Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties




stress-strain state, cortical tissue, bone fractures, bones osteosynthesis, computational model, fixation plates


Background. Bone osteosynthesis is considered one of the most efficient methods of treating fractures of long tubular bones. Deve­lopment of modern computer technology and specialized software makes it possible for a traumatologist to perform preliminary efficiency estimation of osteosynthesis using fixation plates of various designs. Results of such studies can significantly depend on calculation model parameters. In most papers related to the study of a stress-strain state of “bone–fixator” systems, bone tissue is considered as a homogeneous, isotropic, elastic medium. However, in fact it is heterogeneous and has an anisotropy of mechanical characteristics. Accordingly in a case of using a simplified isotropic model of bone tissue, when performing calculations, there is a possibility of obtaining inaccurate results.

Objective. Estimation of influence of orthotropy of the bone tissue physical and mechanical properties on a stress-strain state of the “bone–fixator” system.

Methods. The study is performed in the software environment based on the finite element method. Osteosynthesis of a low transverse fracture of a fibula using a smooth plate is selected as a computational case. Two computational models simplified in terms of geometry are constructed to solve the problem. These models are different only in properties of cortical bone tissue.

Results. Analysis of a stress state in elements of models indicated that normal stresses reached the highest values, and tangential stresses are relatively small. In addition, the character of stress distribution turned out to be significantly inhomogeneous. However, stress state patterns are qualitatively similar for both computational models. A common feature of the maximum stresses both in the bone and in the plate turned out to be that all the maximum stresses are the result of their concentration.

Conclusions. Consideration of orthotropy of elastic parameters of a bone led to significant quantitative changes in the indicators of a stress state. It is established that the minimum safety margins for both models turned out to be considered by the maximum tensile stresses acting in the vertical direction. A similar result in estimating bone strength also occurs in a case when only elastic orthotropy is considered, but the orthotropy of strength indicators is not considered. If the strength orthotropy is considered for the isotropic model of cortical bone, the pattern changes qualitatively. The normal tensile stress directed along the tangent to a circumference of bone cross-section is considered unsafe. Calculations results indicate a possibility of using an isotropic model of cortical tissue when performing comparative estimations in order to identify the most efficient, in terms of strength, fixation plate designs.


Ankin L. Practical traumatology. Moscow: Kniga Plius; 2002.

Lawson K, Ayala A, Morin M, Latt L, Wild J. Ankle fracture-dislocations: a review. Foot Ankle Orthopaedics. 2018;3(3). DOI: 10.1177/2473011418765122

Buckley RE, Moran CG, Apivatthakakul T, editors. AO principles of fracture management. Volume 1. Principles. 3rd ed. Stuttgart: Thieme; 2017.

Buckley RE, Moran CG, Apivatthakakul T, editors. AO principles of fracture management Volume 2. Specific fractures. 3rd ed. Stuttgart: Thieme; 2017.

Wang YZ, Cai M, Sun LF, Zhu QH, Hou CX, Han W, et al. Preoperative finite element analysis of fibula myocutaneous flap for segmental mandibular reconstruction. China J Oral Maxillofacial Surg. 2021;19(4):325-31. DOI: 10.19438/j.cjoms.2021.04.007

Wang M, Deng Y, Xie P, Tan J, Yang Y, Ouyang H, et al. Optimal design and biomechanical analysis of a biomimetic lightweight design plate for distal tibial fractures: a finite element analysis. Front Bioeng Biotechnol. 2022 Feb 21;10:820921. DOI: 10.3389/fbioe.2022.820921

Cao Y, Zhang Y, Huang L, Huang X. The impact of plate length, fibula integrity and plate placement on tibial shaft fixation stability: a finite element study. J Orthop Surg Res. 2019 Feb 15;14(1):52. DOI: 10.1186/s13018-019-1088-y

Li Y, Yang W, Zhang X, Yu C, Ji Z, Sun J, et al. Finite element simulation of treatment with locking platefor distal fibula fractures. Research Square [Preprint] 2022. DOI: 10.21203/

