تجزیه و تحلیل المان محدود برای ارزیابی رفتار ساختاری، پروتز برای جانبازان انتقال درشت نی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|28734||2012||8 صفحه PDF||سفارش دهید||5540 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Medical Engineering & Physics, Volume 34, Issue 1, January 2012, Pages 38–45
The finite element analysis (FEA) has been identified as a useful tool for the stress and strain behaviour determination in lower limb prosthetics. The residual limb and prosthetic socket interface was the main subject of interest in previous studies. This paper focuses on the finite element analysis for the evaluation of structural behaviour of the Sure-flex™ prosthetic foot and other load-bearing components. A prosthetic socket was not included in the FEA. An approach for the finite element modelling including foot analysis, reverse engineering and material property testing was used. The foot analysis incorporated ground reaction forces measurement, motion analysis and strain gauge analysis. For the material model determination, non-destructive laboratory testing and its FE simulation was used. A new, realistic way of load application is presented along with a detailed investigation of stress distribution in the load-bearing components of the prosthesis. A novel approach for numerical and experimental agreement determination was introduced. This showed differences in the strain on the pylon between the experimental and the numerical model within 30% for the anteroposterior bending and up to 25% for the compression. The highest von Mises stresses were found on the foot–pylon connecting component at toe off. Peak stress of 216 MPa occurred on the posterior adjusting screw and maximum stress of 156 MPa was found at the neck of the male pyramid.
The lower-limb prosthesis has come a long way from the days of primitive wooden peg legs to present day electronically controlled prostheses, especially in the last decade, with advancements in anatomy, physiology, material design, computer technology etc. evident in new approaches in prosthetic sockets design, modern prosthetic knee mechanisms, more functional prosthetic feet and advanced manufacturing techniques. As well as an increase in patients’ expectations, more and more requirements are placed on the prosthesis, above all on its functionality, reliability and safety. The prosthesis, in conjunction with an amputee, presents a complex biomechanical system, whose behaviour is influenced by a few factors. In term of the prosthesis, the major factors are prosthesis alignment , , ,  and , the mechanical properties and alignment of the prosthetic foot  and , the length of the prosthesis  and  and the weight of the prosthetic components . For the evaluation of prosthetic walking performance, a gait analysis is widely used . Most studies reported in the literature have focused on the assessments of gait kinematics , ,  and , plantar foot pressure  and  and contact interface between the residual limb and the prosthetic socket  and . A study of the behaviour of the prosthesis is crucial in the phase of prosthetic component design and of prosthetic alignment. In connection with the development of modern computational techniques, besides experimental methods, numerical methods have also been increasingly used, especially in the cases where it is necessary to obtain detailed and complex information about the behaviour of the prosthesis or about the interaction between an amputee and the prosthesis. The finite element analysis (FEA) is the most widely used numerical analysis method in lower-limb prosthetics . By means of the FEA, stress and strain distribution in the whole prosthesis can be determined, which is experimentally or analytically difficult. FEA can be used for parametric analysis such as the study of design, material or alignment parameters effect, whereas the prototype or specimen need not be fabricated in contrary to the experimental analysis. Over the past three decades, FEA has been used to study the interaction between the prosthetic socket and the residual limb. The main goal of these papers was to determine how the socket acts on the residual limb. The stress and the pressure distribution in soft tissues over the residual limb at critical phases of the gait cycle were usually obtained. These papers studied the effects of socket and residual limb geometry , the material properties of the socket and liners ,  and  and the frictional properties at the interface between the limb and socket  with the aim of contributing to the improvement of socket design. The previous FEA models were simplified significantly in terms of geometry, material and boundary conditions . Recently published studies have presented more accurate models including complex geometry models, non-linear material models, interface elements enabling slip-friction conditions , automated contact method used in the interface , pre-stresses applied on the limb  and the effect of inertial loads . In spite of many papers dealing with the FE modelling of socket–limb interaction, only a few have been published about the use of this technique for the study of the behaviour of other lower-limb prosthetic components, especially dealing with prosthetic feet. In Ref. , a FE model of the SACH foot was created and then used to address the effect of viscoelastic heel performance as an example of parametric analysis. Another work dealt with the FE modelling and experimental validation of a prosthetic foot to improve footwear testing by computational tests . Papers describing the behaviour of the whole prosthesis have not been published yet. Some approaches can be found in studies analyzing the monolimb, which is a kind of trans-tibial prosthesis having a socket and a shank moulded into one piece of thermoplastic material. In this work, the structural behaviour of the monolimb for different shank designs and stress distribution at the socket–limb interface were studied . In the later works of the same authors, the monolimb was optimized by FE parametric analysis of design factors , fatigue life was evaluated based on FEA  and experimental fatigue tests were conducted . Previous papers introduced a multidisciplinary approach to FE modelling of lower-limb prosthesis, incorporating gait analysis, reverse engineering, material property testing and structural testing. In the cases where the prosthetic foot was included, ground reaction force (GRF) was found suitable for straight load definition in the FEA. However, in the reported works, it was applied directly to prosthetic foot nodes or on surfaces in spite of a significant geometrical non-linearity of the prosthetic foot–ground interface  and . This fact was reported as the most likely source of error, and incorporation of the prosthetic foot–ground contact and friction elements into the FE model was discussed as possible future work in Ref. . Thus this study was focused on further development of an approach applicable to the trans-tibial prosthesis design and inspection, with the aim to improve the FE boundary conditions and to investigate the stress distribution in load-bearing components of the prosthesis in detail and a new approach to numerical and experimental agreement determination was introduced.
