finite element modeling of the impact loading on … · the impact dynamics of the human tissue...

2004 ABAQUS Users’ Conference 409

Finite Element Modeling of the Impact Loading on Tissue Simulants

Alan Leung1, Kirth Simmonds1, Mark Chase2 and Andrew Geltmacher1 1Naval Research Laboratory

4555 Overlook Ave SW Washington, DC, 20375

2Nova Research 1900 Elkin Street, Suite 230

Alexandria, VA, 22308

Abstract: The development of materials that respond in the same manner as biological tissue is an important factor in studying the mechanisms that lead to the trauma of living organisms. This work investigates the modeling of simulant materials for human tissue. The dynamics of human tissue simulants for use in surrogate development was studied under impact loading conditions and computational methods. A block of human tissue simulant was modeled with impact loading conditions. The hyperelastic mechanical parameters used in this analysis were measured for the modified gelatin materials specifically designed to simulate human tissue. In this analysis, rigid spheres of different diameters, masses and impact velocities were compared to the experimental study of impact energies. The finite element program ABAQUS/Explicit was used to simulate these impact specimens. The displacement histories, pressure contours and Fast Fourier Transforms of the computational models were compared to the experimental data. Numerical analyses provide insight into key areas of interest and information on the optimal placement of sensors in more complex thoracic surrogate models.

1. Introduction

The Naval Research Laboratory has developed a surrogate human thorax model (GelMan) that is comprised of a spine and rib cage from a plastic skeleton reproduction surrounded by ordnance gelatin with high fidelity lungs and heart organs. A GelMan model is shown in Figure 1. This thoracic model has been used to experimentally reproduce the response of different dynamic loading conditions on the human torso. The application of this novel surrogate system for impact studies is advantageous as it eliminates animal testing and provides realistic dynamic response. A clear understanding of the impact mechanisms on the material response of the complex system can provide insight into preventing or mitigating injuries sustained from car accidents, sports and/or battlefield injuries.

This paper uses finite element analysis to study the dynamic behavior of human tissue simulants in a relatively simple geometry under impact loading conditions. This is the first step in a planned series of studies that will add complexity in terms of materials and geometry. The human tissue simulants were designed to reproduce the mechanical properties of different human tissues, such as the lung and heart. Due to the inherent complexity of the GelMan system, simple tests were developed to study the mechanical response of the tissue simulants. These tests consist of blocks of human tissue simulants impacted by steel spheres of different diameters and masses at specific

410 2004 ABAQUS Users’ Conference

kinetic energy values. Figure 2 shows an example of the simple ordnance gel block with a cylindrical “lung” in the middle.

The finite element models presented in this paper are used in conjunction with experimental impact tests to examine the response of the human tissue simulant blocks. The development of the finite element models enhances the understanding of the experimental models and defines areas in which future improvements can be made. This simple study is also used to determine the most appropriate type of constitutive model to be used for the more complex systems such as the “GelMan” surrogate human thorax.

2. Materials and Methods

The impact dynamics of the human tissue simulant blocks were modeled using the finite element program ABAQUS/Explicit. A detailed description of the model geometry, the determination of the material properties and constitutive model, the boundary conditions and finite element parameters will be discussed in the following sections.

2.1 Geometry, Boundary Conditions and Model Description

The experimental and finite element models consist of a rigid sphere impacting a rectangular block of the human tissue simulant situated on a table. A schematic of the test setup and corresponding finite element model is shown in Figure 3. The dimensions of the simulant blocks were 305 mm x 191 mm x 216 mm. The experimental block was created by filling a rectangular mold with the desired tissue simulant of standard ordnance gelatin, leaving a cylindrical hole that was parallel to the impact surface (Figure 3). This cylindrical hole is backfilled with different types of simulant materials: the standard ordnance gelatin or modified ordnance gelatins represented by baseline lung tissue simulant or heart tissue simulant. This manufacturing process produces an interface between the block and embedded cylinder human tissue simulant materials which is only accounted for only by a change of material property in the current finite element models. Thus, sliding or separation which may occur in the experimental models is neglected in the computational simulations. This paper will only focus on providing a comparison between the computational and experimental models using the standard ordnance gelatin as the block and backfilled cylinder material. In the experiments, two accelerometers were placed in the block directly under the initial sphere impact point. The first accelerometer was located 51 mm beneath the impact surface, while the second one is located in the center of the block, 121 mm beneath the surface. The bottom boundary condition consisted of a rigid flat surface, which corresponds to a table in contact with the specimen block. Both contact surfaces, the ball with the top of the specimen and the bottom of the specimen with the table, were modeled without friction. The dimensions of the rigid flat surface were 237 mm x 335 mm.

