extended finite element method

The propagation of incremental cracks in the main components of the structures is an important quandary that can cause irreparable damage in the structures over time. This study proposes a statistical method based on signal processing and machine learning to investigate crack location and propagation in reinforced concrete beams. The assumed beam with different boundary conditions is modeled in finite element software (ABAQUS) and incremental cracks are defined according to Extended Finite Element Method (XFEM) in two default locations along the length of the beam. Then, the incremental distributed load is assigned on the beam and the structure response is obtained through the loading time interval. The responses of the beam are used as a database to process with Continuous Wavelet Transform (CWT) and the wavelet coefficients are extracted in the same nodes that structure responses were. The distribution of wavelet coefficients has an effective and valuable implication to investigate the crack location and propagation. In order to consider the variation of wavelet coefficients during crack propagation, Principal Component Analysis (PCA) is used as a machine learning method. The study indicates that the first few components are highly correlated with the location of the damage. The results show that the proposed algorithm has recognized the crack propagation and localized it with high accuracy.

Today, one of the important issues in the industry is the failure of parts due to the presence of holes or cracks. Among the numerical calculation tools, the classical and extended finite element method is known as the most useful numerical tools in solving engineering science problems. Identifying and investigating the types of cracks, flaws and cavities in structures is one of the most challenging issues in the field of engineering. In this article, the crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with genetic algorithm(GA) and grey wolf optimization method (GWO) to detect the existing crack and flaws by minimizing an error function which is also called as objective function that the evaluation of it, is based on difference between sensor measurements and suggested structure responses in each try of the algorithm.  Damage detecting in 2D domains, as a non-destructive evaluation problem, is investigated using the extended finite element method along with the optimization method of genetic algorithm and grey wolf. The extended finite element method has been used to model the structure containing cracks and holes in the abaqus program, and genetic optimization and grey wolf method have been used to determine the location of the damage in which the codes were in matlab program. The extended finite element method is a powerful tool for the analysis of structures containing cracks without remeshing and is therefore suitable for an iterative process in structural analysis. Also, in these problems, due to the wide range of parameters, it is not logical and rational to use mathematical methods. For this reason, meta heuristic methods have been developed, and grey wolf optimization methods and genetic algorithm are among these common non-gradient methods that are suitable for solving the inverse problem. This problem is set so that the optimizer algorithm finds the existing crack coordinates or holes coordinates by minimizing an objective function based on the values measured by the sensors installed on the structure. Among the limitations of the classical finite element method in the investigation of various problems in the field of fault and crack detection, we can point out the dependence of the crack or cavity on the finite element mesh, re-meshing and in other special cases the use of singular elements, which are completely removed by using The extended finite element. In this research, in order to identify the damage, the genetic optimization algorithm and the gray wolf have been used. These algorithms are designed in such a way to determine the characteristics of the damage by minimizing an error function. The defined error function is defined as the difference between the response obtained from the algorithm analysis and the response recorded in the main structure modeled in ABAQUS software, at the location of the sensors. Finally, three reference numerical examples have been solved to evaluate the capability and accuracy of the proposed method, and the result of the results shows a reduction in the cost of solving and an increase in the accuracy of the results.

The current research seeks to present a novel method for numerical modeling of concrete behavior at meso-scale. In this method, as the stress distribution at the macro scale can be a suitable indicator for critical areas (crack propagate and growth), the areas under stress (critical areas) are identified through numerical modeling at the macro scale (coarse mesh) and using the extended finite element method and topology optimization. Macro-scale critical regions are considered cumulatively using topology optimization. Therefore, critical regions are modeled at the meso-scale, and the rest are modeled on the macro scale. At the meso-scale, the three phases including aggregate, mortar matrix, and ITZ were considered. The aggregate phase was distributed in the mortar matrix using a random algorithm and a Fuller curve. The accuracy of modeling concrete at the meso-scale using topology optimization was investigated by two examples, the results of which show the appropriate accuracy of the method. Furthermore, the method can reduce the computational cost and analysis time compared to modeling the whole sample at the meso-scale. In this research, the piecewise meshing method was used for numerical modeling. Using this method, traction-separation crack growth and expansion are modeled with appropriate accuracy.

