A Finite-Element Model of Seated Human Body Representing the Distribution of Static Pressures and Dynamic Forces over a Rigid Seat During Vertical Vibration for Sitting Postures with Various Thigh Contact

Abstract

Overall sitting comfort is related to both static pressure distribution and dynamic human–seat interaction during vibration. This study proposes a simplified finite-element model of the seated human body that could potentially be used to assess overall sitting comfort. The static pressures of the seated human body measured on a rigid seat with different footrest layouts, together with the overall and localised apparent masses of the human body measured in a previous study, were used for model validation. The proposed model contained homogeneous soft tissues of the buttocks and thighs and rigid bodies connected to represent the torso. The tissue geometry was adjusted to match the measured anthropometry. Viscoelastic material was assigned to the tissues, and the properties were identified by fitting the modelled pressures and apparent masses to the measurement results. The proposed model was capable of reproducing static pressures and dynamic forces over the seat for the three sitting postures.

1. Introduction

Overall sitting comfort of vehicle passengers consists of static sitting comfort when there is no vibration and dynamic sitting comfort subject to vibration [1,2]. The static sitting comfort is related to the static pressure distribution over the sitting surface, while the dynamic sitting comfort depends on the dynamic interaction between the human body and seats. Sitting postures of the human body can affect both the static pressures and the dynamic interactions, hence the overall sitting comfort.

The static pressure distribution of the seated human body has been measured with pressure mapping systems [2,3,4,5]. Ebe and Griffin [2] found that the static sitting comfort was negatively correlated with the pressures beneath the ischial tuberosities. The dynamic pressure distribution under vertical vibration has also been reported [6,7,8]. However, dynamic pressures could be underestimated due to the viscoelastic behaviour of the pressure sensor [9,10], limiting its application in characterising the dynamic response of the seated human body during vibration.

Alternatively, studies have measured with force plates either the total dynamic force over the entire contact area between the human body and the seat [11,12,13] or the local forces beneath the ischial tuberosities and thighs [14,15]. Apparent masses derived from these forces—overall or local—were both sensitive to the contact between the thighs and the seat [14,15].

The static pressure distribution has been reproduced with finite-element models of the human body to study how it was shaped by the body-seat interaction [16,17,18,19,20,21]. These models had continuous representation of the soft tissues of the buttocks and thighs, with various levels of detail in body anatomy. Some models used detailed elements representing muscles at the buttocks and thighs to reproduce the maximum pressures beneath the ischial tuberosities for assessing pressure ulcers [18]. In other models, a homogeneous representation of the soft tissues of the buttocks and thighs without detailed muscles was adopted to represent the static pressure distribution over seats [16,17]. Inclusion of detailed muscles may improve the accuracy in predicting the static pressures, especially for different sitting postures, because the thickness and geometry of the muscles vary depending on sitting postures [18]. However, there is difficulty in identifying the material properties for different muscle groups. The homogeneous representation of the buttocks and thighs showed the capability to reproduce the static pressures for certain sitting postures, but its application for various sitting postures has not been identified.

Numerical modelling is also important for investigating the dynamic interaction between the body and seats and have been widely employed [15,22,23,24,25,26,27,28,29,30]. As most of the models were aimed to predict the total dynamic forces over the seat, the soft tissues of the buttocks and thighs were often simplified as discrete springs and dampers. Some other models, designed to reproduce the motions of the upper body during vibration, incorporated the spine [22] or represented the torso as several rigid segments linked by rotational springs and dampers [15,25,29]. There were also finite-element models including the continuous soft tissues of the buttocks and thighs to reflect human–seat interaction [31,32], whereas none were reported to reproduce the dynamic forces distributed at different locations over the sitting surface. This limitation is worth noting because with thigh support, the assumption of single-point vibration input to the body was not appropriate [14].

A unique model that can simultaneously capture both the static pressures and the dynamic forces over various locations of the sitting surface during vibration is of interest, as it can be used to predict the overall sitting comfort. Finite-element models of the human body require a proper type of material for the soft tissue of the buttocks and thighs. One simple form of the model may include homogenous soft tissues of the buttocks and thighs that were used in the models predicting static pressures [16], and a simplified torso representing its dynamics as in some biodynamic models [25]. In light of the application of viscoelastic models (e.g., the Kelvin–Voigt model) in many lumped-parameter and multi-body models predicting the apparent mass of the human body [23,24,25], finite-element models with viscoelastic material containing damping at the material level may be capable of representing the static and dynamic forces at the human–seat interface simultaneously, which has not yet been explored.

