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Variational fracture mechanics to model compressive splitting of masonry-like materials


A regularized variational model of fracture mechanics for masonry-like materials has been recently proposed: this is based upon the competition between bulk-energy release and surface-energy production due to the nucleation and/or progression of cracks, assumed they can open in mode I only. This model is applied here to derive a theory of strength in confined masonry-like materials, where an inhomogeneous state of stress is due to heterogeneous inclusions or boundary constraints. The theory accords the phenomenon of rupture an energetic interpretation. Under tension, opening of mode I fractures at right angle to the axis of loading is clearly energetically favorable; under compression, the solid splits because in doing so the stress is released so to reduce the total energy. Numerical experiments have been performed for prismatic solids under fixed lateral confinement and increasing uniaxial tension or compression up to failure. Representative domains for the strength under biaxial stress are thus deduced.

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    The variable s is analogous to the classical damage parameter first introduced by Kachanov [26]. To be precise, Kachanov used the complementary variable ψ = 1 − s called continuity, but here we have preferred s instead of ψ to follow [20].

  2. 2.

    The two absolute values of \(\overline{u}\) are different because the resistance under traction is expected to be much lower than under compression.


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Partial support of the Italian MIUR (Ministry of Education, University and Research) under the PRIN2008 program is gratefully acknowledged.

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Correspondence to Gianni Royer-Carfagni.

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Freddi, F., Royer-Carfagni, G. Variational fracture mechanics to model compressive splitting of masonry-like materials. Ann. Solid Struct. Mech. 2, 57–67 (2011).

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  • Uniaxial tension
  • Uniaxial compression
  • Fracture mechanics
  • Variational calculus
  • Strength domain
  • Biaxial loading