Enhanced vector-based model for elastic bonds in solids

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.