The objective of this study was to develop a simple finite-element model of the seated human body that can represent the following static and dynamic responses for sitting postures with different thigh contact:

• The static pressure distribution at the body–seat interface;
• The overall vertical in-line and fore-and-aft cross-axis apparent masses of the human body under vertical vibration;
• The localised vertical in-line and fore-and-aft cross-axis apparent masses measured at the ischial tuberosities, the middle thighs, and the front thighs.

It was hypothesised that a simple form of homogeneous representation of the soft tissues of the buttocks and thighs using a viscoelastic material, and a simplified torso that can reflect its dynamics, could reproduce the above responses for various sitting postures.

2. Measurement of Static Pressure Distribution and Dynamic Forces over the Seat

2.1. Equipment and Stimuli

The modelling presented in this paper was based on a previous dissertation [33]. In the measurement, a rigid seat was secured to a 1 m vertical electro-hydraulic vibrator. A multi-axis force plate (Kistler 9281B) was secured to the seat frame to measure the dynamic force on the seat surface, and the distribution of body pressure was measured using a resistive pressure sensing system located on the force plate. The sensing system included a grid-based flexible pressure mat (width: 48.8 cm; depth: 42.7 cm) with 2016 sensing units and a data acquisition system. The pressure mat was calibrated statically with an indenter rig using the method described in [10]. The calibrated sensor had a range of 160 kPa with a pressure resolution of 0.62 kPa.

The subjects sat on the seat with the upper body upright without back support, adopting three sitting postures with different thigh contact shown in Figure 1: feet hanging posture (i.e., no feet support), normal sitting posture (i.e., in which the thighs were positioned with the upper surface being approximately parallel to the seat surface), and high footrest posture (i.e., no contact between the front thighs and the seat). The distance between the top surface of the footrest and the top surface of the seat was about 38 cm for the normal sitting posture and 27 cm for the high footrest posture.

During measurement of body pressure distribution, the data were acquired for 60 s, at 5 frames per second (each frame contained 2016 pressure sensing points). The data of the last 5 s were averaged to obtain the static pressures. During measurement of apparent masses, the subjects were exposed to 60 s vertical broadband (0.5–20 Hz) random vibration at 0.25 ms⁻² r.m.s.

2.2. Analysis of Static Pressure Distribution

Three areas were defined in a previous study to correlate the pressures with the discomfort of subjects sitting on foam cushions [2], see Figure 2. They were applied in this study to summarise the large amount of pressure data. Area A was defined as a 10 cm × 10 cm square area centred on whichever ischial tuberosity exhibited the higher peak pressure. Area B was a rectangular area over the entire buttocks. Area C was a rectangular area over the entire thigh area. The average pressure over the three areas was compared with that calculated by the model.

2.3. Definition of Overall and Localised Apparent Masses

The transfer functions between the total force in the vertical or fore-and-aft direction measured at the seat and the vertical acceleration at the seat were calculated and referred to as the “overall vertical in-line apparent mass” and the “overall fore-and-aft cross-axis apparent mass” of the human body, respectively, as defined in [14].

The transfer functions between the vertical or fore-and-aft force measured at a certain location (i.e., beneath the ischial tuberosities, front thighs, or middle thighs) and the vertical acceleration at the seat were calculated and referred to as the “localised vertical in-line apparent mass” and the “localised fore-and-aft cross-axis apparent mass” at the location, respectively, as defined in [14].

3. Finite-Element Model of the Seated Human Body

3.1. Structure of the Model

The structure of this model was adapted from a previous model to predict the apparent mass of the seated human body exposed to vertical vibration without a backrest [31,33]. The model consisted of five body segments: upper torso, lower torso, buttocks-thighs, legs, and feet (Figure 3). The buttocks-thighs region was modelled with a rigid pelvis and femurs surrounded by deformable elements representing the soft tissues of the buttocks and thighs. The rest of the segments were modelled as rigid bodies (meshes for model appearance only). The segments were connected by revolute joints with rotational stiffness and damping. The model was developed in LS-DYNA.

