TY - CHAP

T1 - Models of Continuum Mechanics and Their Deficiencies.

AU - Хантулева, Татьяна Александровна

N1 - Bibliographic Information • Book Title Mathematical Modeling of Shock-Wave Processes in Condensed Matter • Book Subtitle From Statistical Thermodynamics to Control Theory • Authors Tatiana Aleksandrovna Khantuleva • Series Title Shock Wave and High Pressure Phenomena • DOI https://doi.org/10.1007/978-981-19-2404-0 • Publisher Springer Singapore • eBook Packages Physics and Astronomy, Physics and Astronomy (R0) • Copyright Information The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 • Hardcover ISBN978-981-19-2403-3 • eBook ISBN978-981-19-2404-0 • Series ISSN 2197-9529 • Series E-ISSN 2197-9537 • Edition Number1 • Number of Pages XV, 336 • Number of Illustrations 19 b/w illustrations, 58 illustrations in colour • Topics Statistical Physics, Classical and Continuum Physics, Condensed Matter, Solid Mechanics

PY - 2022/7/19

Y1 - 2022/7/19

N2 - In order to proceed to the consideration of the peculiarities of complex non-equilibrium processes induced by shock loading in condensed media, one must first have a good idea of what is meant by the macroscopic response of a system to an external action from the generally accepted viewpoint within the framework of continuum mechanics. At the beginning of the first chapter, we briefly look at the fundamental aspects of continuum mechanics, with particular attention to the assumptions underlying the continuum modeling. Section 1.4 describes the problem of closing the system of macroscopic equations for the transport of mass, momentum, and energy. A lot of profound and thorough papers are devoted to these issues [1-8]. The concept of a medium model used in continuum mechanics and its shortcomings in modeling transient processes are discussed in Section 1.5. Hypotheses and relationships connecting macroscopic fields of continuous densities with microscopic behavior of real molecules and other elements of physical systems are considered. The statistical description of macroscopic systems considers the behavior of microscopic elements of the medium as a random process [9-14]. A number of hypotheses about the nature of such processes can significantly simplify the approaches to substantiating the continuum mechanics and the interpretation of experimental results [15]. The connecting basis between the micro and macro levels of description is the averaging procedure. In mechanics, various averaging methods have been developed: in space, in time, statistical methods, etc. [16-17]. Among them, the weight averaging methodology plays an important role [18]. This procedure is discussed in section 1.6. The mathematical apparatus of continuum mechanics is a system of partial differential equations that relate the gradients of macroscopic fields and their rates of change at the same spatial point and at the same time moment under the assumption that the system has forgotten its history and is not related to the conditions of its loading. In the last sections of the chapter, issues related to the insufficiency of this mathematical apparatus and the need to develop new, more universal approaches to describing macroscopic systems in real conditions of interaction with their surroundings are considered.

AB - In order to proceed to the consideration of the peculiarities of complex non-equilibrium processes induced by shock loading in condensed media, one must first have a good idea of what is meant by the macroscopic response of a system to an external action from the generally accepted viewpoint within the framework of continuum mechanics. At the beginning of the first chapter, we briefly look at the fundamental aspects of continuum mechanics, with particular attention to the assumptions underlying the continuum modeling. Section 1.4 describes the problem of closing the system of macroscopic equations for the transport of mass, momentum, and energy. A lot of profound and thorough papers are devoted to these issues [1-8]. The concept of a medium model used in continuum mechanics and its shortcomings in modeling transient processes are discussed in Section 1.5. Hypotheses and relationships connecting macroscopic fields of continuous densities with microscopic behavior of real molecules and other elements of physical systems are considered. The statistical description of macroscopic systems considers the behavior of microscopic elements of the medium as a random process [9-14]. A number of hypotheses about the nature of such processes can significantly simplify the approaches to substantiating the continuum mechanics and the interpretation of experimental results [15]. The connecting basis between the micro and macro levels of description is the averaging procedure. In mechanics, various averaging methods have been developed: in space, in time, statistical methods, etc. [16-17]. Among them, the weight averaging methodology plays an important role [18]. This procedure is discussed in section 1.6. The mathematical apparatus of continuum mechanics is a system of partial differential equations that relate the gradients of macroscopic fields and their rates of change at the same spatial point and at the same time moment under the assumption that the system has forgotten its history and is not related to the conditions of its loading. In the last sections of the chapter, issues related to the insufficiency of this mathematical apparatus and the need to develop new, more universal approaches to describing macroscopic systems in real conditions of interaction with their surroundings are considered.

U2 - 10.1007/978-981-19-2404-0_1

DO - 10.1007/978-981-19-2404-0_1

M3 - Chapter

SN - 978-981-19-2403-3

T3 - Shock Wave and High Pressure Phenomena

SP - 1

EP - 30

BT - Mathematical Modeling of Shock-Wave Processes in Condensed Matter.

PB - Springer Nature

CY - Singapore

ER -