# Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review)

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The basic results of establishing the foundations of the mechanics of fracture of homogeneous materials compressed along cracks and inhomogeneous (composite) materials compressed along interface cracks are analyzed. These results were obtained using elastic, plastic, and viscoelastic material models. This review consists of three parts.

The first part discusses the basic concept that the start (onset) of fracture is the mechanism of local instability near the cracks located in a single plane or parallel planes. The fracture criterion and the basic problems arising in this division of fracture mechanics are also formulated. Two basic approaches to establishing the foundations of the mechanics of fracture of materials compressed along cracks are outlined. One approach, so-called beam approximation, is based on various applied theories of stability of thin-walled systems (including the Bernoulli, Kirchhoff–Love, Timoshenko-type hypotheses, etc.). This approach is essentially approximate and introduces an irreducible error into the calculated stresses. The other approach is based on the basic equations and methods of the three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains. This approach does not introduce major errors typical for the former approach and allows obtaining results with accuracy acceptable for mechanics.

The second part offers a brief analysis of the basic results obtained with the first approach and a more detailed analysis of the basic results obtained with the second approach, including the consideration of the exact solutions for interacting cracks in a single plane and in parallel planes and results for some structural materials.

The third part reports new results for interacting cracks in very closely spaced (or coinciding, as an asymptotic case) planes. These results may be considered a transition from the second approach (three-dimensional linearized theory of elastic stability) to the first approach (beam approximation). This is how the accuracy of results produced by the first approach is evaluated and the boundary conditions near the crack tip are established in the second approach.

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183. I. A. Guz, “On one fracture mechanism for composites with parallel interfacial cracks,” in: Proc. 4th Int. Conf. on Deformation and Fracture of Composites (March 24–26 March, 1997, Manchester, UK), Institute of Materials, London (1997), pp. 579–588.

184. I. A. Guz, “On calculation of critical strains for periodical array of parallel interfacial cracks in layered materials,” in: Proc. 6th EPMESC Conf., Guang-Zhou, China, August 4–7 (1997), pp. 375–380.

185. I. A. Guz, “On fracture of brittle matrix composites: Compression along parallel interfacial cracks,” in: Proc. 5th Int. Symp. (October 13–15, 1997, Warsaw, Poland), Woodhead Publ., Cambridge (1997), pp. 391–400.

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Correspondence to A. N. Guz.

Translated from Prikladnaya Mekhanika, Vol. 50, No. 1, pp. 5–88, January–February 2014.

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Guz, A.N. Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review). Int Appl Mech 50, 1–57 (2014). https://doi.org/10.1007/s10778-014-0609-y

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