The original model represented a 68.4 kg, 176 cm adult. In this study, it was rescaled and adjusted to match the stature and mass of the test subjects. As an example, for a subject with a stature of 170 cm, the shape of the soft tissue was adjusted to fit the dimensions listed in

Table 1. Anthropometric dimensions of the subject in the measurement and in the model ¹.

Anthropometric Dimensions	Measurement	Model
Total mass [kg]	63.5	63.5
Stature [cm]	170.0	170.0
Sitting height [cm]	90.0	90.0
Circumference of front thigh [cm]	38.4	37.4
Circumference of middle thigh [cm]	50.3	49.1
Circumference of rear thigh [cm]	58.5	57.1
Width of front thigh [cm]	11.5	12.1
Width of middle thigh [cm]	15.4	15.5
Width of rear thigh [cm]	20.3	17.1

¹ All dimensions were recorded with the subject seated, except stature and body mass which were measured while the subject was standing.

. The shape of the lower surface of the thighs was adjusted manually to approximate that of the subject’s anatomy (the thigh width was measured with the subject seated close to the front edge of the rigid seat, thighs parallel to the seat surface, and lightly clamped between two wooden boards at the front, middle, and rear locations). The mesh size of the soft tissues and the seat was refined to 0.75 cm to improve the spatial resolution of the pressure distribution (Figure 3). The differences in the pressures were less than 1% with the size being further reduced to 0.4 cm. Similarly, the results of the apparent mass obtained with the 0.75 cm mesh differed by less than 1% from those obtained with the 0.4 cm mesh. Further reduction in the mesh size (<0.4 cm) led to even more marginal differences. Therefore, the mesh size of 0.75 cm delivered converged average pressures over the three areas as defined in Figure 2 and used for the simulation.

3.2. Viscoelastic Material

The viscoelastic model (Figure 4) was assigned to the soft tissues of the buttocks and the thighs. The model consisted of a nonlinear elastic spring (E₁) in parallel with a series of a nonlinear viscous damper (V₂) and a linear elastic spring (E₂). With increasing compressive deformation, the nonlinear elastic stiffness (E₁) and the nonlinear damping (V₂) increased as Equation (1) and Equation (2), respectively:

E₁ = E_1,0 V ^−N₁

(1)

V₂ = V_2,0 |1 − V| ^N₂

(2)

where E_1,0 is the initial Young’s modulus, V is the ratio of the current volume to the initial volume, N₁ is the exponent coefficient, V_2,0 is the initial viscous coefficient, and N₂ is the exponent coefficient.

The deformation of the material with a static load only depends on E₁, because no force is on E₂ and V₂ with zero velocity. Therefore, E₁ was determined by fitting the modelled static pressures to the measured data. The parameters E₂ and V₂ were then identified by fitting the modelled localised apparent masses with the measured values. Determination of the material properties was based on the static pressures and apparent masses measured with the feet hanging posture, because this posture produced significant forces beneath the thighs to identify the parameters for the soft tissues of the thighs.

The soft tissues were partitioned into three regions: the buttocks, the middle thighs, and the front thighs (Figure 5), corresponding to the three locations where the dynamic forces were measured in the experiment. To simultaneously reflect the distribution of static pressures and dynamic forces, after trial-and-error tuning, different material properties were identified at the front thighs compared to other parts of the soft tissues. The determine material properties are listed in

Table 2. Material properties determined for the soft tissues of the buttocks, the middle thighs, and the front thighs.

	Density (kg/m3)	E1 (MPa)	N1	E2 (MPa)	V2	N2	Poisson’s Ratio
Buttocks and middle thighs	1085	0.001	3.6	0.5	6.0 × 10−4	0	0.45
Front thighs	1085	0.001	3.6	0.5	6.0 × 10−3	0	0.45

.

