Issue 47

A. Chouiter et alii, Frattura ed Integrità Strutturale, 47 (2019) 30-38; DOI: 10.3221/IGF-ESIS.47.03 34 purely elastic. Major headings should be typeset in boldface with the first letter of important words capitalized.   1 2 p n tr           (5) where λ and μ are the Lamé coefficients and 1 is the identity tensor of order 2. All other "plastic" variables are equal to their values at time (t n ). If this "elastic predictor" satisfies the condition of the load function f≤ 0 (see Fig. 4), the assumption is then valid, and the calculation procedure for this time increment is completed. In the contrary case f> 0, this elastic state is "corrected" according to the method below to determine the plastic solution: Figure 5 : Plastic flow surface. The constitutive laws (4) are discretized in an incremental form corresponding to the iterative method of Newton that has the advantage of being unconditionally stable (Lemaitre and Doghri, [13]). Consequently, the solutions to time (t n +1) must satisfy the following relations: 0 S eq f         2        tr p p n σ E1 E E E (6) N P    p E YD P S    where:       1 2 3 D n n eq and N                   (7) Substituting ∆E P by its expression in the second equation, the problem is then reduced to two equations where the unknowns are   and p and must satisfy the system: