## 4 Validation of Proposed Empirical Model
### Nonlinear Finite Element Analysis (NLFEA)
From the first subplot of Figure 9, it can be examined that the peak stress value matches the experimental value when the values of the viscosity parameter and dilation angle are 0.0055 and 30\({}^{\circ}\), respectively. For dilation angle, the Drucker-Prager plastic potential function was used as given by Equation (20). \[G(\sigma)\ =\ \sqrt{\left(\varepsilon\sigma_{to}tann\psi\right)^{2}+\vec{q}^{2 }}+\frac{1}{3}I_{1}tan\psi \tag{20}\]  
where, \(\alpha_{p}\) is the dilatancy parameter according to [PERSON] [44] having a value of 0.2, for which the dilation angle should be near to 30\({}^{\circ}\). After the calibration for dilation angle of concrete, the value of 30\({}^{\circ}\) gave the best approximation as compared with the previous experimental stress-strain results of the control specimen. Figure 8: (**a**) Stress-strain curve for reinforced concrete given by Euro code [42] and (**b**) modified tension stiffening model. The numerical model of the control cylinder presented here is highly depending upon the mesh size because of the strain localization phenomena. To achieve better results of control specimen in terms of load-deflection curve, it is important to use smaller mesh size but not enough smaller to enhance the analysis time and burden of computer to solve the equations formed by the FEA procedure. Different mesh sizes ranging from 10 mm to 40 mm were used to see the effect of the variation of the mesh size dependency but found better results at mesh size of 20 mm. From Figure 9, a close agreement with experimental stress was achieved when the mesh size of 20 mm was used with the viscosity parameter of 0.0055 and dilation angle of 30\({}^{\circ}\). Similarly, it can be observed that the strain of 0.0017 was achieved by using viscosity parameter, dilation angle and mesh size of 0.0055, 30\({}^{\circ}\) and 20 mm at the same time, respectively. The influence variation of stress ratio, eccentricity and shape factor for the plastic behavior of concrete in CDP model was also investigated but their effect on stress-strain behavior of cylinders was negligible. Thus, the default values, i.e., \(Kc=0.667\), \(\varepsilon=0.1\) and \(\sigma_{b0}/\sigma_{c0}=1.16\) were used. The effect of different element types of concrete was also studied in this research. All the element library of ABAQUS for the 3D stress elements of concrete was studied to check the effects of elements types of concrete. The hexahedral, tetrahedral and triangular elements with different formulations were analyzed giving the best approximate at C3D8R elements. For the simulations of FRP sheets, the [PERSON] damage model was used. The FRP material can be considered as a 2D filament object having different moduli of elasticity in longitudinal and transverse directions and its behavior can be defined by two stages: the first is elastic stage defined by modulus of elasticity and Poisson's ratio as shown in Table 4 and the second is the plastic stage which is defined by [PERSON]'s [37] failure model. ABAQUS Standard follows the [PERSON]'s theory [36,37] for the prediction of damage criterion of FRPs using four damage mechanisms which are fiber tension and compression and matrix tension and compression. The failure of FRP resulting due to shear can be defined by Equation (21) as presented by [45]:  
\[\gamma_{xy}\ =\ G_{xy}^{-1}\sigma_{xy}+\alpha\sigma_{xy}^{3} \tag{21}\]  
\[\varepsilon_{c1} = 0.0014\big{[}2-e^{-0.024f_{cm}}-e^{-0.140f_{cm}}\big{]} \tag{16}\]0 Effect of (**a**) viscosity parameter, (**b**) dilation angle and (**c**) mesh size on stress–strain behavior of control cylinder specimen (C12.5-1L). where, \(\gamma_{xy}\) is shear strain in x-y plain, \(G_{xy}\) is the shear modulus of elasticity of FRP and \(\alpha\) is the nonlinearity factor having a value of \(55\times 10^{-5}\) MPa\({}^{-3}\).