نتیجه گیری انگلیسی
The multidisciplinary approach presented in this paper was found to be suitable for the evaluation of the stress–strain behaviour of the prosthetic foot and other load-bearing components. Foot analysis has provided information on load and geometric configuration and the results were in accordance with previous studies’ data. For the numerical model verification, foot analysis also included measurement of strain acting on the pylon using strain gauges. This technique could be useful for the evaluation of prosthetic loading during the various walking modes. For the material model determination an approach incorporating non-destructive laboratory testing and FEA simulation was used. All the materials were modeled as linearly elastic, isotropic and homogenous. In reality, the carbon composite material used is orthotropic and non-linear in general. Nevertheless in the over-ball bend test of the composite toe spring, which simulates the real loading character, the material showed nearly linear behaviour. The dominant uniaxial bending load of the prosthetic foot toe and heel springs allows us to use the isotropic material model with Young's modulus given in the test. Another factor to be considered is the possibility of a time-dependent response of the material, such as viscoelasticity. The loading rate of 5 mms−1 was used at the mechanical test, which is much less than the real walking. There was found no difference of response for various loading rates up to loading rate of 10 mms−1, which is the limiting value of the test machine. For further examination, it is appropriate to use an impact test of the foot. The force-deflection results of the laboratory test and the FEA simulation of the whole foot shows excellent agreement. However, different values of Young's modulus at heel strike and toe off tests were stated. In fact this could be explained by the non-linear behaviour of the PUR foam, especially in areas between the base plate and the heel or toe springs edges where huge strains of foot cover were presented. Thus, the defined material models and their material properties should be rather contemplated as a stiffness characteristic of the foot at given loading conditions. A new model of boundary conditions and a new method of load application was introduced, in an effort to reduce the errors reported in previous studies. However, some discrepancies can be found between the numerical and experimental results (Fig. 9). Good agreement is shown between AP bending and tension strains, but much larger differences are shown between ML bending and torsion strains. There is an instance that has not been discussed yet. During the foot analysis, an amputee wore shoes but in the FEA and in the mechanical tests this fact had not been considered for reasons of difficulties in the FE model of the shoe establishment. The question remains of how much it can affect the results. The presence of a shoe influences the damping capacity of the system. The effect of prosthetic feet and shoes on the GRF at heel-strike in amputee gait was numerically modeled using non-linear viscoelastic foot/shoe properties in Ref. , where it was found that wearing a shoe reduced the loading-response peak of vertical component of the GRF by approximately 4%. It can be treated as negligible at the low walking rate. Some influence of the shoe might also lie in slip between the shoe and the prosthetic foot. Much more important could be the effect of the shoe on load distribution between ground and foot. A shoe can significantly change the position of the centre of GRF. If a lateral or medial shift in the centre of GRF occurs, the normal component of force would also contribute to the bending moment in the frontal plane. Because of the dominant normal component of GRF, even a small movement of its centre can cause a large change in the bending moment. Finally an orientation of the moment could also be altered and could explain large discrepancies in ML bending and torsion strains. At foot flat, there are also large deviations in magnitude and orientation of AP bending strain. The same influence of the shoe to the magnitude of AP bending moment as well as to ML moment with other load conditions could be considered. The absence of the heel of a shoe in the FEA could cause the load mainly to be carried over the forefoot instead of the heel in the flat position. This is consistent with the finding in Ref. , where the influence of shoe heel height on loading for trans-tibial amputees during standing was studied. It was found that with increasing shoe heel heights, the loading line shifted from the anterior to the posterior side of the knee centre, and the peak pressure had moved from the heel region to the medial forefoot region . Because of the flat position of the foot, this loading condition is very sensitive to the location of the centre of GRF; however this loading condition is not very significant in terms of total stress. Another source of error is the neglect of an inertia and gravity effect. In Ref. , equivalent loads at the knee joint during walking were calculated using inverse dynamics with and without a consideration of inertial effect. It was shown that without inertial effect, force in an anterior direction was underestimated up to 19% at heel strike and AP bending moment was underestimate up to 27% at toe off. In the case of vertical force, which is the main component of the GRF, there was obvious difference only in the swing phase . Also an energy dissipation of the energy-storing prosthetic foot was not accounted for in the model, which may cause some differences between the FEA results and the directly measured pylon strains . This approach was found to consistently overestimate an ankle join forces and moments in Ref. . It should be emphasized that in spite of the large differences in some results, experimentally and numerically determined strains show a good agreement in major kinds of loading and are thus suitable for stress evaluation. On foot, peak von Mises stresses were found on the heel spring at heel strike and on the toe spring at toe off. Because of the unknown yield stress of a carbon composite, possible failure was not evaluated. The highest stresses were found on the foot–pylon connecting component at toe off. Overall, the maximum von Mises stress of 216 MPa was determined on the posterior adjusting screw. It is 2.2 times lower than the yield stress of the material. However, the real value could be different because of geometry model simplifications. There was no screw thread included and a flat contact surface with the male pyramid was modeled. Also, the FEA was conducted for the simplified case of parallel male and female pyramid axes. The male pyramid was significantly stressed at its neck. According to failure reports , foot adapters fail most often. A fracture caused by the stress concentration at the neck was found in the male pyramid . This is consistent with our findings. Peak von Mises stress of 156 MPa was found here, which was 2.7 times lower than the yield stress of the material. The presented FE model might be suitable for a parametric analysis of a foot and other load-bearing components in a phase of their design. The study of the effect of design and material parameters is possible. The failure of real components may be caused by unequal tightening of adjusting screws and by large tilt angles. Thus other work possibilities include parametric analysis of the influence of prosthesis adjustment on connecting components peak stress. It will require improvements to the model in this area. Because fatigue failure is the most common form of component failure in lower limb prosthetics, live fatigue analysis of the most stressed components will be performed.