The development of the formalism of movable cellular automata for modeling the nonlinear mechanical behavior of viscoelastic materials

Evgeny Shilko,Aleksandr Grigoriev,Ivan Dudkin,V Fomin,L Placidi

doi:10.1051/epjconf/201922101052

Abstract

The paper is devoted to the development of the formalism of the computational method of discrete elements (DEM) for describing the mechanical behavior of consolidated viscoelastic materials. We considered an advanced implementation of DEM, namely, the method of movable cellular automata (MCA). A feature of this implementation of DEM is the use of a generalized many-body formulation of the relations for the forces of element-element interaction. 3D numerical models of viscoelastic material with a spectrum of relaxation times (Kelvin and Maxwell models, the standard model of elastomers, and others) were developed within the formalism of MCA. The correctness of the developed discrete element formalism and its applicability for modeling the processes of deformation and fracture of viscoelastic materials under dynamic loading are shown using the standard model of elastomers as an example. The relevance of the results is determined by the prospects for the further development of DEM and its application to study and predict the mechanical response of viscoelastic materials of various nature under dynamic loading including contact problems.

Highlights

Discrete Element Methods (DEM) are reliable and effective tools for numerical analysis of mechanical behavior of particulate and consolidated materials under complex loading [1,2,3,4]
At present, the most common tool for modeling the mechanical behavior of such consolidated materials are numerical methods based on continuum mechanics [8,9,10,11]
The results indicate the correctness of the developed numerical model and its applicability for studying the behavior of viscoelastic materials described by the standard model of elastomers under complex loading conditions including dynamic impacts

Summary

Introduction

Discrete Element Methods (DEM) are reliable and effective tools for numerical analysis of mechanical behavior of particulate and consolidated materials under complex loading [1,2,3,4]. Despite the wide range of potential applications of the method, nowadays classic DEM implementations are used mainly for modeling brittle materials and granular media This limitation is due to the simplified consideration of a discrete element as a pseudo-rigid body. The developed approach makes it possible to model both the consolidated and granular materials and to implement the complex rheological models of “structural units” (discrete elements). This implementation of the method is called the movable cellular automaton method (MCA). The implementation of viscoelasticity models makes it possible to apply the method of discrete elements for the numerical study of many topical problems, including the study of the laws of friction and wear in technical and natural tribological pairs. The method of moving cellular automata was used as a computational basis for such a model

Model description

Verification of the model

E EK EM i TM TM 2 1 TM 2

Summary