ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

h and h being the thickness of the deformable layer in each solid (Fig. 1)
1 2
Fig. 1. Discrete springs in the EFM
The local pressure corresponding to position discrete spring i is calculated with the
same Eq. 1 but using the equivalent stiffness of the two springs, corresponding to each
solid, connected as two springs in series:
k1⋅k2 k =
k + k
1 2
However, the formulation of the EFM presented in the above equations is limited by its
approximate nature, which leads to inaccuracies in the results, as already reported by
Johnson [12] and confirmed in our previous study [1]. In that work we proposed a
modified model (mEFM) based on the use of three parameters, to adjust the model to
experimental data or FE results. In this model the pressure in each discrete spring is
calculated with Eq. 4:
pi kc δic
(3)
= ⋅ (4)
where kc and δic are the corrected stiffness and corrected deformation of the spring,
given by:
k
c
δo
δic = max(0, δi−
) (5)
f
1−ν
E ⎛δref ⎞
= ⋅ ⋅⎜ ⎟
( 1+ ν) ⋅( 1−2ν) h ⎝ δic
⎠
Where δo represents the maximal interpenetration between the contacting bodies and f,
m, and δref are the three parameters of the model, being f and m non-dimensional
parameters and having δref units of length. The parameter f corrects the contact area to
account for the deformation of the contacting bodies. The value of the parameter m
controls the relation between the pressure (p i) and the corrected deformation (δic)
for
each individual spring, which is equivalent to considering a stiffness variable with
deformation, which is more realistic than a constant stiffness. The parameter δref allows
us to maintain unit homogeneity in Eq. (19) and represents the corrected deformation
for which the stiffness of the mEFM is equivalent to that of the original EFM.
3.2. Experimental data
Experimental data were used in the present work to test the model. Data come from
1−m
(6)