Analytical Generalization of the T and A-theta Integrals for the Study of Cracking in Three-dimensional Orthotropic Medium
Résumé
An analysis of the fracture phenomenon in wood shows that it is significantly influenced not only by mechanical loads and the heterogeneous nature of this material but also by multiple parameters related to thermal and moisture variations. It becomes important to propose predictive models that account for these climatic parameters in order to better assess the risks of failure and ensure the safety of wooden structures. In this paper, a new mathematical formulation of the invariant integral, T and A-theta is proposed to evaluate the energy release rate during the determining od fracture toughness. The formulation is extended to the three-dimensional case and is based on a generalization of Noether’s theorem as a free energy that includes both real and virtual fields for mechanical and moisture loads. The resulting model allows for a decoupling of mixed fracture modes and the analysis of the impact of orthotropy and wood shrinkage-swelling on cracking parameters. The independence of the integration contour is then verified, and a finite element procedure is implemented using the Cast3M software to validate the proposed model.
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