Abstract
The energy release rate, G, is the derivative of the energy with respect to the crack length. Using Lagrangian coordinates, we can derive an expression of G as a surface integral, which is mathematically equivalent to other well known expressions as the J integral of Rice or the expression in terms of stress intensity factors. Using interior error estimates, we derive an error estimate of O (h l−ɛ) on G by using piecewise linear elements. For sake of simplicity, we present these estimates for the Laplace operator. The numerical trials, which show a very good stability of the method, were performed for the elasticity system.
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Destuynder, P., Djaoua, M., Lescure, S. (1985). On a numerical method for fracture mechanics. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076263
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DOI: https://doi.org/10.1007/BFb0076263
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