Abstract
We discuss inelastic media under uncertainty modelled by probabilistic methods. As a prototype inelastic material we consider perfect plasticity. We propose a mathematical formulation as a stochastic variational inequality. The new element vis à vis a stochastic elastic medium is the so-called return map at each Gauss-point. We concentrate on a stochastic version of this, showing how it may be solved via (generalised) polynomial expansion.
Explicit formulas are provided for plane strain, together with results from example computations, giving a stochastic inelastic or irreversible time-step procedure. This may serve as a prototype example for any other irreversible behaviour, especially of the rate-independent kind.
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Matthies, H.G., Rosić, B.V. (2008). Inelastic Media under Uncertainty: Stochastic Models and Computational Approaches. In: Reddy, B.D. (eds) IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media. IUTAM BookSeries, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9090-5_17
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DOI: https://doi.org/10.1007/978-1-4020-9090-5_17
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