3.3. Modelling of Sitting Postures with Different Tight Contact with the Seat

The three heights of the footrest used in the experiment were implemented in the model (Figure 6) with two steps. Firstly, the human body model was settled on the seat under gravity without the feet contacting the footrest, until static equilibrium was reached. A velocity of 0.1 cm/s was then prescribed to the footrest till it achieved the position of the mid-height footrest and the high footrest. The stiffness and damping of the hip joints and the knee joints were disabled during this process until the required footrest position was achieved. Then the input to the model was vertical broadband random vibration (0.5–20 Hz, 0.25 ms⁻² r.m.s.) for the simulation of the apparent masses, identical to the one used during the experiment.

4. Results

4.1. Static Pressure

Comparison between the measured and modelled static pressure distributions of the subject (whose anthropometric dimensions are shown in Table 1) as an example is shown in Figure 7 and Figure 8. They exhibited similar patterns. The model provided reasonable fits to the measured average pressures with small discrepancies (less than 4% at Area A, and less than 10% at Area B and Area C) for all the sitting postures. The discrepancies increased when the thigh contact was reduced.

4.2. Overall and Localised Apparent Masses

With the feet hanging posture, the model provided a reasonable fit to the measured overall vertical in-line and fore-and-aft cross-axis apparent masses, as well as the corresponding localised apparent masses measured at all three locations (Figure 9 and Figure 10). The 8 Hz resonance in the localised vertical in-line apparent mass measured at the front thighs was well presented in the model.

For the other two postures, the model also provided a reasonable fit to the overall and localised vertical in-line apparent masses (Figure 11, Figure 12 and Figure 13). Discrepancies existed in the fore-and-aft cross-axis apparent masses with the normal sitting posture and the high footrest posture.

5. Discussion

5.1. Measured and Modelled Static Pressure and Apparent Masses

The modelled static pressures fitted well with the measured pressures over all three areas (Figure 7 and Figure 8). Discrepancies were less than 4% for Area A but greater in Area B and Area C for all three postures. The model showed the least difference compared to the measured pressures for the feet hanging posture, and greater difference as the height of the footrest increased. This is firstly because the material parameters were determined by fitting the static pressure with the feet hanging posture. Secondly, as the height of the footrest increased, the contact between the thighs and the seat decreased significantly, and this change is expected to be sensitive to the geometric shape of the soft tissues.

The current model represented a reasonable fit to both the overall apparent mass and the localised apparent masses of the human body, especially for the feet hanging posture (e.g., a relative error of less than 5% for the resonance frequencies, Figure 9, Figure 10, Figure 11 and Figure 13). Discrepancies between the modelled and measured apparent masses were observed mainly in the fore-and-aft cross-axis responses with the normal sitting posture and the high footrest posture (e.g., a relative error of more than 40% for the peak moduli, Figure 12). This discrepancy likely arose because during measurements the muscle forces of the upper body may have changed when the subjects adopted different sitting postures with various height of the feet, which affected the movement of the upper body and, consequently, the fore-and-aft forces over the seat. The changes in the muscle forces were not considered in this model.

5.2. Model Structure and Complexity

In this model, the geometric shapes of the soft tissues of the buttocks and thighs were adjusted based on a previous model [31] to approximate the anthropometry of the subject, and the model showed a reasonable fit to the average pressures over the defined areas (Figure 7 and Figure 8). This suggested that the average pressures were not significantly sensitive to the shape of the soft tissues, and the shapes estimated in this way seemed to be sufficient for predicting them.

The initial (i.e., before contacting the rigid seat) thickness of the soft tissues beneath the ischial tuberosities was 2.7 cm in this model (Figure 5), lying within the range between 2.6 and 4.2 cm reported in [18]. During the identification of the model parameters, it was found that the thickness of tissues beneath the ischial tuberosities affected the static pressures and the contact area. A greater thickness led to smaller pressure around the ischial tuberosities and a greater overall area of contact. In this model, the initial thickness beneath the ischial tuberosities was the same for all the sitting postures. However, measurements found that the thickness differed with the angle between the upper body and thighs [18]. This contributed to the greater discrepancies between the modelled and measured pressures with the higher footrest posture.

