<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Actual problems in dentistry</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Actual problems in dentistry</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Проблемы стоматологии</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="print">2077-7566</issn>
   <issn publication-format="online">2412-9461</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">6aa3f717f4b844e68d520e32</article-id>
   <article-id pub-id-type="doi">10.18481/2077-7566-2026-22-3-192-201</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>СТОМАТОЛОГИЯ ДЕТСКОГО ВОЗРАСТА, ПРОФИЛАКТИКА И ОРТОДОНТИЯ. ОРИГИНАЛЬНЫЕ ИССЛЕДОВАНИЯ</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>PEDIATRIC DENTISTRY, PROPHYLAXIS AND ORTHODONTICS. ORIGINAL RESEARCH PAPERS</subject>
    </subj-group>
    <subj-group>
     <subject>СТОМАТОЛОГИЯ ДЕТСКОГО ВОЗРАСТА, ПРОФИЛАКТИКА И ОРТОДОНТИЯ. ОРИГИНАЛЬНЫЕ ИССЛЕДОВАНИЯ</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">EXPERIMENTAL DETERMINATION OF THE MECHANICAL PROPERTIES OF MATERIALS USED FOR THE FABRICATION OF ORTHODONTIC ALIGNERS</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>ЭКСПЕРИМЕНТАЛЬНОЕ ОПРЕДЕЛЕНИЕ МЕХАНИЧЕСКИХ ХАРАКТЕРИСТИК КОНСТРУКЦИОННЫХ МАТЕРИАЛОВ ДЛЯ ИЗГОТОВЛЕНИЯ ОРТОДОНТИЧЕСКИХ ЭЛАЙНЕРОВ</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Московец</surname>
       <given-names>Оксана Олеговна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Moskovets</surname>
       <given-names>Oksana O.</given-names>
      </name>
     </name-alternatives>
     <email>om.stomat@gmail.com</email>
     <bio xml:lang="ru">
      <p>кандидат медицинских наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of medical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Иванова</surname>
       <given-names>Анастасия Вадимовна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Ivanova</surname>
       <given-names>Anastasia V.</given-names>
      </name>
     </name-alternatives>
     <email>anastasiaivanova.ortho@gmail.com</email>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7415-5513</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Игнатьев</surname>
       <given-names>Семен Дмитриевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Ignatyev</surname>
       <given-names>Semen Dmitrievich</given-names>
      </name>
     </name-alternatives>
     <email>ignatyev.s.11@gmail.com</email>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Апресян</surname>
       <given-names>Самвел Владиславович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Apresyan</surname>
       <given-names>Samvel S.</given-names>
      </name>
     </name-alternatives>
     <email>apresyan@rudn.ru</email>
     <bio xml:lang="ru">
      <p>доктор медицинских наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of medical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Степанов</surname>
       <given-names>Александр Геннадьевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Stepanov</surname>
       <given-names>Alexander G.</given-names>
      </name>
     </name-alternatives>
     <email>stepanovmd@list.ru</email>
     <bio xml:lang="ru">
      <p>доктор медицинских наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of medical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-5"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Статник</surname>
       <given-names>Евгений Сергеевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Statnik</surname>
       <given-names>Evgeny S.</given-names>
      </name>
     </name-alternatives>
     <email>eugene.statnik@skoltech.ru</email>
     <bio xml:lang="ru">
      <p>PhD технических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>PhD of technical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-6"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Дун</surname>
       <given-names>Артем </given-names>
      </name>
      <name xml:lang="en">
       <surname>Dun</surname>
       <given-names>Artem </given-names>
      </name>
     </name-alternatives>
     <email>dun.artem@inbox.ru</email>
     <xref ref-type="aff" rid="aff-7"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Апресян</surname>
       <given-names>Карина Сергеевна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Apresyan</surname>
       <given-names>Karina S.</given-names>
      </name>
     </name-alternatives>
