Vitaly A. Kuzkin, Igor E. Asonov
A new model for computer simulation of solids, composed of bonded particles,
is proposed. Vectors rigidly connected with particles are used for description
of deformation of a single bond. The expression for potential energy of the
bond and corresponding expressions for forces and moments are proposed.
Formulas, connecting parameters of the model with longitudinal, shear, bending
and torsional stiffnesses of the bond, are derived. It is shown that the model
allows to describe any values of the bond stiffnesses exactly. Two different
calibration procedures depending on bond length/thickness ratio are proposed.
It is shown that parameters of model can be chosen so that under small
deformations the bond is equivalent to either Bernoulli-Euler or Timoshenko rod
or short cylinder connecting particles. Simple expressions, connecting
parameters of V-model with geometrical and mechanical characteristics of the
bond, are derived. Computer simulation of dynamical buckling of the straight
discrete rod and discrete half-spherical shell is carried out.
View original:
http://arxiv.org/abs/1202.0001
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