13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 42 , 0 = ϕ which is in agreement with the test results. 4. Proposed Damage Model The proposed damage model [8, 11] based on interface finite elements is presented in order to simulate damage onset and growth into the core of a sandwich structure. A linear constitutive relationship between stresses σand relative displacements δ between homologous points of the interface elements with zero thickness is considered. At first developing the pure-mode model, the constitutive equation before damage starts to grow, is given by: D σ δ = (8) where D is the diagonal matrix containing the penalty parameters (d) in each mode. The values of the penalty parameter must be quite high in order to hold together and prevent interpenetration of the element faces. According to a considerable number of numerical simulations [8, 11], it was determined d =106N/mm3. For this value the produced results converge and numerical problems during the nonlinear procedure have been avoided. After the peak stress , ( ) u i σ is reached a gradual softening process between the stress and the relative displacement is observed and is defined as: ( )D σ Ι Ε δ = - (9) where I is the identity matrix and E is a diagonal matrix containing the damage parameter: , , , , ( ) , , , ( ) u i o i i u i o i i e i I II δ δ δ δ δ δ − = = − (10) and, ,o iδ , is the displacement corresponding to the onset of damage, and iδis the current relative displacement. In pure-mode loading, the strength along other directions is abruptly cancelled. The maximum relative displacement, ,u i δ for which complete failure occurs, is obtained by equating the area under the softening curve to the respective critical fracture energy: , , , 1 2 c i u i u i G σ δ = (11)
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