     <email>apresyanks@mail.ru</email>
     <xref ref-type="aff" rid="aff-8"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Российский университет дружбы народов</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Peoples' Friendship University of Russia</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Российский университет дружбы народов имени Патриса Лумумбы</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Peoples' Friendship University of Russia named after Patrice Lumumba</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">ФБУН ФНЦГ им. Ф.Ф. Эрисмана Роспотребнадзора</institution>
     <city xml:lang="ru">Мытищи</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">F.F. Erisman FSCH of Rospotrebnadzor</institution>
     <city xml:lang="en">Mytishchi</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Российский университет дружбы народов имени Патриса Лумумбы</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Peoples' Friendship University of Russia named after Patrice Lumumba</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-5">
    <aff>
     <institution xml:lang="ru">Российского университета дружбы народов имени Патриса Лумумбы</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Peoples' Friendship University of Russia named after Patrice Lumumba</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-6">
    <aff>
     <institution xml:lang="ru">Сколковский институт науки и технологий</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Skolkovo Institute of Science and Technology</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-7">
    <aff>
     <institution xml:lang="ru">Московский авиационный институт</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Moscow Aviation Institute</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-8">
    <aff>
     <institution xml:lang="ru">Российский университет дружбы народов имени Патриса Лумумбы</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Peoples' Friendship University of Russia named after Patrice Lumumba</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-09-23T23:06:12+03:00">
    <day>23</day>
    <month>09</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-09-23T23:06:12+03:00">
    <day>23</day>
    <month>09</month>
    <year>2026</year>
   </pub-date>
   <volume>22</volume>
   <issue>3</issue>
   <fpage>192</fpage>
   <lpage>201</lpage>
   <history>
    <date date-type="received" iso-8601-date="2026-09-11T00:00:00+03:00">
     <day>11</day>
     <month>09</month>
     <year>2026</year>
    </date>
   </history>
   <permissions>
    <copyright-statement xml:lang="ru">© 2026 Московец О.О., Иванова А.В., Игнатьев С.Д., Апресян С.В., Степанов А.Г., Статник Е.С., Дун А., Апресян К.С. Все права защищены.</copyright-statement>
    <copyright-statement xml:lang="en">© 2026 Moskovets O.O., Ivanova A.V., Ignatyev S.D., Apresyan S.S., Stepanov A.G., Statnik E.S., Dun A., Apresyan K.S. All rights reserved.</copyright-statement>
    <copyright-year>2026</copyright-year>
    <copyright-holder xml:lang="ru">Московец Оксана Олеговна, Иванова Анастасия Вадимовна, Игнатьев Семен Дмитриевич, Апресян Самвел Владиславович, Степанов Александр Геннадьевич, Статник Евгений Сергеевич, Дун Артем, Апресян Карина Сергеевна</copyright-holder>
    <copyright-holder xml:lang="en">Moskovets Oksana O., Ivanova Anastasia V., Ignatyev Semen Dmitrievich, Apresyan Samvel S., Stepanov Alexander G., Statnik Evgeny S., Dun Artem, Apresyan Karina S.</copyright-holder>
   </permissions>
   <self-uri xlink:href="https://dental-press.ru/en/nauka/publications/6aa3f717f4b844e68d520e32/view">https://dental-press.ru/en/nauka/publications/6aa3f717f4b844e68d520e32/view</self-uri>
   <abstract xml:lang="ru">
    <p>Актуальность. Клиническая эффективность ортодонтических элайнеров во многом определяется механическими свойствами конструкционного полимера, от которых зависят жесткость каппы, характер ее деформации и величина передаваемых на зубы сил. Использование усредненных характеристик материалов при конечно-элементном моделировании может снижать достоверность расчетов, поскольку коммерческие полимеры различаются составом, слоистостью и термомеханическим поведением. &#13;
Цель исследования. Определить и сопоставить механические характеристики материалов для изготовления ортодонтических элайнеров и сформировать экспериментальную базу для последующего конечно-элементного анализа. &#13;