In this study, stress formulas in the extended finite element method are investigated. The stress components for the enriched DOFs are developed and conventional stress components of the standard DOFs are modified. The modified stresses for the standard DOFs have a unique value for the whole domain of the cracked element, whereas the stress components for the enriched DOFs have different values at each side of the crack faces. New formulations are obtained by investigating the restoring forces equations. To do so, new polynomial functions are developed by eliminating the element partitioning when the shifted Heaviside function is utilized. The proposed stress formulas are verified by the force convergence criterion. It is shown that the proposed formulations for the standard DOFs are more compatible with the characteristics of the crack propagation within the cracked body and the stress components for the enriched DOFs represent the tractions at the crack faces, although properties of material nonlinear behavior are not considered. It is proven that the internal forces calculated utilizing the proposed formulation are in equilibrium with the external loads.

Fracture mechanics is a vast and growing open research field of sciences which concerned with the study of crack propagation. Stiffness matrix is an inherent feature of a numerical method. Its condition has a great influence on numerical calculation and the stability of the solution. Since the application of numerical methods such as the standard finite element method, the extended finite element method and the isogeometric analysis approach in the problems of fracture mechanics has been approved, in this contribution, a theoretical comparison between stiffness matrices is conducted. For this purpose, three computer codes are prepared to make a comparison on the stiffness matrix geometry and mathematical properties such as matrix sparsity, stiffness index, bandwidth, number of independent rows and columns, zero and non-zero elements, symmetric/ nonsymmetric and hermitian/ nonhermitian. The 8-node singular element is used in the framework of the finite element method. And in the case of extended finite element, the principles of enrichment of the interpolation functions of finite element and the application of the partition of unity method is considered. Also in the isogeometric analysis approach repetition of two different control points between two patches can create a discontinuity and also demonstrates a singularity in the stiffness matrix. In addition, the NURBS of order 3 are utilized as the basis functions to approximate the geometry and the solution. By comparing the stress distribution, the accuracy of the calculations and the smoothness of the results are investigated. It is found that, stiffness matrix obtained from the isogeometric analysis method is non-diagonal in the fracture problems. Extended finite element stiffness matrix in comparison with the other methods possess a better numerical conditions.

Initiation and progression of cracks in a saturated porous media is an important topic which has attracted considerable attention from researchers in the recent years. Extended finite element method (EFEM) is a contemporary technique removing the necessity of consecutive meshing of the problem in the analysis process. In the EFEM by enriching the elements whose discontinuity there exists, there is no need for re-meshing at each step of the analysis. .In this paper, EFEM is used to evaluate progression of cohesive crack in a two phase saturated porous media. To analyze the saturated porous media, at the first, the equations of mass conservation, momentum conservation, and energy conservation are established to consider simultaneous effects of displacement, pressure, and temperature on the crack progression. The cohesive model is used to simulate crack progression. Heavy-side functions are used to enrich finite elements and the resulting system of equations are solved by Newton Raphson method. Finally, the two numerical models were analyzed by other researchers is considered to evaluate the derived relationships. Numerical result show that maximum variation by other researchers is 5%.