The specimen blocks were dynamically loaded by dropping different spherical ball masses to produce specific impact energies for both the finite element and experimental tests. Experimentally, the selected impact energies were used to calculate the height that a specific ball was dropped. From this data, the final velocity of the ball just prior to contact with the specimen block was calculated. These velocities are used as the initial conditions on a rigid hemisphere in the finite element simulations. The ball diameters, masses and impacted energies used for the


computational and experimental tests are shown in Table 1. These cases were selected in order to provide an understanding of how both different sphere impact energies with the same ball diameter as well as different ball diameters with the same impact energy influences the specimen’s dynamic response.

ABAQUS/Explicit was used to model the impact cases. The block consisted of 32,306 C3D8R elements and 35,497 nodes. Contact pairs were defined for the rigid master surfaces, the spherical sphere and the table, against the slave surrogate tissue block. An adaptive mesh with hourglass stiffness and an orthogonal kinematic split was used to prevent element distortion. Gravity effects were also included in the model for a more accurate response to the dynamic loading conditions.

2.2 Material Properties

Accurate finite element predictions require the application of the appropriate constitutive models. Previous experience has shown that a hyperelastic constitutive model provides the most accurate description for the ordnance gelatin. A hyperelastic constitutive model was also selected to describe the dynamic behavior of the other two tissue simulant materials. Uniaxial and planar compression tests were performed on the different simulant materials and used as test input data. Uniaxial tension experiments were not performed due to the materials’ limited tensile strengths. Figure 4 shows the input uniaxial compression and plane strain compression experimental data used in the simulations for the ordnance gelatin. The Ogden form of the *HYPERELASTIC card was used for the strain energy potential equation with N set to 3. A linear-elastic parametric study has also been performed showing negligible influence of the Poisson’s ratio on the material’s response. The Poisson’s ratio of the material was thus chosen to be 0.475, which is the default choice used in ABAQUS/Explicit. The density of the ordnance gelatin was 1.067 grams/cm3.

3. Results and Discussion

Ball drop tests on human tissue simulant blocks were performed using computational and experimental methods for different impact energies and sphere masses. The results presented below are for the case where the simulant block and the cylindrical “lung” are made solely from the ordnance gelatin base material. The displacement histories at the center of the surrogate block for the finite element and experimental models were extracted in the impact direction. Figure 5 shows the measured displacements histories for the experimental cases at impact energies of 2, 3, 5, and 10 Joules for the 1045 gram ball for the accelerometer placed at the center of the block. As expected, the displacement magnitude increases as the impact energy is increased. The 10 Joule ball drop case also exhibits higher secondary oscillations than that of the 2, 3, and 5 Joule cases. This effect may be due to different deformation mechanisms activated at higher energies. Also, a definite widening of the displacement history in the 10 Joule case is observed and hypothesized to be a result of the simulant material entering the nonlinear regime.

Figures 6a and 6b show the predicted displacement history from the finite element and experimental models’ response for the 1045 gram ball at the center of the block with impact energies of 3 and 5 Joules, respectively. There is relatively good agreement between the


magnitudes of the predicted displacements of the finite element models to the experimental models for these cases. However, some differences between the models exist. There is a time lag after the initial compression response between the finite element analyses versus the experiments. It is believed this time lag to be due to the lack of the interface in the computational models. The interface could cause the backfilled center material to deform out of phase with the motion of the remainder of the specimen block. The experimental displacement data show secondary oscillations at times 0.14 seconds and 0.22 seconds for the 3 Joule case, while for the 5 Joule case, these oscillations occur at 0.13 seconds and 0.22 seconds. The finite element model does not exhibit these secondary oscillations in the 3 Joule case. In the 5 Joule case, the finite element model shows the initial development of these oscillations with a delayed formation at 0.25 seconds.

Figure 7 compares the predicted displacement responses of the specimen using 1045 and 1390 gram balls with an impact energy of 5 Joules at the center of the specimen (Figure 7a) and at 51 mm from the impact surface (Figure 7b). Both figures show only minor deviations in displacements for the different ball sizes. This indicates that for these type ball sizes there is a negligible effect on displacements.

The Fast Fourier Transforms of the finite element and the experimental displacement data at the center of the specimen block for the 3 and 5 Joule, 1045 gram ball cases are shown in Table 2. The finite element and experimental frequencies match fairly well. An additional frequency peak is observed in both cases of the experimental model which is not observed in the finite element model. These additional frequencies are most likely caused by the interface between the block gelatin and embedded cylinder gelatin of the cylindrical hole and indicate the importance of including these interface in future computational models.