Материалы и методы. Проведено сравнительное исследование 60 образцов шести материалов: Ustom, Avantis, Aligners, 3A Medes, StarSmile однослойный и StarSmile трехслойный, по 10 образцов в каждой группе. После вакуумного термоформования выполняли испытания на одноосное растяжение на универсальной разрывной машине при скорости нагружения 2 мм/мин и преднагрузке около 10 Н. Локальные деформации оценивали методом цифровой корреляции изображений с обработкой данных в программе Ncorr. Статистический анализ включал однофакторный дисперсионный анализ, тест Левена и апостериорный тест Games-Howell. &#13;
Результаты. Максимальные значения модуля Юнга и предела прочности выявлены у Ustom – 1177,73 и 35,98 МПа соответственно. Минимальный модуль Юнга установлен у трехслойного StarSmile – 261,87 МПа; этот материал также характеризовался наибольшей деформацией при достижении предела прочности – 10,72 %. Минимальные значения прочности зарегистрированы у трехслойного StarSmile и Avantis. Тип материала статистически значимо влиял на модуль Юнга и предел прочности (p &lt; 0,001). &#13;
Заключение. Состав и многослойность материала существенно определяют его механический ответ. Полученные значения следует использовать как специфические для каждого материала параметры при построении конечно-элементной модели системы «элайнер – зуб – периодонтальная связка – альвеолярная кость».</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Relevance. The clinical effectiveness of orthodontic aligners is largely determined by the mechanical properties of the polymer material, which influence aligner stiffness, deformation behavior, and the magnitude of forces transmitted to the teeth. The use of averaged material properties in finite element modeling may reduce the accuracy of calculations, since commercially available polymers differ in their composition, layered structure, and thermomechanical behavior.&#13;
Objective. To determine and compare the mechanical properties of materials used for the fabrication of orthodontic aligners and to establish an experimental database for subsequent finite element analysis.&#13;
Materials and Methods. A comparative study was performed on 60 specimens of six materials: Ustom, Avantis, Aligners, 3A Medes, single-layer StarSmile, and three-layer StarSmile, with 10 specimens in each group. Following vacuum thermoforming, uniaxial tensile testing was carried out using a universal testing machine at a crosshead speed of 2 mm/min and a preload of approximately 10 N. Local strains were assessed using digital image correlation, with data processed in Ncorr software. Statistical analysis included one-way analysis of variance, Levene’s test, and the Games–Howell post hoc test.&#13;
Results. The highest Young’s modulus and ultimate tensile strength were recorded for Ustom, at 1,177.73 MPa and 35.98 MPa, respectively. The lowest Young’s modulus was observed for three-layer StarSmile at 261.87 MPa. This material also demonstrated the highest strain at ultimate tensile strength, reaching 10.72 %. The lowest strength values were recorded for three-layer StarSmile and Avantis. Material type had a statistically significant effect on both Young’s modulus and ultimate tensile strength (p &lt; 0.001).&#13;
Conclusion. Material composition and multilayer structure substantially influence the mechanical response of orthodontic aligner materials. The obtained values should be used as material-specific input parameters when developing a finite element model of the “aligner–tooth–periodontal ligament–alveolar bone” system.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>ортодонтические элайнеры</kwd>
    <kwd>полимерные материалы</kwd>
    <kwd>модуль Юнга</kwd>
    <kwd>предел прочности</kwd>
    <kwd>коэффициент Пуассона</kwd>
    <kwd>цифровая корреляция изображений</kwd>
    <kwd>метод конечных элементов</kwd>
    <kwd>математическое моделирование</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>orthodontic aligners</kwd>
    <kwd>polymeric materials</kwd>
    <kwd>Young’s modulus</kwd>
    <kwd>ultimate tensile strength</kwd>
    <kwd>Poisson’s ratio</kwd>
    <kwd>digital image correlation</kwd>
    <kwd>finite element method</kwd>
    <kwd>mathematical modeling</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">Статья подготовлена в рамках выполнения государственного задания Министерства науки и высшего образования Российской Федерации (FSSF-2026-0012).</funding-statement>
