📝 Finite Element Modelling
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⏭ Calibration of Concrete Masonry Prism
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💻Computerized Modeling
💊 Elements
Masonry:
- 3D solid (eight-node brick solid element)
- 3 DOFs in each node
- Single point integration (by Gaussian quadrature)
- Smeared crack analogy (for crushing in compression and cracking in tension)
- Capable of plastic deformation, cracking in three orthogonal directions and crushing
- Hourglass control (to avoid the zero energy modes)
Boundaries and Loading:
- Induced an increasing displacement to the prisms’ ends (which is helpful to define an imposed nodal motion)
- Displacement control of the top nodes, rather than pressure control (to capture the softening behavior of the material)
- Explicit time integration solution (of LS-DYNA)
- Sensitivity analyses (to determine the optimum applied displacement rate to minimize the inertial effects)
- Loading rate of 0.001 mm/s
- translational degrees of freedom of nodes were fixed in the lateral directions at the top and bottom faces (to mimic Support restraint and confinement pressure)
📉 Constitutive Masonry Material Model
🔹Properties & Behavior
- Size of the member and confinement level
- Multi directional stresses behavior
- Calibrated concrete models
⚠️ lack of coarse aggregate in grouted masonry is addressed: which slow downs propagation of the cracks
⚠️ Strength degradation and softening branch of the stress-strain curve is steeper
- Mortar layers effect
⚠️ Ungrouted masonry: mortar layers are week layers, vulnerable to cracking, and Zigzag cracks is common failure mode
Numerical modelling
🔹 Accurately simulate the volumetric response of masonry material under multi-axial stress, to be able to capture the interaction between inner and outer elements
🔹 Masonry model is K & C concrete damage material
🔹 If an appropriate calibration simulate the behavior and yield excellent results
🔹 Concrete damage material model is a three invariant model (failure surface is interpolated between two of three independent shear failure surfaces: the yield surface, maximum surface and residual surface which represent the onset of damage, ultimate and residual strength of the material)
🔹 To obtain the shear surfaces at least three tri-axial compression tests are required
🔹 For a given confinement pressure, the value of yield, maximum and residual stresses are obtained from compression tests
🔹 Under compression the material response is considered to be linear, until it reaches the yield surface. After yielding a strain hardening response governs the behavior before it reaches the maximum strength. response is then followed by a softening branch until the strength reaches the residual strength.
🔹 The tri-axial compression tests reflect the effect of confinement on the behavior and strength of concrete/masonry material
💣 Damage Function
🔹 After the stress reaches the initial yield surface and before it reaches the maximum surface, the current stress surface is determined using a simple linear interpolation between the two surfaces
🔹 Damage function is scaled using damage parameters: compression softening, tension softening, and tri-axial tension softening
⚱️ Volumetric Strain
material model used here for masonry, decouples the volumetric and deviatoric response. volumetric behavior is governed by a compaction curve or an equation of state (EOS).
✂️ Shear Dilation
Material expansion due to formation and propagation of cracks can be described by the shear dilation parameter. The dilation continues as the cracks grow, and stops when the cracks open up enough to clear the aggregates.
To consider the effects of shear dilatancy, a proper flow rule must be employed.
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⏭ Calibration of Concrete Masonry Prism
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