Enhanced vector-based model for elastic bonds in solids

Abstract

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.

Toward large scale modeling of carbon nanotube systems with the mesoscopic distinct element method

“…In this section, we describe the features of the new implementation of MDEM. The core difference with the previous implementation [13 -15] is the usage of scalable dynamic engine [18] and energy conserving elastic bonds [19,20]. For the purpose of completeness, we provide a brief yet complete description of our model.…”

“…On the other hand, it is hard to generalize parallel bond for the case of nonlinear constitutive behavior, occurring at large deformations of CNT. In order to bypass these limitations, in the new implementation we have replaced parallel bonds with more general and stable enhanced vector model (EVM) of an elastic bond developed recently [19,20]. The EVM is based on a binding potential, describing the behavior of an elastic bond linking two rigid bodies.…”

“…In order to ensure the stability of large-scale simulations of CNT assemblies, we use the recently developed enhanced vector model (EVM) [19,20] for the description of the bonds between rigid CNT segments. Unlike previously employed parallel bonds [21], EVM provides precise energy conservation in zero-damping simulations, and can be easily generalized to capture nonlinear effects and bond fracture.…”

“…Therefore, any values of stiffnesses can be fitted. In the simplest case, parameters B 1 , B 2 , B 3 , B 4 can be calibrated using Euler-Bernoulli beam theory as follows (see papers[19,20] for more details):…”

Distinct Element Simulation of Mechanical Properties of Hypothetical CNT Nanofabrics

“…Elasticity of fibers in our model is represented with the formalism of enhanced vector model (EVM) [22,23]. The EVM is based on a binding potential, describing the behavior of an elastic bond linking two rigid bodies.…”