    <funding-statement xml:lang="en">This article was prepared as part of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (FSSF-2026-0012).</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Inoue S., Yamaguchi S., Uyama H., Yamashiro T., Imazato S. Influence of constant strain on the elasticity of thermoplastic orthodontic materials. Dental Materials Journal. 2020;39(3):415-421. https://doi.org/10.4012/dmj.2019-104</mixed-citation>
     <mixed-citation xml:lang="en">Inoue S., Yamaguchi S., Uyama H., Yamashiro T., Imazato S. Influence of constant strain on the elasticity of thermoplastic orthodontic materials. Dental Materials Journal. 2020;39(3):415-421. https://doi.org/10.4012/dmj.2019-104</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Cenzato N., Di Iasio G., Martín Carreras-Presas C., Caprioglio A., Del Fabbro M. Materials for Clear Aligners - A Comprehensive Exploration of Characteristics and Innovations: A Scoping Review. Applied Sciences. 2024;14(15):6533. https://doi.org/10.3390/app14156533</mixed-citation>
     <mixed-citation xml:lang="en">Cenzato N., Di Iasio G., Martín Carreras-Presas C., Caprioglio A., Del Fabbro M. Materials for Clear Aligners - A Comprehensive Exploration of Characteristics and Innovations: A Scoping Review. Applied Sciences. 2024;14(15):6533. https://doi.org/10.3390/app14156533</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Delgado J.I., Kehyaian P., Fernández-Blázquez J.P. Thermoplastics for Clear Aligners: A Review. Polymers. 2025;17(12):1681. https://doi.org/10.3390/polym17121681</mixed-citation>
     <mixed-citation xml:lang="en">Delgado J.I., Kehyaian P., Fernández-Blázquez J.P. Thermoplastics for Clear Aligners: A Review. Polymers. 2025;17(12):1681. https://doi.org/10.3390/polym17121681</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Singh J.R., Kambalyal P., Jain M., Khandelwal P. Revolution in Orthodontics: Finite element analysis. Journal of International Society of Preventive and Community Dentistry. 2016;6(2):110-114. https://doi.org/10.4103/2231-0762.178743</mixed-citation>
     <mixed-citation xml:lang="en">Singh J.R., Kambalyal P., Jain M., Khandelwal P. Revolution in Orthodontics: Finite element analysis. Journal of International Society of Preventive and Community Dentistry. 2016;6(2):110-114. https://doi.org/10.4103/2231-0762.178743</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kawamura J., Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics. Progress in Orthodontics. 2019;20(1):3. https://doi.org/10.1186/s40510-018-0255-8</mixed-citation>
     <mixed-citation xml:lang="en">Kawamura J., Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics. Progress in Orthodontics. 2019;20(1):3. https://doi.org/10.1186/s40510-018-0255-8</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chen J., Zhu D., Zhao M., Cheng Z., Pan Y., Liu X. Three-dimensional finite element analysis of the optimal mechanical design for maximum inward movement of the anterior teeth with clear aligners. Scientific Reports. 2024;14:13203. https://doi.org/10.1038/s41598-024-63907-x</mixed-citation>
     <mixed-citation xml:lang="en">Chen J., Zhu D., Zhao M., Cheng Z., Pan Y., Liu X. Three-dimensional finite element analysis of the optimal mechanical design for maximum inward movement of the anterior teeth with clear aligners. Scientific Reports. 2024;14:13203. https://doi.org/10.1038/s41598-024-63907-x</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gao H., Luo L., Liu J. Three-dimensional finite element analysis of maxillary molar distalization treated with clear aligners combined with different traction methods. Progress in Orthodontics. 2024;25(1):47. https://doi.org/10.1186/s40510-024-00546-y</mixed-citation>
     <mixed-citation xml:lang="en">Gao H., Luo L., Liu J. Three-dimensional finite element analysis of maxillary molar distalization treated with clear aligners combined with different traction methods. Progress in Orthodontics. 2024;25(1):47. https://doi.org/10.1186/s40510-024-00546-y</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Tarraf N.E., Darendeliler M.A. Present and the future of digital orthodontics. Seminars in Orthodontics. 2018;24(4):376-385. https://doi.org/10.1053/j.sodo.2018.10.002</mixed-citation>
