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A model (further referred to as the enhanced vector-based model or EVM) forelastic bonds in solids, composed of bonded particles is presented. The modelcan be applied for a description of elastic deformation of rocks, ceramics,concrete, nanocomposites, aerogels and other materials with structural elementsinteracting via forces and torques. A material is represented as a set ofparticles (rigid bodies) connected by elastic bonds. Vectors rigidly connectedwith particles are used for description of particles orientations. Simpleexpression for potential energy of a bond is proposed. Corresponding forces andtorques are calculated. Parameters of the potential are related tolongitudinal, transverse (shear), bending, and torsional stiffnesses of thebond. It is shown that fitting parameters of the potential allows one tosatisfy any values of stiffnesses. Therefore, the model is applicable to bondswith arbitrary length/thickness ratio. Bond stiffnesses are expressed in termsof geometrical and elastic properties of the bonds using three models:Bernoulli-Euler beam, Timoshenko beam, and short elastic cylinder. An approachfor validation of numerical implementation of the model is presented.Validation is carried out by a comparison of numerical and analytical solutionsof four test problems for a pair of bonded particles. Benchmark expressions forforces and torques in the case of pure tension/compression, shear, bending andtorsion of a single bond are derived. This approach allows one to minimize thetime 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.

Enhanced vector-based model for elastic bonds in solids