Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms.

*(English)*Zbl 0661.73058Rate-independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non-smooth fashion are considered in detail. It is shown that the standard Kuhn-Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed-form expression of the so-called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed- form algorithm is developed based on the rate-independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non-smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74P99 | Optimization problems in solid mechanics |

74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |

65K05 | Numerical mathematical programming methods |

##### Keywords:

closest point projection algorithm; arbitrary number of yield surfaces; Kuhn-Tucker optimality conditions; plastic loading; unconditionally convergent return mapping algorithm; yield condition; flow rule; hardening law; exact linearization; closed-form expression; consistent (algorithmic) tangent moduli; closed-form algorithm; rate-independent solution; elastic domain; non-smooth boundary
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\textit{J. C. Simo} et al., Int. J. Numer. Methods Eng. 26, No. 10, 2161--2185 (1988; Zbl 0661.73058)

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