塑性理论

Plasticity theory provides the framework for analyzing materials stressed beyond their elastic limit. The transition from elastic to plastic behavior is governed by a yield criterion, which defines a surface in stress space (the yield surface). For stress states inside this surface, the material behaves elastically. When the stress state reaches the surface, plastic deformation begins. Two of the most common yield criteria for metals are the Tresca (maximum shear stress) and von Mises (maximum distortion energy) criteria.

一旦发生屈服，塑性应变的演变就可用流动法则来描述。最常见的是关联流动法则，该法则指出塑性应变的增量发生在屈服面的法向方向上。这决定了塑性应变分量的相对比例。

Finally, a hardening rule describes how the yield surface changes as plastic deformation accumulates. Isotropic hardening assumes the yield surface expands uniformly in all directions, meaning the material’s yield strength increases equally regardless of the loading direction. Kinematic hardening, on the other hand, assumes the yield surface translates in stress space without changing its size, which is useful for modeling the Bauschinger effect observed in cyclic loading. More complex models combine both isotropic and kinematic hardening to accurately capture real material behavior under complex loading paths. These three components—yield criterion, flow rule, and hardening rule—form the core of classical plasticity theory.