PSI - Issue 47

Luciano Feo et al. / Procedia Structural Integrity 47 (2023) 800–811 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Figure 3 . Concrete behavior in tension: (a) stress-strain bilinear relation for � � 0.00015 ; (b) stress-crack opening softening law for � � 0.00015 . Finally, the model assumes that the fibers can slip from one of the two sides of the crack into which they are incorporated; hence the axial stress of the fibers, � , � , is assumed to be related to bond stresses, , mobilized on the lateral surface due to the crack opening displacement, � , and can be expressed as � , � � � , � ; � , � ; � �� 4 ∙ � � � , � � � , � ; � , � ; � � � ∙ � � , � � � , � ; � , � ; � �� (18) The distributed bond stress, , is modeled (Figure 4) through the following trilinear bond-slip law, depending on five parameters, �� , � , � , �� ,and � � ⎩⎪⎨ ⎪⎧ �� ∙ �� � �� ��� �� �� � � �� � � �� � � �� �� � � � ��� � � � � � ��� (19) Moreover, the parameter introduced in Equations 19 (a-c), is assumed to be equal to the opening displacement at the level of the k-th fiber, � , � .

Figure 4 . Local bond-slip law for steel fibers.