Three-dimensional movable cellular automata simulation of elastoplastic deformation and fracture of coatings in contact interaction with a rigid indenter

Abstract

The paper considers 3D movable cellular automata (MCA) models of contact interactions involved in nanoindentation, sclerometry, and tribospectroscopy. The system under study is a titanium substrate with a hardening coating. The substrate and coating materials are both described in the elastoplastic approximation. It is shown that the MCA method of numerical simulation provides correct description of the contact interaction of elastoplastic materials under different types of loads with explicit account for fracture. The possibility to detect damages in material surface layers from friction force estimates is assessed.

Numerical Modeling of Shockwave Treatment of Knee Joint

“…To describe the mechanical behavior of biological tissues, herein we used the model of a poroelastic body, implemented in the method of movable cellular automata (MCA) [30,31], which is an efficient method of computational particle (discrete) mechanics. It has been established that discrete methods have proven themselves to be very promising for modeling contact loading of different materials at both the macroscale and the mesoscale [32,33]. In the MCA method, a solid is considered as an ensemble of discrete elements of finite size (cellular automata) that interact with each other according to certain rules, which, within the particle approach, and due to many body interaction forces, describe the deformation behavior of the material as an isotropic elastoplastic body.…”

“…Automata interact among each other through their contacts. The initial value of the contact area is determined by the size of the automata and their packing [31,32].…”

“…For isotropic material, the volume-dependent part of the total force can be written as follows [31,32]:…”

“…To compute the components of the average stress tensor in the bulk of automaton i we can use the homogenization procedure described in [31,32]:…”

“…where the symbol ∆ denotes increment of the corresponding variable for time step ∆t of the numerical scheme of integration of the motion Equation (A1); ∆ε ij and ∆γ ij are the increments of normal and shear strains [31,32] of the automaton i in i-j pair; G i is the shear modulus of the material of the automaton i; K i is the bulk modulus; D i = 1-2G i /K i . Formulas (A1)-(A7) describe the mechanical behavior of a linearly elastic body in the framework of the MCA method.…”