13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 1 n n n n A t (4) nA is a pseudo compliance function which enables us to traduce the instantaneous strain response induced by the mechanical stress increment. 1 n is the complete past history effects of moisture content and loadings on strains. Finally, the finite element structuring integrates the orthotropic properties in the radial tangential referential. In this condition, the uniaxial incremental formulation (4) can be generalized in the following finite element form: n 1 n n t A (5) n and n designate increments of strain and stress tensors, respectively. In order to solve this equation by a finite element algorithm, let us employ the technique proposed by Ghazlan et al. which is derived from the virtual work principle. If the nodal displacement vector increment is noted n U t , the balance equation, in the discretized domain V, can be written as follow 1 ext T n n n U t F t F t K (6) TK is an equivalent tangent matrix assembled from the tensor A. 4.3. Finite element results As shown in Figure 9, the finite element mesh is realized according to a global positioning system centered on the heart specimen allowing defining the center of the cylindrical orthotropic reference. The contact surface between specimen and balance is operated by blocking its vertical displacements. A referential point is also blocked in its vertically in order to eliminate a rigid body displacement. We assume a perfect slice of this surface according to isostatic boundary conditions. Specific lines (radius and crowns) have been integrated in mesh in order to have a concordance with experimental black mark displacements, Figure 1. Figure 9. Finite element mesh According to the last finite element algorithm, mechanical fields are computed versus moisture content level with an increment of 1%. In accordance with Figure 2, the fiber saturation point is assumed to be around 30% inducing representative strain evolutions. All mechanical fields are calculated in the local orthotropic system. For a final moisture content of 8% corresponding to the crack growth initiation, the numerical displacements are plotted in Figure 10 with an amplification factor of 2.
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