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• W1767968145 abstract "SUMMARY This work outlines a theoretical and computational framework of gradient plasticity based on a rigorous exploitation of mixed variational principles . In contrast to classical local approaches to plasticity based on locally evolving internal variables, order parameter fields are taken into account governed by additional balance‐type PDEs including micro‐structural boundary conditions. This incorporates non‐local plastic effects based on length scales, which reflect properties of the material micro‐structure. We develop a unified variational framework based on mixed saddle point principles for the evolution problem of gradient plasticity, which is outlined for the simple model problem of von Mises plasticity with gradient‐extended hardening/softening response. The mixed variational structure includes the hardening/softening variable itself as well as its dual driving force. The numerical implementation exploits the underlying variational structure, yielding a canonical symmetric structure of the monolithic problem. It results in a novel finite element (FE) design of the coupled problem incorporating a long‐range hardening/softening parameter and its dual driving force. This allows a straightforward local definition of plastic loading‐unloading driven by the long‐range fields, providing very robust FE implementations of gradient plasticity. This includes a rational method for the definition of elastic‐plastic‐boundaries in gradient plasticity along with a post‐processor that defines the plastic variables in the elastic range. We discuss alternative mixed FE designs of the coupled problem, including a local‐global solution strategy of short‐range and long‐range fields. This includes several new aspects, such as extended Q1P0‐type and Mini‐type finite elements for gradient plasticity. All methods are derived in a rigorous format from variational principles. Numerical benchmarks address advantages and disadvantages of alternative FE designs, and provide a guide for the evaluation of simple and robust schemes for variational gradient plasticity. Copyright © 2013 John Wiley & Sons, Ltd." @default.
• W1767968145 created "2016-06-24" @default.
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• W1767968145 date "2013-05-06" @default.
• W1767968145 modified "2023-10-13" @default.
• W1767968145 title "Mixed variational principles and robust finite element implementations of gradient plasticity at small strains" @default.
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• W1767968145 doi "https://doi.org/10.1002/nme.4486" @default.
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