## 8.2. Interaction of Elastic-Plastic Particles

### 8.2.1. Yield

In many industrial processes, particles are subject to high forces or impact at high speeds, as a consequence of which plastic deformation can take place. ToÂ define the onset of plastic deformation, the theory of plasticity introduces two yield criteria:
1. The von Mises yield criterion, in which plastic deformation is initiated when the distortion energy exceeds the distortion energy for yield in simple tension, i.e., when the second invariant J2 of the stress deviator tensor (sij) reaches a critical value:

$J2=12sijsij=16[(Ï1âÏ2)2+(Ï2âÏ3)2+(Ï3âÏ1)2]=k2=Y23$

(8.76)

where Ï1, Ï ...

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