“…A yield stress at the reference strain rate _ " 0 B pre-exponential factor at the reference strain rate _ " 0 c specific heat capacity C strain-rate factor D initial spherical-particle diameter E elastic modulus E p elastic modulus of the particle E 1 , E 2 elastic moduli of the contact solids g strain-gradient coefficient G shear modulus G p shear modulus of the particle h contact gap height ( Figure 1) " h 1 , " h 2 micro-hardnesses of the contact solids at average local temperature (equation (7)) h c central film thickness in the absence of the particle H height of a particle block ( Figure 1) H p dynamic hardness of the particle (equation (9)) H ð0Þ p nominal, cold hardness of the particle H 1 , H 2 cold macro-hardnesses of the contact solids i, j discrete coordinates of a particle block K f thermal conductivity of the lubricant at bulk temperature f K x , K y , K z principal thermal conductivities of a contact solid m thermal-softening exponent n strain-hardening exponent Nu surface-length Nusselt number p contact pressure on a particle block p f local fluid static pressure ( Figure 1) q thermal power of frictional heating (equation (10)) q b thermal power transmitted by a peripheral block to the lubricant during one time step (equation (12)) q c thermal power transmitted by a surface sector to the lubricant (equation (13)) q p thermal power generated at the core of a particle block (equation (11)) r effective radius of spherical indenter (equation (8)) R radius of the deforming particle disc (Figure 1) t time u 1 , u 2 tangential velocities of the contact surfaces ( Figure 1) u 1 , u 2 magnitudes of the tangential velocities of the contact surfaces U, V, W thermoelastic displacements (equation (14)) V extr particle extrusion velocity (equation (4)) V M speed of the particle in relation to a contact surface V x , V y local tangential velocities (equation (3)) w 1 , w 2 normal surface displacements w e ð Þ 1 , w e ð Þ 2 normal elastic displacements of the contact surfaces w ðrÞ 1 , w ðrÞ 2 local indents of the contact surfaces x, y, z spatial coordinates ( Figure 1) x b , y b continuous coordinates of a particle block x M , y M coordinates of particle's centre (Figure 1) Y 0.2%-offset yield strength Y p yield stress in uniaxial compression of the particle thermal expansion coefficient 1 , 2 local, normal plastic displacements of the contact surfaces (equation (17)) Áh approach of the contact solids during a time step Ás dimension of a particle block (Figure 1 -bottom) Át time step Á temperature change (equations (15) and (16)) "…”