Karpiński R, Jaworski Ł, Czubacka P. The structural and mechanical properties of the bone. J Technol Exploit Mech Eng. 2017;3(1):43-50. DOI: 10.35784/jteme.538

Lin CY, Kang JH. Mechanical properties of compact bone defined by the stress-strain curve measured using uniaxial tensile test: a concise review and practical guide. Mate-rials (Basel). 2021 Jul 28;14(15):4224. DOI: 10.3390/ma14154224

Petrovici IL, Tenovici MC, Vaduva RC, Tarnita DN, Vintila G, Popa DL. About three-dimensional models of osteosynthesis systems. J Industr Design Eng Graph. 2019;14(1):159-62.

Münch M, Barth T, Studt A, Dehoust J, Seide K, Hartel M, et al. Stresses and deformations of an osteosynthesis plate in a lateral tibia plateau fracture. Biomed Eng. 2022;67(1):43-52. DOI: 10.1515/bmt-2021-0166

Lorkowski J, Pokorski M. In silico finite element modeling of stress distribution in osteosynthesis after pertrochanteric fractures. J Clin Med. 2022 Mar 28;11(7):1885. DOI: 10.3390/jcm11071885

Pahr DH, Reisinger AG. A review on recent advances in the constitutive modeling of bone tissue. Curr Osteoporos Rep. 2020 Dec;18(6):696-704. DOI: 10.1007/s11914-020-00631-1

Obraztsov I. Strength problems in biomechanics. Moscow: Vysshaia Shkola; 1988.

Krasovsky V, Panchenko S, Golovakha M. On the strength of fixation of tibial fragments in high opening corrective osteotomy. In: Theoretical foundations of civil engineering. Vol. 17. Warsaw: Politechnika Warszawska; 2009. p. 165-78.

Panchenko S, Loskutov O, Krasovsky V. Biomechanical substantiation of osteosynthesis of a high fracture of the lateral malleolus. In: Theoretical foundations of civil engi-neering. Vol. 18. Warsaw: Politechnika Warszawska; 2010. p. 251-8.

Krasovsky V, Loskutov A, Postolov O. Methodology and results of the study of deformation and strength properties of the distal tibiofibular syndesmosis. In: Theoretical foundations of civil engineering. Vol. 6. Warsaw: Politechnika Warszawska; 1998. p. 481-8.

Maintz M, Seiler D, Thieringer F, Wild M. Topology-optimized patient-specific osteosynthesis plates: Methodology to semi-automatically design additive-manufactured osteosynthesis plates for the fixation of mandibular fractures. Curr Direct Biomed Eng. 2022;8(2):177-80. DOI: 10.1515/cdbme-2022-1046

Li J, Jiao J, Luo T, Wu W. Biomechanical evaluation of various internal fixation patterns for unilateral mandibular condylar base fractures: A three-dimensional finite element analysis. J Mech Behav Biomed Mater. 2022;133. DOI: 10.1016/j.jmbbm.2022.105354

Panchenko SP, Loskutov O., Krasovsky VL. Stresses and deformations of the "bone-fixator" system of osteosynthesis in low fractures of the lateral malleolus. Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture. 2010;6:13-20.

Loskutov OA, Panchenko SP, Krasovsky VL. Biomechanical substantiation of some variants of minimally invasive osteosynthesis in suprasyndesmotic fractures of the lateral malleolus. Orthopaed Traumatol Prosthet. 2010;3:67-71.

Golovakha ML, Kozhemyaka MA, Panchenko SP. Evaluation of stresses and deformations of the "bone-fixator" system during bone osteosynthesis of fractures of the lateral malleolus. Orthopaed Traumatol Prosthet. 2014;4:14-9.



How to Cite

Panchenko S, Kolosov D, Onyshchenko S, Zub T, Chechel T. Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties. Innov Biosyst Bioeng [Internet]. 2022Nov.2 [cited 2023May30];6(2):75-83. Available from: