On characteristic relations for stresses and displacement velocities: A case of the spatial problem for a perfectly plastic body satisfying the condition of full plasticity

On a mechanical analogy in the ideal plasticity theory

“…The stress tensor defined by equalities (2) with allowance for (3) satisfies the Tresca plasticity condition…”

“…The characteristic relations for system (6) were derived in [2]. System (6), which is similar to a system that describes a steady-state flow of an ideal incompressible fluid [3, p. 73], can be written as [4, p. 105] 2(ω × n) + θn = −∇p, n 2 1 + n 2 2 + n 2 3 = 1, ω = (1/2)∇ × n.…”

“…(1) t 1 = (σ 11 , σ 12 , σ 13 ) t , t 2 = (σ 21 , σ 22 , σ 23 ) t , t 3 = (σ 31 , σ 32 , σ 33 ) t ; ( 2 ) σ ij = σδ ij + 2kε(n i n j − δ ij /3), σ= σ ij δ ij /3, ε= ±1,…”