Mechanics and Geometry of Enriched Continua

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 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.

Presents a powerful new continuum theory for enriched continua Clear and systematic presentation including background and introduction Takes a rigorous approach both to modelling and mathematical derivations

Auteur
Dr. Espath obtained his Engineering Diploma in 2007 at PUCRS, Brazil. He completed a Master's and Doctorate at UFRGS, Brazil, in 2013. Dr. Espath was appointed postdoctoral fellow at KAUST, until 2019. Subsequently, he assumed the role of Research Scientist at RWTH Aachen, Germany, until 2021. In 2022, at RWTH Aachen, Dr. Espath defended his Habilitation thesis in Mathematics in the field of Theoretical Mechanics. His research interests are theoretical and computational mechanics, uncertainty quantification, stochastic optimization, and machine learning.

Contenu
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.