# Retrofitting Masonry Walls against Out-Of-Plane Loading with Timber Based Panels
## 4 Numerical Study
### Numerical Simulation of Compression Test on a Masonry Cubic (MC) Specim  
#### 4.1.1 Description of the Masonry Cubic Model  
The compression test on MC specimens described in Section 3.1 was simulated by FE analysis using the ABAQUS software [29] to obtain the full mechanical properties of the unit, mortar and the interfacial properties of the unit-mortar joint that is necessary to produce a detailed numerical analysis of the masonry wall. The MC numerical model was calibrated through the following four steps:  
* Material elastic properties for the unit and mortar joint were estimated based on the results of the compression tests on the individual components.
* The concrete damage plasticity (CDP) nonlinear material properties for the unit and joint were calculated using the ductility index and fracture energy data available in many literature reports [28; 30; 31; 32; 33]. These data were compared with the stress-displacement envelope given in ABAQUS.
* The brick-mortar interfaces were calibrated with the ABAQUS default penalty stiffness enforced while adjusting the coefficient of friction based on the comparison of the numerical results with those obtained in the experiments.
* Lastly, the influence of the mesh density, i.e., the approximate global size of mesh, was studied.  
The numerical model of a masonry cube (MC) was created using a three-dimensional solid (or continuum) element in ABAQUS. In particular, hexahedral 8-node linear brick, reduced integration and hourglass control (C3D8R) were selected to generate the mesh that represents the brick and mortar joint. The unit and joint (bed and perpend) were defined using their respective elastic properties obtained experimentally. The nonlinear behaviour of the brick unit and mortar, both in a compression and tension regime, were accounted for in the FE model using the CDP constitutive model. The brick-mortar bond failure behaviours were also considered by using the nonlinear cohesive interfaces. ABAQUS  
Figure 11: Observed failure pattern of a masonry wall: (**a**) plain wall (PW1115) geometry, (**b**) failure pattern (PW1115-1 sample), (**c**) one side retrofitted wall (ISRW1115) geometry, (**d**) failure pattern (ISRW1115-2 sample), (**e**) two side retrofitted wall (2 SRW1115) geometry and (**f**) failure pattern (2 SRW1115-1 sample).  
contact penalty approach was enforced for the interaction between the brick and mortar interface. This means that the contact between the mortar interface and the unit interface is enforced by contact constraints in the normal direction. [PERSON] [26] iterated that the penalty method typically does not generate additional degrees of freedom, unlike the contact constraint options, which would always generate Lagrange multiplier degrees of freedom. In tangential, the frictional behaviour between the unit-mortar interface was calibrated using a coefficient of friction (\(\upmu\)) of 0.75.  
For the boundary condition, the nodes at the top of the cubes were restrained in the x- and z-direction while the bottom nodes were restrained in all the three directions (x, y, z) to replicate the friction in the test condition of the specimen. Figure 12 shows the general assemblage of the masonry cubic model, FE mesh and the boundary condition.