Automatic step length adaption for the numerical solution of nonlinear mechanical problems discretized by finite elements

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This work deals with the theoretic aspects of the elasto-plastic boundary value problem, describe the cincepts for the development of numerical methods for the solution of the discretized partial differential equations an discusses the common procedures. Based upon the results of this discussion the fundamentals and ideas are presented which lead to a new automatic step-length procedure that makes use of an estimation of the size of the Kantorovitch neighbourhood. The derived algorithm is analyzed from a theoretical point of view, and its computational implementation for a direct and iterative solution of the arising linear systems of equations is given in detail. The developed procedures are applied to two selscted model problems in two and three spatial dimensions, thoroughly examined and compared to the traditional method.