Mechanics and Geometry of Enriched Continua / by Luis Espath.

Format:

Book

Author/Creator:

Espath, Luis.

Language:

English

Subjects (All):

Continuum mechanics.

Mathematical physics.

Computer simulation.

Thermodynamics.

Materials science—Data processing.

Optical materials.

Continuum Mechanics.

Computational Physics and Simulations.

Computational Materials Science.

Optical Materials.

Local Subjects:

Continuum Mechanics.

Computational Physics and Simulations.

Thermodynamics.

Computational Materials Science.

Optical Materials.

Physical Description:

1 online resource (161 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-28934-X

OCLC:

1389609952