A One-Step Solution Technique for Elastic-Plastic Self-Similar Problems

• At self-similarity the strain history is implicit in and deducible from the strain field at each instance of the loading process. This fact is taken advantage of in a FEM-technique which allows the load to be applied in one single step, only, even when the incremental theory of plastic flow has to be used.Two self-similar problems are solved. Firstly an analytically solvable anti-plane strain crack problem is treated and the numerical one step solution is found to agree very well with the analytical one and significantly better than a step-by-step solution. Secondly a mode I crack problem for asymptotic small scale yielding in plane stress is examined. The result suggests that the plasticity correction for the crack length is significantly less than estimated by Tada et al. [1].

• At self-similarity the strain history is implicit in and deducible from the strain field at each instance of the loading process. This fact is taken advantage of in a FEM-technique which allows the load to be applied in one single step, only, even when the incremental theory of plastic flow has to be used. Two self-similar problems are solved. Firstly an analytically solvable anti-plane strain crack problem is treated and the numerical one step solution is found to agree very well with the analytical one and significantly better than a step-by-step solution. Secondly a mode I crack problem for asymptotic small scale yielding in plane stress is examined. The result suggests that the plasticity correction for the crack length is significantly less than estimated by Tada et al. [1].

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Materialteknik -- Textil-, gummi- och polymermaterial (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Materials Engineering -- Textile, Rubber and Polymeric Materials (hsv//eng)

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