tesi A. Caggiano.pdf - EleA@UniSA - Università degli Studi di Salerno

2 0 . 0 01 8 . 0 01 6 . 0 01 4 . 0 01 2 . 0 01 0 . 0 08 . 0 06 . 0 04 . 0 02 . 0 00 . 0 03.3. Fracture energy-based model for plain mortar/concrete interface____ d ξ pid w crSerie6 cosine-based lawSerie7linear law-0.2 0 0.2 0.4 0.6 0.8 1 1.2w cr /G fIor w cr /G fIIaFigure 3.9: Comparison of the derivates between the cosine-based law against the linear rule.3.3.3 An overview of the interface model for plain concrete/mortarIn the above subsections a rate-independent fracture energy-based plasticity modelhas been presented and the main aspects of the interface formulation have completelybeen detailed.Table 3.1: Overview of the interface model for Plain Concrete/Mortar.Constitutive equationFracture - based energy interface modelṫ i = C · ( ˙u − ˙u cr )˙u = ˙u el + ˙u crYield condition f ( t i ,κ ) = σ 2 T − (c − σ N tanφ) 2 + (c − χtanφ) 2Flow ruleCracking work evolutionEvolution law˙u cr = ˙λ mm = A · n˙κ = ẇ crẇ cr = σ N · ˙u cr + σ T · ˙v cr if σ N ≥ 0ẇ cr = [ σ T − |σ N | t an(φ) ] · ˙v cr if σ N < 0p i = [ 1 − ( 1 − r p)S[ξpi ] ] p 0iKuhn - Tucker / Consistency ˙λ ≥ 0, f(t i ,κ ) ≤ 0, ˙λ f(t i ,κ ) = 0, ˙ f(t i ,κ ) = 0This final subsection is aimed at compactly reporting all the interface ingredients55