Pressure contour plots of the 10 Joule, 1390 gram ball drop case for times of 0.027, 0.066, 0.076, and 0.081 seconds are shown in Figures 8 a-d, respectively. The contour values have been selected to emphasize the negative regime. Previous research has shown that negative pressures causes more blunt trauma damage to biological tissue than positive pressures. Figure 8a is the pressure contour at the point of maximum sphere indentation. A high pressure area forms immediately below the impact region. Figure 8b shows the formation of two symmetric pressure regions at approximately 40 mm from the impact surface. As the ball rebounds from the impact surface (Figure 8c), the block begins to lift off the surface of the table and pressure zones at the sides develop. Figure 8d shows a negative pressure region as it expands from the base of the block to the impact surface with the maximum pressure occurring along the sides of the block.

4. Conclusions

Finite element methods were applied to study the dynamics of human tissue simulant materials and compared to experimental tests. The computational displacement and frequency histories compared well to the experimental models. The computational predictions also provided pressure contours from ball impacts on tissue simulants. The interface present in the experimental model is unaccounted for in the existing finite element simulations. The lack of this interface may be the leading source of discrepancy in the results. The understanding of these interface properties will be very important in finite element modeling of the more complex GelMan thoracic surrogate.


5. References

1. ABAQUS/Explicit User’s Manual, Vol. I & II (ver. 6.3), (2002). Hibbit, Karlsson & Sorensen, Inc., Pawtucket, Rhode Island.

2. Fung, Y.C., Biomechanics: Motion, Flow, Stress, and Growth. New York, Springer-Verlag, 1990.

3. Gendy, A.S., Saleeb, A.F., “Nonlinear Material Parameter Estimation for Characterizing Hyper Elastic Large Strain Models”, Computational Mechanics, Vol. 25, n. 1, 2000, pp. 67-77.

4. Humphrey, J.D., Cardiovascular Solid Mechanics: Cells, Tissue, and Organs. New York, Springer-Verlag, 2002.

5. Maurel, W., Biomechanical Models for Soft Tissue Simulation. New York, Springer-Verlag, 1998.

6. Lippert, S., Rang, E. Grimm, M., “The ‘Wave-In-A-Tube’ Technique to Determine Material Properties of Brain Tissue and other Gel-Like Substances”, BED-Vol. 50, Bioengineering Conference, ASME 2001.

Table 1. Ball diameters, masses and energies.

2 Joules 3 Joules 5 Joules 10 Joules

Experimental Tests

Ball Diameter

Ball Mass

63.5 mm

1045 grams

63.5 mm

1045 grams

63.5 mm

1045 grams

63.5 mm

1045 grams

Finite Element Tests

Ball Diameter

Ball Mass

63.5 mm

1045 grams

63.5 mm

1045 grams

Ball Diameter

Ball Mass

69.8 mm

1390 grams

69.8 mm

1390 grams


Table 2. Fast Fourier Transforms of finite element and experimental displacement data at center, 1045 gram ball.

Computational Model (Hz) Experimental Model (Hz)

Resonance Peak 3 Joules

1 9.89 9.57

2 − 14.85

3 21.36 22.92

4 32.53 36.25

Resonance Peak 5 Joules

1 7.7 9.25

2 − 15.18

3 22.29 22.90


Figure 1. GelMan surrogate thoracic model.

Figure 2. Tissue simulant block specimen.


Figure 3. Impact test setup and finite element model.

Figure 4. Uniaxial and plane strain compression tests for hyperelastic constitutive model.

Steel Sphere

Simulant Block Tissue

Accelerometer

y

x

z

- - - - - -


Figure 5. Experimental displacement at center of the specimen for 2, 3, 5 and 10 Joules, 1045 gram ball impacts.

Figure 6a. Displacement at center of the specimen for 3 Joule, 1045 grams ball impact.


Figure 6b. Displacement at center of the specimen for 5 Joule, 1045 grams ball impact.

Figure 7a and 7b. Finite element displacements for the 5 Joules, 1045 and 1390 gram ball impacts at (a) center and (b) 51 mm from impact surface.

Figure 7a Figure 7b


Figure 8a. Pressure contour for 10 Joule, 1390 gram ball drop, time = 0.027 sec.

Figure 8b. Pressure contour for 10 Joule, 1390 gram ball drop, time = 0.066 sec.


Figure 8c. Pressure contour for 10 Joule, 1390 gram ball drop, time = 0.076 sec.

Figure 8d. Pressure contour for 10 Joule, 1390 gram ball drop, time = 0.081 sec.

finite element modeling of the impact loading on … · the impact dynamics of the human tissue...

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