Material section definition - eesd-epfl/OpenSees GitHub Wiki

The flexural behaviour of the macroelement is defined by the three sectional deformation models applied at the two extremities and in the middle of the element. These sectional models can be either analytically solved or numerically integrated.

For the first approach there is no need of defining a sectional response model before the definition of the macroelement, and this part can therefore be skipped.

The sectional model does not describe the response in terms of sectional displacements but in terms of sectional deformations. Finite rotations and axial displacements are retrieved from the sectional deformations through integration along an integration length, optionally specified when declaring the macroelement. Therefore, the stiffness values passed to the sectional model are always, directly, the masonry material properties.

If the sectional model is numerically integrated, a fibre section must be defined and passed to the element. The standard commands in OpenSees for the definition of a uniaxial material model, and a fibre section, can be used. Any uniaxial material model can be used, being particularly interesting for the modelling of masonry the use of concrete models (Concrete01, Concrete02, ..) capable of capturing the main features of its uniaxial cyclic response.

The modelling of spandrels could require the use of a material model including a tensile strength contribution, deriving from friction along bed-joints, depending on the compression stress acting on the node and the interlocking of the masonry texture. One approximation can be obtained through the use of a material model featuring a constant tensile strength and a certain postpeak strength degradation. The user should consider in this case that the postpeak behaviour would be very fragile if the failure mechanism involves the tensile cracking of the units, while it features negligible strength degradation if failure is reached for sliding along bed-joints.

The material model postulated in Tremuri has zero tensile strength and a damage behaviour in compression, with limited compressive strength and no strength degradation. A new material model, loaded from the external library CompressionDamage1d.dll, fully equivalent to the one postulated in the Tremuri sectional model, can be defined as:

uniaxialMaterial CompressionDamage1d   $uniMatTag   $E   $fc

Parameters:

Any set of consistent units can be used. A rectangular patch of fibres can be defined through:

section Fiber $tagSection -GJ $GJ {
     patch rect $matTag $nFibersIP $nFibersOOP \
     [expr -$L/2.] [expr -$t/2.] [expr $L/2.] [expr $t/2.]  }

Where:

Any other fibre section type defined in OpenSees can be used (circular, polygonal, etc.) and it can be equipped with single reinforcement fibres for modelling reinforced masonry or elements retrofitted through application of FRP layers or lime/concrete jacketing.

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The analytically-solved sectional model, equivalent to the model implemented in Tremuri, in terms of in-plane response, can be used without the explicit definition of a tagged sectional model. If, for other reasons, a section model of this kind has to be defined, the input format is as follows (being it a section ForceDeformation model it cannot be provided through a library - download a 64bit OpenSees binary here compiled for Windows or build your own).

section NoTensionSection3d $secTag $E $G $L $t $J $fc $numSlices

Where:

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