  A model (further referred to as the enhanced vector-based model or EVM) for
elastic bonds in solids, composed of bonded particles is presented. The model
can be applied for a description of elastic deformation of rocks, ceramics,
concrete, nanocomposites, aerogels and other materials with structural elements
interacting via forces and torques. A material is represented as a set of
particles (rigid bodies) connected by elastic bonds. Vectors rigidly connected
with particles are used for description of particles orientations. Simple
expression for potential energy of a bond is proposed. Corresponding forces and
torques are calculated. Parameters of the potential are related to
longitudinal, transverse (shear), bending, and torsional stiffnesses of the
bond. It is shown that fitting parameters of the potential allows one to
satisfy any values of stiffnesses. Therefore, the model is applicable to bonds
with arbitrary length/thickness ratio. Bond stiffnesses are expressed in terms
of geometrical and elastic properties of the bonds using three models:
Bernoulli-Euler beam, Timoshenko beam, and short elastic cylinder. An approach
for validation of numerical implementation of the model is presented.
Validation is carried out by a comparison of numerical and analytical solutions
of four test problems for a pair of bonded particles. Benchmark expressions for
forces and torques in the case of pure tension/compression, shear, bending and
torsion of a single bond are derived. This approach allows one to minimize the
time required for a numerical implementation of the model.
  Keywords: granular solid, elastic bond, torque interactions, V-model,
discrete element method, distinct element method, particle dynamics.
