Stochastic Description of Large Strain Elastoplasticity

Abstract eng:
The stochastic description of large strain plasticity is required in many practical problems in which material properties (e.g. concrete, bone, rock) and/or external loadings (e.g. the metal safety nets against snow, rock fall) are of uncertain character [1]. Within the framework of large strain analysis we focus on the rate-independent evolutionary problem with general hardening whose material characteristics are assumed to have positively-definite distributions. By introducing the stochastic mulitplicative split we describe the irreversible and work-dissipating process via a quasi-convex energy function and evolution equations for internal variables. This allows the reformulation of the problem into a stochastic minimisation of a smooth convex energy functional on discrete tensor product subspaces, whose unique minimizer is obtained via a stochastic closest point projection algorithm [2,3]. Its numerical computation is performed with the help of methods of functional approximation and high-dimensional integration, which are then contrasted with respect to the accuracy of the solution and its efficiency.

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