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001471543 001__ 1471543
001471543 003__ OCoLC
001471543 005__ 20230908003302.0
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001471543 008__ 230708s2023\\\\sz\\\\\\o\\\\\000\0\eng\d
001471543 019__ $$a1389485595
001471543 020__ $$a9783031289347$$q(electronic bk.)
001471543 020__ $$a303128934X$$q(electronic bk.)
001471543 020__ $$z3031289331
001471543 020__ $$z9783031289330
001471543 0247_ $$a10.1007/978-3-031-28934-7$$2doi
001471543 035__ $$aSP(OCoLC)1389609952
001471543 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE
001471543 049__ $$aISEA
001471543 050_4 $$aQA808.2
001471543 08204 $$a531.7$$223/eng/20230717
001471543 1001_ $$aEspath, Luis.
001471543 24510 $$aMechanics and geometry of enriched continua /$$cLuis Espath.
001471543 260__ $$aCham :$$bSpringer,$$c2023.
001471543 300__ $$a1 online resource (161 p.)
001471543 5050_ $$aIntro -- Preface -- Acknowledgments -- Contents -- Part I Point of Departure and Machinery -- 1 Introduction -- 1 Fields, Hyperfields & Couple-Fields -- 2 The Principle of Virtual Powers' Formalism -- 2 Integro-Differential Machinery -- 1 Differential Relations on a part -- 2 Differential Relations on surfaces -- 3 Differential Relations on curves -- 4 Integro-Differential Relations on surfaces -- 5 Integro-Differential Relations on curves -- 6 Transport Relations and Mass Balance -- Part II The Principle of Virtual Powers and Complementary Balances -- 3 Power Balance, Fields, and Hyperfields
001471543 5058_ $$a1 The Principle of Virtual Powers on bar P in B -- 2 Inertia Components -- 4 Complementary Balances, Jump Conditions, and Couple-Fields -- 1 Frame Indifference -- 2 Partwise Balances on P in B -- 3 Action-Reaction Principle -- 4 Balances on S in P -- 5 Jump Conditions -- 5.1 Jump Conditions Arising from Surface Balances -- 6 The Principle of Virtual Powers on bar S in bar P -- Part III Thermodynamics and Constitutive Relations -- 5 Thermodynamics -- 1 First and Second Laws of Thermodynamics for a Spatial Part Pt
001471543 5058_ $$a2 Partwise and Pointwise Free-Energy Imbalances for Isothermal Processes for a Spatial Part Pt -- 3 First and Second Laws of Thermodynamics for a Control Volume bar P -- 4 Partwise Free-Energy Imbalances for Isothermal Processes for a Control Volume bar P -- 5 Derivatives, Inner Products, and Consequences in Constrained Spaces -- 5.1 Derivatives -- 5.2 Inner Products -- 6 Representation Theorem for Isotropic Tensors -- 6.1 Decomposition of Tensors -- 6.2 Fourth-Order Isotropic Tensor -- 6.3 Sixth-Order Isotropic Tensor -- 6.4 Eighth-Order Isotropic Tensor -- 6 Coupling
001471543 5058_ $$a1 Nonconserved Coupling with an Incompressible Fluid -- 2 Conserved Coupling with an Incompressible Fluid -- Part IV Environmental Conditions and Boundary Conditions -- 7 Environmental Surface Balances and Imbalances -- 1 Surface Balances -- 2 Surface Imbalances -- 3 Uncoupled Conditions -- 8 Boundary Conditions -- 1 Natural Boundary Conditions -- 2 Essential Boundary Conditions -- 3 Mixed Boundary Conditions -- Part V A Special Theory -- 9 Bulk-Surface Dynamics -- 1 Introduction -- 1.1 Synopsis of Purely Variational Models -- 1.2 Synopsis of this Work -- 2 Virtual Power Principle
001471543 5058_ $$a3 Conserved Species -- 4 Free-Energy Imbalance -- 5 Additional Constitutive Response Functions -- 5.1 Further Connections: Boundary Conditions -- 5.2 Specialized Equations -- 6 Decay Relations -- 6.1 Decay Relations for Mixed Boundary Conditions -- Part VI Conclusion -- 10 Summary and Specializations -- 1 Final Remarks -- Appendix Bibliography
001471543 506__ $$aAccess limited to authorized users.
001471543 520__ $$aThis monograph presents a comprehensive and rigorous new framework for the theoretical description and modelling of enriched continua. In other words, continua that exhibit more complex behaviour than their conventional counterparts and, in particular, multicomponent systems. It employs gradient theories, exhibiting multiple transition layers described by phase fields. As a point of departure, we account for multiple continuum kinematic processes, including motion and various phase fields. These gradient theories arise by considering various kinematic processes which are tightly linked to the level of the arbitrariness of the EulerCauchy cuts. The surface defining the EulerCauchy cut may lose its smoothness along a curve, and the curve may also lose its smoothness at a point. Additionally, we postulate the principle of virtual power on surfaces. Then, the first and second laws of thermodynamics with the power balance provide suitable and consistent choices for the constitutive equations. Finally, the complementary balances, namely the balances on surfaces, are tailored to coincide with different parts of the boundaries of the body. These surface balances are then called environmental surface balances and aid in determining suitable and consistent boundary conditions. Ultimately, the environmental surface power balance is relaxed to yield an environmental surface imbalance of powers, rendering a more general type of boundary condition. A detailed introduction sets the scene for the mathematical chapters that follow, ensuring that graduate students and newcomers can profit from the material presented.
001471543 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 17, 2023).
001471543 650_0 $$aContinuum mechanics.
001471543 650_0 $$aContinuum mechanics$$xMathematics.
001471543 655_0 $$aElectronic books.
001471543 77608 $$iPrint version:$$aEspath, Luis$$tMechanics and Geometry of Enriched Continua$$dCham : Springer International Publishing AG,c2023$$z9783031289330
001471543 852__ $$bebk
001471543 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-28934-7$$zOnline Access$$91397441.1
001471543 909CO $$ooai:library.usi.edu:1471543$$pGLOBAL_SET
001471543 980__ $$aBIB
001471543 980__ $$aEBOOK
001471543 982__ $$aEbook
001471543 983__ $$aOnline
001471543 994__ $$a92$$bISE