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Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms
Author(s) -
Simo J. C.,
Kennedy J. G.,
Govindjee S.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620261003
Subject(s) - viscoplasticity , convexity , mathematics , boundary value problem , plasticity , algorithm , tangent , linearization , tangent modulus , domain (mathematical analysis) , mathematical analysis , mathematical optimization , finite element method , geometry , modulus , structural engineering , nonlinear system , materials science , constitutive equation , engineering , physics , quantum mechanics , financial economics , economics , composite material
Rate‐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.