The present paper investigates and compares the crack propagation in concrete gravity dams using two models of linear fracture mechanics and plasticity damage concrete. The first model is based on linear concrete behavior using the extended finite element method without considering the effect of strain softening on the crack tip while the second model is based on the nonlinear concrete behavior and the strain softening in tension with damage parameter. According to two different algorithms and based on two models, several benchmark examples are reviewed and the results compared with those reported in the literature. Then, path of the crack growth in Koyna gravity dam due to a seismic excitation of Koyna earthquake in 1962 has been performed by considering the dam-reservoir interaction. The results show that due to low compressive stresses during analysis of concrete gravity dams, consideration of compressive nonlinear behavior has no effect on crack initiation and almost is the same for two models. However because of crack opening and closing with tapping the crack faces together in extended finite element model, the compressive stress will be more than the allowable stress of concrete. Crack initiation at downstream and upstream face occurred at angle of 90 and zero degrees respectively, which in both models, the numerical results are in agreement with the experimental model. The crack in the extended finite element model grows faster such that the crest block of dam in this model is separated from the dam body, earlier than the concrete plastic damage model. Also the values of dam crest displacement and hydrodynamic pressure in the reservoir in extended finite element model with linear elastic fracture mechanic are more than the other model, which can be attributed to the linear and nonlinear behavior of concrete in extended finite element and concrete plastic damage model respectively. In the extended finite element model, due to using linear fracture mechanic, the maximum principal stress in the cracked elements reaches the values greater than the maximum tensile strength, but in the concrete plastic damage model as soon as the stress reaches a tension limit value, elements are damaged and the stress is reduced. In both models, the crack located at the slope change area, propagates with the downward slope from downstream dam face and connects to the crack at upstream face which is growth horizontally. Because of laboratory sample dimension and boundary condition of dam-reservoir compared with actual manner, neither of two crack profiles covered the experimental model, accurately. But it is shown that the crack profiles in the extended finite element model are more consistent with experimental results. Finally, the results show that the crack profile are slightly different in the two models because of quasi brittle behavior of the dam concrete, which can be attributed to the small fracture process zone of the crack tip in comparison with the dimension of the concrete gravity dams such that by removing strain softness part, the error in the amount of additional computation can be neglected.

Challenging and complex nature of the numerical analysis of crack problems have attracted the interest of many researchers in past decades and several techniques have been proposed for these problems. One of these techniques is the extended finite element method in which the crack tip field modeling is improved by enrichment of shape functions and the crack can intersect the elements. On the other hand, we have adaptive finite element method which aims to improve the accuracy of displacement and stress fields near the crack tip by remeshing process. Researchers have reported the drawbacks of each of these two techniques. In this paper the drawbacks of the previous techniques are covered with proper combination of these two techniques. By this combination the crack can pass through the elements and there is no need for crack tracking by mesh. In addition the estimated error is limited to desirable bands and stress intensity factor can be computed numerically with acceptable accuracy.

Interactive crack-internal heterogeneous boundaries have been of a great concern to researchers and engineers. Extended finite element method (X-FEM) has recently emerged as an approach to implicitly create a discontinuity based on discontinuous partition of unity enrichment (PUM) of the standard finite element approximation spaces. The extended finite element method (X-FEM) in the combination with level set method (LSM) has been utilized. In this contribution, predefined cracks and internal boundaries are created without meshing the internal boundaries. Soft/hard circular inclusions (interfaces), voids and linear interfaces are considered as internal discontinuities. In addition, the stress intensity factors for mixed mode crack problems are numerically calculated by using interaction integral approach. The interaction integral method is based on the path independent J-integral. The 4-noded rectangular element is considered to discretize the assumed plates. The effects of shape, size and schemes of internal boundary distributions are numerically simulated. The results are shown that the crack paths are attracted to soft internal boundaries and move away from the hard internal boundaries. Also, the influences of internal voids are much more than inclusions. In addition, the linear internal interface has affected the crack growth paths entirely and is created a complicate crack path. All numerical examples are demonstrated the flexibility and capabilities of X-FEM in the applied fracture mechanics

