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A catastrophe theory approach to fracture mechanics

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Abstract

A cohesive crack model is applied to analyze the crack stability in elastic-softening materials. The shape of the global load-displacement response changes substantially by varying size-scale and keeping the geometrical shape of the structure unchanged. The softening branch becomes steeper and when the size-scale increases. A critical size-scale does exist for which the softening slope is infinite. In such a case, the load carrying capacity drastically decreases for relatively small displacement increments. Then, for larger size-scales, the softening slope becomes positive and a cusp catastrophe appears. It is proved that such a bifurcation point can be revealed by the simple LEFM condition.

Résumé

On utilise un modèle de fissure basé sur la cohésion pour analyser les conditions de fissuration stable dans des matériaux sensibles à l'adoucissement en condition élastique.

A formes géométriques égales, le profile de la courbe globale charge-déplacement se modifie considérablement avec une variation des dimensions d'une structure.

Lorsque l'échelle des dimensions est accrue, la portion correspondant à l'adoucissement devient de plus en plus raide, pour atteindre une pente infinite à une certaine échelle.

Il y correspond une décroissance brutale de la capacité de tenir la charge, pour de faibles accroissements de la déformation. Puis, pour des dimensions plus importantes, la pente de la coube d'adoucissement devient positive, et il apparaît des conditions de dégénérescence catastrophique.

On établit qu'un tel point de bifurcation peut être mis en évidence par la simple condition d'égalité de la mécanique linéaire élastique de la rupture.

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Authors and Affiliations

  1. Department of Structural Engineering, Politecnico di Torino, 10129, Torino, Italy

    Alberto Carpinteri

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  1. Alberto Carpinteri
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Carpinteri, A. A catastrophe theory approach to fracture mechanics. Int J Fract 44, 57–69 (1990). https://doi.org/10.1007/BF00012552

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  • DOI: https://doi.org/10.1007/BF00012552

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