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Mathematical methods in continuum me...

Kruzik, Martin.

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Mathematical methods in continuum mechanics of solids

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Mathematical methods in continuum mechanics of solids/ by Martin Kruzik, Tomas Roubicek.
作者:	Kruzik, Martin.
其他作者:	Roubicek, Tomas.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xiii, 617 p. :ill. (some col.), digital ;24 cm.
內容註:	Static Problems -- Description of Deformable Stressed Bodies -- Elastic Materials -- Polyconvex Materials: Existence Of Energy-Minimizing Deformations -- General Hyperelastic Materials: Existence/Nonexistence Results -- Linearized Elasticity -- Evolution Problems -- Linear Rheological Models at Small Strains -- Nonlinear Materials with Internal Variables at Small Strains -- Thermodynamics of Selected Materials and Processes -- Evolution at ﬁnite Strains.
Contained By:	Springer eBooks
標題:	Continuum mechanics - Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-030-02065-1
ISBN:	9783030020651

Mathematical methods in continuum mechanics of solids
Kruzik, Martin.

Mathematical methods in continuum mechanics of solids[electronic resource] /by Martin Kruzik, Tomas Roubicek. - Cham :Springer International Publishing :2019. - xiii, 617 p. :ill. (some col.), digital ;24 cm. - Interaction of mechanics and mathematics,1860-6245. - Interaction of mechanics and mathematics..

Static Problems -- Description of Deformable Stressed Bodies -- Elastic Materials -- Polyconvex Materials: Existence Of Energy-Minimizing Deformations -- General Hyperelastic Materials: Existence/Nonexistence Results -- Linearized Elasticity -- Evolution Problems -- Linear Rheological Models at Small Strains -- Nonlinear Materials with Internal Variables at Small Strains -- Thermodynamics of Selected Materials and Processes -- Evolution at ﬁnite Strains.

This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear, quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

ISBN: 9783030020651

Standard No.: 10.1007/978-3-030-02065-1doiSubjects--Topical Terms:

1015241
Continuum mechanics
--Mathematics.

LC Class. No.: QA808.2 / .K783 2019

Dewey Class. No.: 531.015

Mathematical methods in continuum mechanics of solids
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505 0 $a Static Problems -- Description of Deformable Stressed Bodies -- Elastic Materials -- Polyconvex Materials: Existence Of Energy-Minimizing Deformations -- General Hyperelastic Materials: Existence/Nonexistence Results -- Linearized Elasticity -- Evolution Problems -- Linear Rheological Models at Small Strains -- Nonlinear Materials with Internal Variables at Small Strains -- Thermodynamics of Selected Materials and Processes -- Evolution at ﬁnite Strains.
520 $a This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear, quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.
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