Damage detection of structures is an important issue for maintaining structural safety and integrity. In order to evaluate the condition of structures, many structural health monitoring (SHM) techniques have been proposed over the last decades. Major approaches of SHM are non-destructive in nature and are widely used for damage detection in engineering structures such as aerospace, civil and marine structures. The existence of damage in a structure may be traced by comparing the response of time-domain wave traveling in the structure at its present state with a base-line response. A difference from the base-line response is correlated to the damage location through estimation of time of arrival of the new peaks (scattered waves). Thus, by employing the wave based methods, presence of damage in a structure is detected by inspecting at the wave parameters affected by the damage. The wave parameters that are commonly used for damage detection are the parameters representing attenuation, reflection and mode conversion of waves due to damage. Although detection of flaws is extremely important for many industrial applications, current approaches are severely restricted to specific flaws, simple geometries and homogeneous materials. In addition, the computational burden is very large due to the inverse nature of the problems where one solves many forward and backward problems. For instance, conventional ultrasonic methods measure the time difference of returning waves reflected from a crack; however, for laminated composite plates, the ultrasonic wave would be partially reflected at the interface of two layers where no crack actually exists, and partially continues to propagate further where it eventually is reflected back by the true crack. Numerical methods employed in crack detection algorithms require the solution of inverse problems in which the spatial problem is often discretized in space using finite elements in association with an optimization scheme. The solution of these problems is not unique, and sometimes the optimization algorithm may converge to local minima which are not the real optimal solution. Moreover, they often require hundreds of iterations to converge considering the algorithm used in the process. On the other hand, an accurate detection of cracks requires the re-meshing of the finite element domain at each iteration of the optimization. This is a severe limitation to any numerical approach when the conventional finite element method is employed for crack modeling, as the re-meshing of a domain is often not a trivial task. This paper investigates crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with particle swarm optimization (PSO) algorithm. The XFEM is utilized to model the cracked structure as a forward problem, while the PSO is employed for finding crack location as an optimization scheme. The XFEM is a robust tool for analysis of structures having discontinuities without re-meshing. Therefore, it is an efficient tool for an iterative process. Also, the PSO is a well-known non-gradient based method which is suitable for this inverse problem. The problem is formulated such that the PSO algorithm searches crack coordinates in order to detect the existing crack by minimizing an error function based upon sensor measurements. This problem is a non-destructive evaluation of a structure. Three benchmark numerical examples are solved to demonstrate capability and accuracy of the XFEM and the PSO for crack detection of 2D domains.

Experimental and numerical study have carried out on behavior of Steel Plate Shear Wall (SPSW) and also, its good performance during past earthquakes have been testified a capable system against lateral load. The system have high ductility, stiffness and strength under seismic loading during a sever earthquake. Although, enormous studies have been performed till now, there are several unkhown problems about this system. Effect of crack on SPSW behavior is obviously one of the important between the unkhowns that have considerable effect on the behavior of SPSW. Therefore, in this study the effect of crack on SPSW is investigated. Results indicated that central crack is more critical than edge cracks. The results show that long central cracks cause the system fails in a brittle manner. In addition, a model have been proposed to obtain load-displacement curve without finite element modeling. On the proposed model the crack and its propagation is consider.

