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Problems of stress concentrations taking into account the physical nonlinearity of the material (review)

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Soviet Applied Mechanics Aims and scope

Conclusions

Up to the present, a considerable number of problems have been investigated on stress concentrations of plane physically nonlinear elasticity theory for simply connected and multiply connected media, which allow us to draw the following conclusions:

  1. 1.

    Qualitatively new results have been obtained for the coefficients stress concentration, consisting of the fact that the concentration coefficients do not remain constant, as in the linear theory, but depend significantly on the mechanical properties of the material and the magnitude of the external load.

  2. 2.

    From a quantitative point of view, account of a physical nonlinearity in the material leads to a decrease in the value of the stresses and concentration coefficients by an average of 25% depending on the material and the value of the external forces.

  3. 3.

    Taking account of the nonlinear-elastic properties leads to a more uniform distribution of stresses in the concentration zones and to a smoothing of the stress peaks at the most dangerous points.

In the future, the following investigations should be carried out to develop the given problem:

  1. a)

    in the presence of a sufficiently large number of developed methods it is advisable to study questions of the rigorous mathematical basis of these methods;

  2. b)

    since taking into account the physical nonlinearity decreases the stresses near the concentrators, it is promising to study contact problems and problems for bodies having cracks, as applied to questions of fracture.

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  1. I. A. Tsurpal
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Ukrainian Agricultural Academy, Kiev. Translated from Prikladnaya Mekhanika, Vol. 10, No. 7, pp. 3–22, July, 1974.

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Tsurpal, I.A., Kuliev, G.G. Problems of stress concentrations taking into account the physical nonlinearity of the material (review). Soviet Applied Mechanics 10, 687–703 (1974). https://doi.org/10.1007/BF00886295

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