This book gathers papers presented at the international workshop PMSDAM'19. The respective contributions offer valuable insights for researchers working on numerical solutions to advanced materials problems. The problems concerning the remineralization of teeth are considered. Of particular interest are articles exploring topics at the interface of different disciplines.

Gathers papers from the international workshop PMSDAM'19 Includes articles on the remineralization of teeth Presents numerical solutions for advanced materials problems

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Prof. Dr.Sci. Sergei M. Aizikovich received his Ph.D. degree in Physics and Maths from Rostov State University, Rostov-on-Don, Russia, in 1980. He was in the Vorovich Research Institute of Mechanics and Applied Mathematics, South Federal University (former Rostov State University), Rostov-on-Don, Russia, where he started as a junior researcher and finally he was the head of Contact Interactions Lab. Since 2010, he is the head of Functionally Graded and Composite Materials Lab, a professor and a leading researcher at the Don State Technical University, Rostov-on-Don, Russia. Prof. Aizikovich has coauthored more than 150 scientific papers. He has published 3 monographs. Scientific interests of Prof. Aizikovich are contact problems for functionally graded coating-substrate system; analytical methods in contact and wear problems for functionally graded materials; determination of mechanical properties of the coating-substrate systems; and cracks in functionally gradedmaterials, plates and shells based on graded foundations. In 2016, he had an honor to receive the Professor of the Year Award of Russian Professors Society. He has been the principal investigator of projects with the focus on numerical-analytical methods of calculating efficiency and reliability of welded joints under simultaneous thermal and mechanical impact, taking into account inhomogeneities and defects, mechanics of functionally graded coatings, elastic contact with and without friction, development of effective numerical-analytical methods for solution of the mode I crack problem in a functionally graded material, when its elastic properties arbitrarily vary and asymmetric with respect to the crack..

Prof. Dr.-Ing. habil. Dr. h.c. mult. Holm Altenbach is a member of the International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), Italy, and International Association of Applied Mathematics and Mechanics (GAMM). In 1996, he was appointed as a full professor (Engineering Mechanics) at the Martin Luther University Halle-Wittenberg, and since 2011, he has been a full professor at the Otto von Guericke University Magdeburg. He graduated from Leningrad Polytechnic Institute in 1980 (diploma with a distinction), defended his Ph.D. and obtained his postgraduate degree (habilitation) from the same university in 1983 and 1987, respectively. His areas of scientific interest are theory of plates and shells with applications, continuum mechanics and material modeling, generalized media, sandwiches and laminates. He is an Editor-in-Chief of the Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik (the oldest journal in mechanics in Germany) and of Springer's Advanced Structured Materials series. He is a member of the editorial board of several journals: among them Continuum Mechanics and Thermodynamics, Technische Mechanik, Mechanics of Composite Materials, and Journal of Strain Analysis for Engineering Design. He was awarded the Polish Humboldt Prize in 2018. In November 2019, he was elected as a Foreign Member of the Russian Academy of Sciences.

Prof. Dr. hab. Victor Eremeyev is a member of American Mathematical Society; the International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), Italy; and Polish Society of Theoretical and Applied Mechanics. Employment history includes positions at Rostov State University/South Federal University, Don State Technical University, and Southern Scientific Center of Russian Academy of Science, Rostov on Don, at Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia; at Martin Luther University Halle-Wittenberg and Otto von Guericke University Magdeburg, Germany; at Rzeszow University of Technology, Rzeszów; and Gdäsk University of Technology, Gdäsk, Poland. He is graduated from Rostov State University at 1985 (diploma in Mechanics with a distinction). He defended Ph.D. at Rostov State University in 1990 (title: The stability of two-phase nonlinear thermo-elastic bodies). Dr.hab was awarded Doctor of science in Physics & Mathematics in 2004 at Institute of Problems of Mechanical Engineering of Russian Academy of Science, Saint Petersburg, Russia (title: Mechanics of two-phase bodies with microstructure under finite deformations). His areas of interest are theory of plates and shells with applications, continuum mechanics, generalized media, nonlinear elasticity and nano- and micromechanics:

He is the author/editor of 13 books written in Russian/English/Spanish, author/co-author of ca. 150 scientific peer-reviewed papers indexed by Scopus/Web of Science. He is a member of editorial board of the following journals: Journal of Applied Mathematics and Mechanics (ZAMM); Mathematics and Mechanics of Solids; Acta Mechanica; Mathematics and Mechanics of Complex Systems; Technische Mechanik; Nanoscience and Technology: An International Journal; PNRPU Mechanics Bulletin. He was awarded with International Prize "Tullio Levi-Civita" for the Mathematical and Mechanical Sciences - 2018.

Prof. Michael Vincent Swain made a significant contribution to the development and understanding of modern ceramic materials. He developed and showed a close relationship between the study of the properties of the microstructure of partially stabilized zirconia ceramics and ceramic composites. He was one of the pioneers in the development of zirconia ceramics and co-author of the classic work on the theme "Transformation of Hardened Ceramics."

As a lead researcher at CSIRO, Swain and his colleagues developed a nanoindentation test system for the material and its application to the study of the micromechanical properties of the material. He and his colleagues for the first time in this field began to use small indenters with spherical tips. They showed the importance of such indenters for the critical determination of the elastic-plastic behavior of materials. This approach is now implemented in most commercial devices that allow nanoindentation. His recent research is focused on biomaterials, with an emphasis on teeth, bones, dental materials and, most recently, eye tissue. The modeling of stresses in prosthetic structures was studied to understand the consequences of using ceramic structures, choosing the material and their shape. Another area of research was the use of nanoindentation to determine the mechanical properties of teeth and the effect of diseases on their characteristics. Two commercially relevant and highly successful research projects were related to the selection and evaluation of coatings for a heart pump. These pumps and related coatings are clinically tested and approved for international distribution. In addition, a number of patented portable devices were developed with colleagues from the RoyalNorth Shore Hospital in Sydney to quantify the viscoelastic properties of biological tissues, ranging from articular cartilage to skin. Prof. Alexander Galybin obtained his Ph.D. from Moscow State University. He has over 30 years of research experience in the areas of Applied Mathematics and Mechanics of Solids. Prof. Galybin has spent more than 10 years UWA (Western Australia) as a research scientist and more than 5 years as the head of Damage Mechanics Division at WIT…