Study the Impact Behavior of the Prosthetic Lower Limb Lamination Materials Due to Low Velocity Impactor

This work involves three parts , first part is manufacturing different types of laminated below knee prosthetic socket materials with different classical laminated materials used in Baghdad center for prosthetic and orthotic (4perlon layers+2carbon fiber layer+4 perlon layers) , two suggested laminated materials(3perlon layers+2carbon fiber layer+3 perlon layers) and (3perlon layers+1carbon fiber layer+3 perlon layers) ) in order to choose perfect laminated socket . The second part tests (Impact test) the laminated materials specimens used in socket manufacturing in order to get the impact properties for each socket materials groups using an experimental rig designed especially for this purpose. The interface pressure between the residual leg

checked with Dyneema armours and predicted accurately the residual velocity of the Fragment Simulating Projectiles. The model has been completed with a delamination equation taken from Beaumont in order to include the composite characteristics of delamination. Serge,2007. Showed that composite structures are sometimes subjected to impacts in partial penetration or the complete perforation. Tests are conducted to determine the velocity required to achieve complete penetration for a given projectile, and a model is required for data reduction purposes in order to understand the effect of the various parameters and to extrapolate for other test conditions. Here, a systematic approach for developing engineering models for composite structures is presented and the models obtained are used to analyze the experimental results. Mohd,2008. suggested a computational model to analyze the behavior of the composite material that was subjected to the impact load tensile load. A general purposed commercial finite element code was employed to develop the computational model. Fiber glass that reinforced composite, one of the commonly used structural composites, was chosen to be used as the test material. The computational model was constructed 2-D axissymmetric finite elements. Alastair ,2008. described the recent progress on the materials modeling and numerical simulation of the impact and crash response of fiber reinforced composite structures. The work is based on the application of explicit finite element (FE) analysis codes to composite aircraft structures under both low velocity crash and high velocity impact conditions. The detailed results are presented for the crash response of the helicopter subfloor box structures using a strain based damage and failure criterion for fabric reinforced composites. Thibaut,et al. ,2010. concluded that the dynamic fracture in shock-loaded materials is governed by the propagation, reflection ,and interactions of the stress waves. The post-shock analyses of the residual damage observed in samples recovered from laser shock experiments, less destructive than the more conventional techniques, can provide valuable insight into the key aspects of wave propagation prior to fracture, such as the effects of the structural anisotropy, the role of lateral waves associated to edge effects, or the influence of polymorphic phase transformations on the response to the shock loading. The impact literatures and papers are concerned with the impact of the general composite materials .This mean that this paper deals with the impact problem in B-K prosthetic socket is very limited , therefore , this work is devoted to enrich this field of work and also stands as a benchmark for other investigators in the future .

2.EXPERIMENTAL WORK 2.1Material and Laminations
The materials of the B-K prosthetic socket chosen are randomly laminated. This means that the material is Isotropic . In this work, the material needed for socket are laminated using vacuum technique as it is shown in Fig. 1 . Perlon stockinet white, Carbon fiber sheet ,Lamination resin 80:20 polyurethane ,Hardening powder, and Polyvinyalcohol PVA bag are used in the B-K prosthetic socket lamination. All the lamination materials are tested using tensile and bending instruments by manufacturing tensile and bending specimens for each lamination according to ASTM D638 for tensile specimens and ASTM D790 for bending specimens. Three type of lamination materials are used in this work, namely (3Perlon+1 carbon fiber+3Perlon), (3Perlon+ 2 carbon fiber+3Perlon) and (4Perlon+2 carbon fiber+4Perlon) as shown in Table1.

Impact Testing
In this work all below-knee prosthetic socket lamination are tested using low velocity impact instrument ,Nasser, 2011. Fig. 2 shows all parts of this instrument. All impact specimens are with dimension of (50*200)mm*mm and different thickness according to laminations layers to be suitable for the impact instrument requirements . All specimens are tested by a drop-weight low velocity impact tester with different high and different impact energy as it is shown in Table 2.

2.3The Interface Pressure Measurement
The interface pressure between the residual leg and prosthetic socket is measured by using piezoelectric sensor shown in Fig. 3 The pole of the sensor is connected with multi-meter devise to obtain the magnitude of the voltage that resulted from the response of the sensor through the stance phase. The multi-meter and piezoelectric are interface with the computer and recording data as shown in Fig. 4 .The pressure is measured in the region between residual limb and B-K prosthetic socket in four lines (Interior, Lateral ,Posterior and medial).Each line is divided into three parts longitudinally as it is shown in Fig. 5. A male with age of 42 years, height of 164 cm, mass of 67 Kg, and stump length of 13 cm with a right transtibial amputation is chosen to achieve the above mentioned testing procedures. Fig. 6 shows the amputee during IP test.
The program of multi-meter giving maximum and minimum value of voltage with time .This reading can be calibrated to the interface pressure against gait cycle time .

