The Axisymmetric Boussinesq Problem for Solids with Surface Energy

  • D. Maugis
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 288)


Besides Young’s modulus E and Poisson ratio v, isotropic elastic solids have a surface energy γ. E and v reflect the behaviour of intermolecular forces for small displacements of atoms around their equilibrium position and 2γ is the work needed to cut these bonds along an imaginary plane of unit area and to reversibly separate the two parts of the solid. Surface energy thus characterises the nature of bonds ensuring the cohesion of the solid through this imaginary plane. Accordingly, metals and covalents have high surface energy (from 1000 to 3000 mJ.m −2), ionic crystals (100 to 500 mJ.m −2) and molecular crystals (γ < 100 mJ.m −2) have lower surface energy. The first to have coupled surface energy and elasticity was Griffith1: to extend the area of a crack by dA the work 2γdA is needed; it is taken from the elastic field and/or the potential energy of the system. Later Irwin2 introduced the strain energy G released when the crack area varies by dA, and stated the Griffith criterion for a crack in (stable or unstable) equilibrium as G = 2γ. The singularity of stresses near a crack tip was pointed out by Sneddon3; Irwin4,5 introducing the stress intensity factor K controlling the intensity of the stress fields showed the relation between the energy approach and that in terms of stress fields.


Stress Intensity Factor Adherence Force Elastic Solid Strain Energy Release Rate Adhesive Contact 
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Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • D. Maugis
    • 1
  1. 1.CNRS — LCPCParisFrance

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