Plasticity is the theory describing the deformation of a solid material undergoing non-reversible changes of shape in response to applied forces. Unlike elasticity, where deformation is recovered upon unloading, plastic deformation is permanent. The theory involves a yield criterion to define the onset of plasticity, a flow rule to describe the evolution of plastic strain, and a hardening rule.
塑性理论为分析材料在超过其弹性极限时的应力提供了框架。从弹性到塑性行为的转变受屈服准则控制，该准则定义了应力空间中的一个表面（屈服面）。当应力状态位于该表面内时，材料表现出弹性行为。当应力状态达到该表面时，塑性变形开始。金属最常见的两种屈服准则是Tresca（最大剪应力）和von Mises（最大变形能）准则。
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.
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