     <mixed-citation xml:lang="en">Tarraf N.E., Darendeliler M.A. Present and the future of digital orthodontics. Seminars in Orthodontics. 2018;24(4):376-385. https://doi.org/10.1053/j.sodo.2018.10.002</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lahoud P., Faghihian H., Richert R., Jacobs R., EzEldeen M. Finite element models: A road to in-silico modeling in the age of personalized dentistry. Journal of Dentistry. 2024;150:105348. https://doi.org/10.1016/j.jdent.2024.105348</mixed-citation>
     <mixed-citation xml:lang="en">Lahoud P., Faghihian H., Richert R., Jacobs R., EzEldeen M. Finite element models: A road to in-silico modeling in the age of personalized dentistry. Journal of Dentistry. 2024;150:105348. https://doi.org/10.1016/j.jdent.2024.105348</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lee H., Kim K., Choi Y.-K., Kim S.-H., Kim Y.-I., Kim S.-S. Iterative Finite Element Analysis of Buccolingual Width on Canine Distal Movement in Clear Aligner Treatment. Applied Sciences. 2025; 15(12):6946. https://doi.org/10.3390/app15126946</mixed-citation>
     <mixed-citation xml:lang="en">Lee H., Kim K., Choi Y.-K., Kim S.-H., Kim Y.-I., Kim S.-S. Iterative Finite Element Analysis of Buccolingual Width on Canine Distal Movement in Clear Aligner Treatment. Applied Sciences. 2025; 15(12):6946. https://doi.org/10.3390/app15126946</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Elshazly T.M., Bourauel C., Ismail A., Ghoraba O., Aldesoki M., Salvatori D. et al. Effect of material composition and thickness of orthodontic aligners on the transmission and distribution of forces: an in vitro study. Clinical oral investigations. 2024;28(5):258. https://doi.org/10.1007/s00784-024-05662-x</mixed-citation>
     <mixed-citation xml:lang="en">Elshazly T.M., Bourauel C., Ismail A., Ghoraba O., Aldesoki M., Salvatori D. et al. Effect of material composition and thickness of orthodontic aligners on the transmission and distribution of forces: an in vitro study. Clinical oral investigations. 2024;28(5):258. https://doi.org/10.1007/s00784-024-05662-x</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Bunta O., Festila D., Muresan V., Coloși T., Stan O.P., Unguresan M.L. et al. Mathematical Modeling and Digital Simulation of Teeth Dynamics for the Approximation of Orthodontic Treatment Duration. Applied Sciences. 2023;13(10):5932. https://doi.org/10.3390/app13105932</mixed-citation>
     <mixed-citation xml:lang="en">Bunta O., Festila D., Muresan V., Coloși T., Stan O.P., Unguresan M.L. et al. Mathematical Modeling and Digital Simulation of Teeth Dynamics for the Approximation of Orthodontic Treatment Duration. Applied Sciences. 2023;13(10):5932. https://doi.org/10.3390/app13105932</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Merema B.B.J., Kraeima J., Glas H.H., Spijkervet F.K.L., Witjes M.J.H. Patient-specific finite element models of the human mandible: Lack of consensus on current set-ups. Oral Diseases. 2021;27(1):42-51. https://doi.org/10.1111/odi.13381</mixed-citation>
     <mixed-citation xml:lang="en">Merema B.B.J., Kraeima J., Glas H.H., Spijkervet F.K.L., Witjes M.J.H. Patient-specific finite element models of the human mandible: Lack of consensus on current set-ups. Oral Diseases. 2021;27(1):42-51. https://doi.org/10.1111/odi.13381</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Xue J., Ye N., Yang X., Wang S., Wang J., Wang Y. et al. Finite element analysis of rapid canine retraction through reducing resistance and distraction. Journal of Applied Oral Science. 2014;22(1):52-60. https://doi.org/10.1590/1678-775720130365</mixed-citation>
     <mixed-citation xml:lang="en">Xue J., Ye N., Yang X., Wang S., Wang J., Wang Y. et al. Finite element analysis of rapid canine retraction through reducing resistance and distraction. Journal of Applied Oral Science. 2014;22(1):52-60. https://doi.org/10.1590/1678-775720130365</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Blaber J., Adair B., Antoniou A. Ncorr: Open-Source 2D Digital Image Correlation Matlab Software. Experimental Mechanics. 2015;55(6):1105-1122. https://doi.org/10.1007/s11340-015-0009-1</mixed-citation>
     <mixed-citation xml:lang="en">Blaber J., Adair B., Antoniou A. Ncorr: Open-Source 2D Digital Image Correlation Matlab Software. Experimental Mechanics. 2015;55(6):1105-1122. https://doi.org/10.1007/s11340-015-0009-1</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
