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Mechanics and geometry of enriched continua

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mechanics and geometry of enriched continuaby Luis Espath.
作者:	Espath, Luis.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xi, 159 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Continuum mechanics.
電子資源:	https://doi.org/10.1007/978-3-031-28934-7
ISBN:	9783031289347$q(electronic bk.)

Mechanics and geometry of enriched continua
Espath, Luis.

Mechanics and geometry of enriched continua[electronic resource] /by Luis Espath. - Cham :Springer International Publishing :2023. - xi, 159 p. :ill., digital ;24 cm.

Introduction -- Integro-differential machinery -- Power balance, fields and hyperfields -- Complementary balances, jump conditions and couple fields -- Thermodynamics -- Coupling -- Environmental surface balances and imbalances -- Boundary conditions -- Final remarks.

This monograph presents a comprehensive and rigorous new framework for the theoretical description and modelling of enriched continua. In other words, continua that exhibit more complex behaviour than their conventional counterparts and, in particular, multicomponent systems. It employs gradient theories, exhibiting multiple transition layers described by phase fields. As a point of departure, we account for multiple continuum kinematic processes, including motion and various phase fields. These gradient theories arise by considering various kinematic processes which are tightly linked to the level of the arbitrariness of the Euler-Cauchy cuts. The surface defining the Euler-Cauchy cut may lose its smoothness along a curve, and the curve may also lose its smoothness at a point. Additionally, we postulate the principle of virtual power on surfaces. Then, the first and second laws of thermodynamics with the power balance provide suitable and consistent choices for the constitutive equations. Finally, the complementary balances, namely the balances on surfaces, are tailored to coincide with different parts of the boundaries of the body. These surface balances are then called environmental surface balances and aid in determining suitable and consistent boundary conditions. Ultimately, the environmental surface power balance is relaxed to yield an environmental surface imbalance of powers, rendering a more general type of boundary condition. A detailed introduction sets the scene for the mathematical chapters that follow, ensuring that graduate students and newcomers can profit from the material presented.

ISBN: 9783031289347$q(electronic bk.)

Standard No.: 10.1007/978-3-031-28934-7doiSubjects--Topical Terms:

190274
Continuum mechanics.

LC Class. No.: QA808.2

Dewey Class. No.: 531.7

Mechanics and geometry of enriched continua
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505 0 $a Introduction -- Integro-differential machinery -- Power balance, fields and hyperfields -- Complementary balances, jump conditions and couple fields -- Thermodynamics -- Coupling -- Environmental surface balances and imbalances -- Boundary conditions -- Final remarks.
520 $a This monograph presents a comprehensive and rigorous new framework for the theoretical description and modelling of enriched continua. In other words, continua that exhibit more complex behaviour than their conventional counterparts and, in particular, multicomponent systems. It employs gradient theories, exhibiting multiple transition layers described by phase fields. As a point of departure, we account for multiple continuum kinematic processes, including motion and various phase fields. These gradient theories arise by considering various kinematic processes which are tightly linked to the level of the arbitrariness of the Euler-Cauchy cuts. The surface defining the Euler-Cauchy cut may lose its smoothness along a curve, and the curve may also lose its smoothness at a point. Additionally, we postulate the principle of virtual power on surfaces. Then, the first and second laws of thermodynamics with the power balance provide suitable and consistent choices for the constitutive equations. Finally, the complementary balances, namely the balances on surfaces, are tailored to coincide with different parts of the boundaries of the body. These surface balances are then called environmental surface balances and aid in determining suitable and consistent boundary conditions. Ultimately, the environmental surface power balance is relaxed to yield an environmental surface imbalance of powers, rendering a more general type of boundary condition. A detailed introduction sets the scene for the mathematical chapters that follow, ensuring that graduate students and newcomers can profit from the material presented.
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