1) To analyze and synthesize from reviewed papers the design criteria for subunits of the shock-absorption mat that would attenuate the impact force of human’s falling down on the side of his or her body and that took the physical properties of subunits’ material into account;

2) To analyze and synthesize possible form factors of subunits that affect the shock-absorbing capacity of a mat’s structural layer from reviewed papers (Table 1).

The authors have reviewed the literature regarding floor mats for reducing fatigue from standing for a long time, shock-absorbing structural layer, and physical parameters of elderly’s slipping and falling on their hip and found valuable information in 7 articles [14, 16, 21, 25, 27-29]. From the review, the following design criteria and form factors that would be used in the simulation were formulated: (a) design criteria: 1) the fall was to one side of the body and the impact force of the fall was around ~4.050 N.m/s [23, 25, 30]; and 2) the mechanical properties of rubber as the chosen material for the mat among concrete, rubber foam, rubber, polyvinyl chloride, wood-plastic, and steel shown in (Table 1 and 2) form factors: Form of edges was chosen as an appropriate variable to use in our study because three of the articles mentioned above reported a wide range of impact forces that shock-absorption mats with different forms of edges in several nursing homes were able to withstand without damage. Similarly, the form of cross-section was chosen because a paper on shock absorption mats for various applications reported a wide range of impact forces that their subunits had to withstand [27, 31, 32]. The paper reported that shock absorption mats for the floor of a laboratory, an industrial factory, and a nursing home had different forms of a cross-section of subunits and were able to absorb the intended force without damage. Specific design criteria and form factors [14, 21] were also investigated in this study. All of these form factors are shown in Table 1.

Table 1. Shock absorbing products reported in the 7 articles from literature reviews.

No.	Side View	Perspective View	Design Criteria		Form Factors				Details
			Impact Force	Physical Properties of Rubber Material	Cross-Section	Edge	Arrangement Pattern of Subunits	Dimensional Proportion
L 01			= ~4.050 N.m/s	No data			Cross-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 8 mm.	This mat was used in a laboratory
L 02							Table-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 5 mm.	This mat was used in speed boat that carries emergency patients
L 03							Table-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 8 mm.	This mat were used in a laboratory, industrial factory, and airport
L 04							Table-arrangement	Width 5 mm. Length 5 mm. Height 28 mm. Gbas 1 mm.	This mat was used in nursing home
L 05							Table-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.	This mat was used in military vehicles
L 06							Line-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.	This mat was used in nursing home
L 07							Line-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.	This mat was used in a car parking lot

*Note: the physical properties of rubber material were obtained in Phase 2.

The results of Phase 1 are described here. The selected design criteria were the followings: 1) impact force of a fall and 2) the physical property of rubber material. The selected form factors of subunits were the followings: 1) form of cross-section, 2) form of edges, (3) arrangement pattern of subunits, and 4) dimensional proportion of subunits of width x length x height x gap between adjacent subunits (gbas). Table 1 shows all of the form factors discussed in those articles along with summarized information about them that influenced our decision to choose particular form factors: side view, perspective view, design criteria, and form factors.

1) To obtain control variables for inputting into ANSYS engineering simulation software 16.0 gleaned from reviewed papers, design criteria would be encoded into simulation conditions. (Fig. 3).

2) To obtain independent variables that would be used to construct various models of shock absorption mat with 3ds Max software before they would be subsequently inputted into ANSYS.

A finite element method for simulating impact force was used to simulate the action and reaction forces of a fall event on the mat; the method was packaged in the form of a software program called ANSYS; A simulation of a fall event is absolutely necessary because an actual experiment that has an elderly person intentionally make his or her body fall down is definitely not possible without any injuries; ANSYS is an established simulation software program that has been widely used in engineering and material science, hence it was most suitable for our objective.

From the literature review, an analysis and synthesis of control and independent variables needed to be inputted into ANSYS were performed. The variables involved were the following: (a)control variables: (1) the value of the impact force of a fall on the hip from a reliable paper [14] was entered in the ANSYS simulation software under the menu ‘static shortcut (A5)’ and submenu ‘impact force’ as x = 2.400, y =2.400, and z = -2.400 then the software displayed an impact force of ~4.157 N.m/s with a tolerance of not more than ± 0.1 N.m/s (Figs. 4 and 2) rubber material was chosen as the most suitable material for this purpose because it can absorb impact force and return to the original shape well [25]; the physical properties of the kind of rubber that would be used were determined in a laboratory and reported in [26]; these values were inputted into ANSYS under the menu ‘hyperelastic experimental data’, submenu ‘property of outline’, and input boxes called ‘biaxial test data’, ‘uniaxial test data’, and ‘shear test data’; under the submenu ‘coefficient name’, the ANSYS software then generated fitted curves of these data to be applied to the tested models (Fig. 6) independent variables: (1) form of cross-section, (2) form of edges, (3) arrangement pattern of subunit, and (4) dimensional proportion of subunits were inputted into 3ds Max software to construct a 3D model for each combination of the variables; the various resulting models were in .stl file format which could be inputted directly into ANSYS (Fig. 5).