The mass effect of the torso can be simply represented with a lumped mass for the models predicting the static pressure of the seated human body, as implemented in a previous model of static pressures [16]. However, the absence of torso dynamics prevented that model from predicting the apparent mass. A series of rigid bodies connected with rotational stiffness and damping can represent the first few bending orders of the spine required for the reproduction of the vertical in-line apparent mass and fore-and-aft cross-axis apparent mass [31]. This form of structure has been widely adopted in many non-finite element models of the apparent mass [15,25,29]. Compared with the above models that targeted either static pressure or apparent mass alone, the present model captured both static pressures and dynamic apparent masses simultaneously with tissues having viscoelastic material damping and rigid bodies for torso motions, an approach not previously reported.

5.3. Material Properties

In this model, homogeneous soft tissues covering the pelvis and the femurs were used for the buttocks-thighs region, sufficient for the representation of the static pressure distribution, which differed from existing models with soft tissues having different compositions of muscle and fat at different locations along the thighs [35]. Different material properties had been obtained at the buttocks and the thighs in this model (Table 2). As shown in Figure 4, the viscoelastic material model contained a nonlinear elastic spring (E₁) in parallel with a series of a nonlinear viscous damper (V₂) and a linear elastic spring (E₂). While the same values of the elastic elements were determined for the soft tissues at the front thighs and buttocks, the damping was determined to be greater at the front thighs than at other locations (Table 2). A greater damping elevated the participation of E₂, therefore increasing the overall stiffness of the material at the front thighs. This was consistent with the greater overall stiffness of the soft tissues measured at the thighs than at the ischial tuberosities [18].

A brief sensitivity analysis on the soft tissue parameters at the thigh revealed that increasing the Young’s modulus raised the principal resonance frequency in both the vertical in-line and fore-and-aft cross-axis apparent mass; reducing Poisson’s ratio led to a decrease in the modulus of the vertical in-line apparent mass; and a lower damping coefficient dramatically amplified the resonance magnitude. These observations align with the stiffness and damping relations: a higher Young’s modulus increased effective stiffness, thus increasing resonance frequency and redistributing apparent mass from low to high frequencies. A decrease in Young’s modulus slightly reduced bulk stiffness and increased the damping ratio, which led to a lower resonance peak of the vertical apparent mass. Lower damping directly reduces the damping ratio, yielding the observed increase in resonance amplitude, consistent with earlier findings that peak apparent mass is strongly governed by soft tissue damping [25,29].

5.4. Implications for Prediction of Overall Sitting Comfort

The overall sitting comfort was found to contain both the static component linked to the static pressures beneath the ischial tuberosities and the dynamic component related to the vibration acceleration measured at the same location [1,36]. The form of model proposed in this study provided both the static pressures over the seat and the apparent masses of the human body during vertical vibration. Hence, it may be used to predict the overall sitting comfort. The simple structure of the current model was also capable of providing reasonable predictions of the aforementioned responses for a range of sitting postures with various thigh contact, which may widen its application in the prediction of overall sitting comfort. When coupled with seat or full-vehicle models, it can be used to guide early-stage design, helping to optimize foam hardness, cushion geometry, and suspension settings, while avoiding the cost and time of repeated volunteer tests.

A few limitations should be noted. In this study, one subject (1.70 m, 63.5 kg) who lay within ±5% of the 50th-percentile data for the Chinese adult male population [37] was used to validate the model with homogeneous tissue; in future work, the same protocol needs to be repeated on a broader range of body sizes, BMI values, genders, and ages to capture the potential inter-subject variability. Future work may also introduce spatially varying soft-tissue properties and a backrest module to refine the modelling of local pressure distribution and capture the interaction between the torso and the backrest under vibration, thereby enhancing the model’s fidelity for predicting overall sitting comfort under more realistic and diverse driving conditions. Additionally, recent finite-element enrichment techniques [38,39,40] offer new possibilities to improve element accuracy and could be explored in future refinements of the human-body model for whole-body vibration applications.

6. Conclusions

A simple form of a finite-element model of the seated human body was proposed. The model used homogeneous representation for the soft tissues of the buttocks and thighs assigned with nonlinear viscoelastic material, and the torso was represented by rigid bodies connected with rotational stiffness and damping. The model simultaneously captured the static pressure distribution at the body–seat interface and the localised vertical in-line and fore-and-aft cross-axis apparent masses at the ischial tuberosities, mid-thighs, and front thighs under vertical vibration for various sitting postures with different thigh contact.