D‌u‌e t‌o m‌o‌r‌e t‌h‌a‌n o‌n‌e h‌u‌n‌d‌r‌e‌d y‌e‌a‌r‌s o‌f o‌i‌l a‌n‌d g‌a‌s e‌x‌t‌r‌a‌c‌t‌i‌o‌n, m‌o‌s‌t r‌e‌s‌e‌r‌v‌o‌i‌r‌s, e‌s‌p‌e‌c‌i‌a‌l‌l‌y t‌h‌o‌s‌e w‌i‌t‌h h‌i‌g‌h ‌e‌r‌m‌e‌a‌b‌i‌l‌i‌t‌y, a‌r‌e g‌r‌a‌d‌u‌a‌l‌l‌y r‌u‌n‌n‌i‌n‌g o‌u‌t. H‌e‌n‌c‌e, t‌h‌e t‌e‌n‌d‌e‌n‌c‌y i‌s t‌o‌w‌a‌r‌d‌s u‌t‌i‌l‌i‌z‌a‌t‌i‌o‌n o‌f r‌e‌s‌e‌r‌v‌o‌i‌r‌s w‌i‌t‌h l‌o‌w p‌e‌r‌m‌e‌a‌b‌i‌l‌i‌t‌y. A‌l‌s‌o, a‌f‌t‌e‌r c‌o‌n‌t‌i‌n‌u‌o‌u‌s e‌x‌t‌r‌a‌c‌t‌i‌o‌n o‌f h‌y‌d‌r‌o‌c‌a‌r‌b‌o‌n p‌r‌o‌d‌u‌c‌t‌s, n‌a‌t‌u‌r‌a‌l r‌e‌s‌e‌r‌v‌o‌i‌r p‌r‌e‌s‌s‌u‌r‌e i‌s r‌e‌d‌u‌c‌e‌d, c‌r‌a‌c‌k‌s a‌r‌e ‌l‌o‌s‌e‌d ‌n‌d ‌h‌e ‌r‌o‌d‌u‌c‌t‌i‌o‌n o‌f t‌h‌e r‌e‌s‌e‌r‌v‌o‌i‌r i‌s r‌e‌d‌u‌c‌e‌d. I‌t i‌s, t‌h‌e‌r‌e‌f‌o‌r‌e, n‌e‌c‌e‌s‌s‌a‌r‌y t‌o u‌n‌d‌e‌r‌t‌a‌k‌e a‌d‌d‌i‌t‌i‌o‌n‌a‌l m‌e‌t‌h‌o‌d‌s i‌n o‌r‌d‌e‌r t‌o e‌n‌h‌a‌n‌c‌e t‌h‌e c‌a‌p‌a‌c‌i‌t‌y o‌f s‌u‌c‌h r‌e‌s‌e‌r‌v‌o‌i‌r‌s; h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g i‌s s‌u‌c‌h a m‌e‌t‌h‌o‌d, w‌h‌i‌c‌h i‌s p‌o‌p‌u‌l‌a‌r‌l‌y a‌p‌p‌l‌i‌e‌d t‌o 50% o‌f o‌i‌l a‌n‌d 70% o‌f g‌a‌s w‌e‌l‌l‌s i‌n N‌o‌r‌t‌h A‌m‌e‌r‌i‌c‌a.I‌n h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g, t‌h‌e f‌l‌u‌i‌d w‌i‌t‌h p‌r‌e‌s‌s‌u‌r‌e m‌o‌r‌e t‌h‌a‌n t‌h‌e i‌n-s‌i‌t‌u s‌t‌r‌e‌s‌s o‌f t‌h‌e r‌e‌g‌i‌o‌n i‌s i‌n‌j‌e‌c‌t‌e‌d i‌n‌t‌o t‌h‌e p‌l‌a‌c‌e o‌f t‌h‌e w‌e‌l‌l t‌h‌a‌t h‌a‌d b‌e‌e‌n i‌s‌o‌l‌a‌t‌e‌d b‌y p‌a‌c‌k‌e‌r‌s. W‌h‌e‌n t‌h‌e f‌l‌u‌i‌d p‌r‌e‌s‌s‌u‌r‌e e‌x‌c‌e‌e‌d‌s t‌h‌e i‌n-s‌i‌t‌u s‌t‌r‌e‌s‌s, h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g w‌i‌l‌l o‌c‌c‌u‌r. O‌n‌e n‌u‌m‌e‌r‌i‌c‌a‌l m‌e‌t‌h‌o‌d r‌e‌c‌e‌n‌t‌l‌y d‌e‌v‌e‌l‌o‌p‌e‌d f‌o‌r s‌i‌m‌u‌l‌a‌t‌i‌o‌n o‌f h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g i‌s t‌h‌e e‌x‌t‌e‌n‌d‌e‌d f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d (X‌F‌E‌M). I‌n t‌h‌i‌s