Fig. (5). Inputs of (a) control variables into ANSYS simulation program: (2) physical properties of subunit’s rubber material; stress = -60 MPa, biaxial = 0.43 mm/min, planar shear = 0.43 mm/min, and uniaxial = 1 mm/min.

The control variables obtained were the level of impact force of a fall on the side of the body of ~4.050 N.m/s or more and the actual physical properties of subunit’s rubber material (stress of ~0.60 MPa, axial and planar strains of 0.43 mm/min, and uniaxial strain of mixed rubber material of around 1 mm/min) [26]. The independent variables were the following: 1) form of cross-section: Square, circular, and triangular shape; 2) form of edges: Straight, rounded, spring-like, diamond, and trapezoidal shape; 3) arrangement pattern of subunits in the structural layer: Cross, table, and line arrangement; and 4) dimensional proportion of subunits: 28 mm x 25 mm x 25 mm x 5 mm of width x length x height x gap between adjacent subunits (gbas).

To simulate the forces of a fall absorbed by various models of subunits with ANSYS engineering simulation 16.0 software. The simulated absorbed forces would show which kind of subunits are suitable for constructing a reliable shock absorption mat: the higher the force a type of subunits could absorb and withstand, the more suitable that type is for constructing a shock absorption mat.

Fig. (6). Inputs of (b) independent variables into 3ds Max software program: (1) form of cross-section, (2) form of edges, (3) arrangement pattern of subunits [33, 34], and (4) dimensional proportion of subunits.

Seven subunit models were constructed from 3dsMax software, each with a combination of the synthesized independent variables: 1) pattern of arrangement of subunits in the structural layer, 2) form of cross-section, 3) form of edges, and 4) dimensional proportion of subunits. The constructed models were inputted into the ANSYS simulation software in combination with the design criteria which were the control variables: 1) impact force of a fall (~4.050 N.m/s or more) and 2) physical properties of the rubber material. The intended simulation outcomes were the force that each subunit and structural layer model was able to absorb without damage. The simulation software was run on a PC on Windows platform with an i5 CPU and 8 gigabytes of RAM. In this study, a different level of force that a type of subunits could withstand is represented by a different color-the lowest level is represented by red color and the highest is represented by blue as shown in the color scale in (Fig. 5).

Fig. (7) shows a color-coded scale of force absorption capacity of an area in the simulation models depicted in Table 2. An area in the image of each model in this table has a color that indicates its force absorption capacity. An orange of a red color indicates that the area would collapse under an impact force of a fall. Adequate attenuation is color-coded as light-blue to light-green. It can be seen clearly from the results of the simulation in Table 2 that the subunits of models M 02 met our force-absorbing requirement: it was able to attenuate force of more than 4.050 N.m/s, shown as dark-blue to dark-green color in Fig. (5), and the structural layer of these models did not collapse. Three models failed to meet our requirement, M05, M06 and M07. Their force attenuating capacity is shown as yellow to red in Fig. (7). Their structural layers were damaged by the level of the force of a fall from slipping and would not be able to prevent hip injury in elderlies.

The model M 03 was able to withstand an amount of force but not as high as the set level of impact force at 4.050 N.m/s. Similarly, the models M 01 and M 04 were not able to attenuate it adequately, hence they would not help reduce the reaction force to the hip of a fallen body adequately.

Table 2. Simulations results of the forces of fall absorbed by different models of subunits and structural layer.

No.	Control Variables		Side View	Perspective View	Independent Variables				Simulation View	Result (N.m/s)
	Impact Force	Physical Properties of Rubber Material			Cross-Section	Edge	Arrangement of Pattern of Subunits	Dimensional Proportion
M 01	= ~4.050 N.m/s	Stress of = ~0.60 MP., Axial strains = 0.43 mm/min, Planar strains = 0.43 mm/min, and Uniaxial strain = 1 mm/min					Cross-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 8 mm.		1.1190
M 02							Table-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 5 mm.		6.4900
M 03							Table-arrangement	Width 28 mm. Length 25 mm. Height 25 mm. Gbas 8 mm.		4.0262
M 04							Table-arrangement	Width 5 mm. Length 5 mm. Height 28 mm. Gbas 1 mm.		1.2391
M 05							Table-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.		2.6003
M 06							Line-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.		8.2280
M 07							Line-arrangement	Width 28 mm. Length 20.3 mm. Height 25 mm. Gbas 3 mm.		6.0476

From the results shown in Table 3 , it can be observed that several suitable form factors of subunits are following: 1) form of cross-section of subunits can be circular, 2) form of edges of subunits can be hourglass-like, 3) arrangement pattern of subunits can be table pattern, and 4) dimensional proportion of subunits can be 28 mm x 25 mm x 25 mm x 5 mm of width x length x height x gap between adjacent subunits (gbas).

Fig. (7). Color-scale of the force absorption capacity of an area in the simulation models (in ANSYS simulation program).

Table 3. Suitable form factors of subunits.

No.	Picture	Form Factor of Subunits	Details
(1)		Form of cross-sections	Circular shape
(2)		Form of edges	Spring-like
(3)		Arrangement pattern of subunits	Table-arrangement
(4)		Dimensional proportion	Width 28 mm. Length 25 mm. Height 25 mm. Gap between adjacent subunits (Gbas) 5 mm.