Theoretical Consideration
Process shown in Fig. 2 in order to calculate the deflection, force, impact energy , and absorbed energy. The simulated model can be treated as a beam fixed to a supporting plate which in turn fixed to the base during which the impact ball hits the specimens at the midpoint. It is clear that deflection will result from bending and shear deformation but the beam is impacted by the impact ball with different impact energy .This means that the Castigliano's theorem must be used to estimate the total and dynamics deflection formula for all types of B-K prosthetic socket laminations materials. Table 3. lists the total and dynamics deflections formula for all types of laminations.
The total absorbed energy can be derived according to normal and shear by using the following general formula with the element length of d x. Defor..energy= ] (1) Finally the absorbed energy also resulted due to momentum conversation using the general formula. (2) (3)

NUMERICAL ANALYSIS
The general analysis by using ANSYS has three distinct steps that: o Building the geometry as a model. In this work (below -knee )prosthetic sockets model was drawn by using CAD system (Auto CAD) which was processed according to an default pattern in three dimensions .The dimension was taken from the same B-K socket that done on it measurement of experimental part. The aim of drawing models by AUTOCAD is to use in ANSYS workbench program for modeling, meshing and defining boundary condition such as applied load. The models is illustrated in Fig.  7,this figure shows the FEM meshing model and loading boundary condition in a and b respectively .

Mechanical Properties
The mechanical properties for each sample can be calculated by taking the average value of the mechanical properties ( , σ y E ult , σ and G)according to the tensile and flexural test . The mechanical properties for all laminations are listed in Table.4.

Impact Results
The experimental impact test result can be divided into two groups. The first one is the force behavior of the specimen that includes oscillatory phenomena visible in the force-time trace .The second group is the deflection behavior according to the impact energy shown in Table 2. Fig. 8 shows the force behavior for the first lamination(L1) which consists of three layers of perlon plus one layer of carbon fiber plus three layers of perlon . It is clear that the general behavior is near to the sinusoidal waves . Fig. 8 shows the force behavior of the lamination materials according to three levels of impact energy, which are (8.82,18.12,and 36.12)) J for the impact load of (1)Kg with different impact height of (0.25,0,5 and 1)respectively .The figure shows that the maximum force is recorded at the mass 1 kg with height 1m In the same manner , it can be concluded that the maximum deflection recorded with the specimen subjected to 1kg with 1m height as it is shown in Fig. 9. The impact results for all lamination specimens are listed in Table 5. The above table shows that the best behavior of absorbed energy is recorded for the below knee prosthetic socket which consists of three outer perlon layers plus one central carbon fiber layer plus three inner perlon layers .The ranges of the absorbed energy recorded for this lamination were between (74.8-89.40% ) for all levels of the impact mass and height. While the second lamination which consists of(3perlon layer+2carbon fiber layers+3perlon layers)has the range of absorbed energy of(67.9-80)%. The third lamination which consists of(4perlon layer+2carbon fiber layers+4perlon layers)recorded the range of absorbed energy of(60.9-68.3)%.

Interface Pressure Results
The interface pressures results shows that the maximum value is recorded at socket interior region exactly at patella tendon with 202.6Kpa as it is shown in Fig. 10 which shows the general IP behavior against gait cycle time during which two peaks are recorded at loading response , and toe off of gait cycle and small reduced will be noticeable at midstance of gait cycle. This behavior is the same for all measuring regions during which other maximum values IP are recorded at ( popliteal depression, lateral tibia, medial gastrocnemius , and distal gastrocnemius) with values of (186.6,92.71,65.87, and 54.32) respectively as shown in Table 6 .

87
According to the loading boundary condition for the belowknee prosthetic socket of the testing amputee the Von -Mises stresses are shown in Fig. 11 which shows that the stress distribution is a mirror of interface pressure distribution shown in Fig. 7 and Table 6 . The Von-Mises stresses results shows that the maximum value is recorded at socket 5 interior region exactly at patella tendon with 0.8155 Mpa,while the values of stresses are recorded at ( popliteal depression, lateral tibia, medial gastrocnemius and distal gastrocnemius) with values of (0.7212,0.5445,0.3954, and 0.2943) Mpa respectively . Fig. 12 shows the stress distribution according to the interface pressure boundary condition and impact with impactor of 1 Kg of mass from 1 m height at the mid distance of socket interior length .It is clear that the values of stresses jump to the maximum value of 16.2 Mpa at impact contact point at center of anterior wall of prosthetic socket . Table 7 shows all cases of the numerical solution for both inteterface pressure boundary condition and impact with different impact mass and impact height for all type of lamination .

CONCLUSION
1-The Maximum absorbed energy percent is recorded with B-K prosthetic socket lamination which consist of (3perlon +1 carbon fiber+3perlon) layers with 89.4%. 2-The maximum value of the interface pressure is recorded at socket interior region exactly at patella tendon with 202.6Kpa 3-The maximum value of the Von-Mises stress due to interface pressure boundary condition is recorded at B-K prosthetic socket at the interior region exactly at patella tendon with 0.8155 Mpa. 4-The maximum value of the Von-Mises stress due to interface pressure and impact boundary condition is recorded at B-K prosthetic socket lamination which consists of (3perlon +1 carbon fiber+3perlon) layers at the region of the impact contact in the center of anterior socket wall with 16.2 Mpa a0.8155 Mpa. 5-All types of B-K prosthetic socket lamination are safety used . 6-The suggested lamination which consists of (3perlon +1 carbon fiber+3perlon) is the best to be used due to its safety and because it reduces the cost and weight of the prosthetic socket.