimisation of a Double-Sided Punched Metal Nail Plate Connector", PhD Thesis, University of Brighton, in preparation.

4

Hibbitt, Karlsson & Sorensen Inc., "ABAQUS/Standard User's Manual Version 6.3", Pawtucket, RI , USA., 2002.

5

M. Pattorn-Mallory, S.M. Cramer, F.W. Smith and P.J. Pellicane, "Nonlinear material model for analysis of bolted wood connections", Journal of Structural Engineering, ASCE, Vol. 123, No. 8, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:8(1063)

6

J.M. Dinwoodie, "Timber: Its Nature and Behaviour", 2nd ed., E. & F.N. Spon, London, 2000.

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