m‌e‌t‌h‌o‌d, t‌h‌e n‌o‌d‌e‌s s‌u‌r‌r‌o‌u‌n‌d‌i‌n‌g t‌h‌e c‌r‌a‌c‌k‌s a‌r‌e e‌n‌r‌i‌c‌h‌e‌d t‌h‌r‌o‌u‌g‌h s‌p‌e‌c‌i‌a‌l f‌u‌n‌c‌t‌i‌o‌n‌s. A‌c‌c‌o‌r‌d‌i‌n‌g‌l‌y, f‌o‌r s‌u‌c‌h n‌o‌d‌e‌s, t‌h‌e d‌e‌g‌r‌e‌e‌s o‌f f‌r‌e‌e‌d‌o‌m a‌r‌e i‌n‌c‌r‌e‌a‌s‌e‌d, w‌h‌i‌c‌h r‌e‌s‌u‌l‌t‌s i‌n g‌r‌e‌a‌t‌e‌r d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t a‌r‌o‌u‌n‌d e‌a‌c‌h c‌r‌a‌c‌k. I‌n t‌h‌i‌s r‌e‌s‌e‌a‌r‌c‌h, a X‌F‌E‌M c‌o‌d‌e w‌a‌s d‌e‌v‌e‌l‌o‌p‌e‌d t‌o s‌i‌m‌u‌l‌a‌t‌e t‌h‌e h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g p‌r‌o‌b‌l‌e‌m.T‌h‌e c‌o‌d‌e p‌r‌o‌v‌i‌d‌e‌s t‌h‌r‌e‌e i‌n‌t‌e‌r‌a‌c‌t‌i‌o‌n p‌r‌o‌c‌e‌s‌s‌e‌s: (I) M‌e‌c‌h‌a‌n‌i‌c‌a‌l d‌e‌f‌o‌r‌m‌a‌t‌i‌o‌n d‌u‌e t‌o f‌l‌u‌i‌d p‌r‌e‌s‌s‌u‌r‌e o‌n t‌h‌e c‌r‌a‌c‌k, (I‌I) F‌l‌u‌i‌d f‌l‌o‌w i‌n t‌h‌e c‌r‌a‌c‌k a‌n‌d (I‌I‌I) C‌r‌a‌c‌k p‌r‌o‌p‌a‌g‌a‌t‌i‌o‌n d‌u‌e t‌o f‌l‌u‌i‌d m‌o‌t‌i‌o‌n. T‌h‌e r‌e‌s‌u‌l‌t‌s o‌f n‌u‌m‌e‌r‌i‌c‌a‌l a‌n‌a‌l‌y‌s‌i‌s b‌y t‌h‌e p‌r‌o‌v‌i‌d‌e‌d c‌o‌d‌e, w‌h‌i‌c‌h i‌s e‌x‌a‌m‌i‌n‌e‌d o‌n a c‌l‌a‌s‌s‌i‌c h‌y‌d‌r‌a‌u‌l‌i‌c f‌r‌a‌c‌t‌u‌r‌i‌n‌g p‌r‌o‌b‌l‌e‌m, e‌x‌h‌i‌b‌i‌t d‌e‌c‌r‌e‌a‌s‌i‌n‌g f‌l‌u‌i‌d p‌r‌e‌s‌s‌u‌r‌e a‌n‌d i‌n‌c‌r‌e‌a‌s‌i‌n‌g c‌r‌a‌c‌k o‌p‌e‌n‌i‌n‌g‌s a‌t t‌h‌e b‌o‌r‌e‌h‌o‌l‌e w‌e‌l‌l, a‌s t‌h‌e c‌r‌a‌c‌k l‌e‌n‌g‌t‌h p‌r‌o‌g‌r‌e‌s‌s‌e‌s. T‌h‌e‌s‌e r‌e‌s‌u‌l‌t‌s a‌r‌e i‌n l‌i‌n‌e w‌i‌t‌h t‌h‌e r‌e‌s‌u‌l‌t‌s o‌b‌t‌a‌i‌n‌e‌d b‌y t‌h‌e K‌G‌D a‌n‌a‌l‌y‌t‌i‌c‌a‌l s‌o‌l‌u‌t‌i‌o‌n. A‌l‌s‌o, i‌t w‌a‌s o‌b‌s‌e‌r‌v‌e‌d t‌h‌a‌t t‌h‌e w‌i‌d‌t‌h o‌f t‌h‌e c‌r‌a‌c‌k o‌p‌e‌n‌i‌n‌g s‌h‌o‌u‌l‌d b‌e i‌n‌c‌r‌e‌a‌s‌e‌d t‌o e‌n‌h‌a‌n‌c‌e t‌h‌e e‌x‌p‌l‌o‌i‌t‌a‌t‌i‌o‌n o‌f h‌y‌d‌r‌o‌c‌a‌r‌b‌o‌n p‌r‌o‌d‌u‌c‌t‌s. I‌n o‌r‌d‌e‌r t‌o r‌e‌a‌c‌h t‌h‌i‌s g‌o‌a‌l, t‌h‌e f‌l‌u‌i‌d v‌i‌s‌c‌o‌s‌i‌t‌y a‌n‌d/o‌r i‌n‌j‌e‌c‌t‌i‌o‌n r‌a‌t‌e o‌f t‌h‌e f‌l‌u‌i‌d s‌h‌o‌u‌l‌d b‌e i‌n‌c‌r‌e‌a‌s‌e‌d.