13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- ( ) ( ) ( )2 6 4 2 * , 6 1 4 1 , 2 1 p p D p Bp C p F A l c − + ∇ − − = χ σ δ δ δ δ , (1) where zz σ σ= is the stress, χ is the non-locality parameter, A B C D , , , are the material parameters, *δ and cδ are characteristic values of structural-scaling parameter (bifurcation points) that define the areas of typical nonlinear material responses on the defect growth (quasi-brittle, ductile and fine-grain state) in corresponding δ–ranges: 1.3 , 1, * * > ≈ < ≈ < < δ δ δ δ δ δ δ c c . The damage kinetics is determined by the kinetic equations for the defect density pand scaling parameter δ , p F F p p δ δ δ Δ ∂ = −Γ = −Γ Δ ∂ & & , (2) where δ Γ Γ, p are the kinetic coefficients, (...) t Δ Δ is the variation derivative. Kinetic equations Eq.2 and the equation for the total deformation p C= + σ ε ˆ (Cˆ is the component of the elastic compliance tensor) represent the constitutive equations of materials with mesodefects. Material responses on the loading realize as the generation of characteristic collective modes – the solitary waves in the range of * δ δ δ < < c and the “blow-up” dissipative structure in the range 1 < ≈ c δ δ . The generation of these collective modes under the loading provides the change of the system symmetry and initiates specific mechanisms of the momentum transfer (plastic relaxation) and damage-failure transition on the scales of damage localization with the blow-up kinetics. The damage-failure scenario includes the “blow-up” kinetics of damage localization as the precursor of crack nucleation according to the self-similar solution: ( ) ( )ξ p g t f = , H x L ξ= , m c t g t G − = − ) ( ) (1 τ , (3) where cτ is the so-called "peak time" ( →∞ p at c t τ → for the self-similar profile ( )ξ f localized on the scale HL , 0, 0 > > G m are the parameters of non-linearity, which characterise the free energy release rate for c δ δ< . The self-similar solution Eq.3 describes the blow-up damage kinetics for c t τ → on the set of spatial scales L kL k K c H , 1,2,... = = , where cL and HL corresponds to the so-called “simple” and “complex” blow-up dissipative structures. Generation of the complex blow-up dissipative structures appears when the distance SL between simple
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