This book provides a unified treatment of continuum physics. A systematic approach to the balance equations is elaborated for wide-ranging classes of materials (classical continua, micropolar continua, mixtures, electromagnetic continua) following the lines of the encyclopedic handbook articles of Truesdell and Toupin and Truesdell and Noll. As is standard in Rational Thermodynamics, the constitutive properties are required to obey the objectivity principle and to be consistent with the second law of thermodynamics. Yet here a rather new approach is developed by viewing the entropy production as a constitutive function per se as is the case for the entropy and the entropy flux. While this does not determine any new result for simple materials, it proves conceptually and practically advantageous in the modelling of nonlinear phenomena such as those occurring in hysteretic continua, e.g. in plasticity, electromagnetism, and physics of shape-memory alloys. The book is suitable for engineers, physicists, and mathematicians. The derivations of the sought results are fairly detailed through careful proofs. Though a wide variety of subjects are examined, the contents are developed so as to get a self-contained and consistent presentation of the various topics.
Mathematical modelling of continuum physics
Claudio Giorgi
2023-01-01
Abstract
This book provides a unified treatment of continuum physics. A systematic approach to the balance equations is elaborated for wide-ranging classes of materials (classical continua, micropolar continua, mixtures, electromagnetic continua) following the lines of the encyclopedic handbook articles of Truesdell and Toupin and Truesdell and Noll. As is standard in Rational Thermodynamics, the constitutive properties are required to obey the objectivity principle and to be consistent with the second law of thermodynamics. Yet here a rather new approach is developed by viewing the entropy production as a constitutive function per se as is the case for the entropy and the entropy flux. While this does not determine any new result for simple materials, it proves conceptually and practically advantageous in the modelling of nonlinear phenomena such as those occurring in hysteretic continua, e.g. in plasticity, electromagnetism, and physics of shape-memory alloys. The book is suitable for engineers, physicists, and mathematicians. The derivations of the sought results are fairly detailed through careful proofs. Though a wide variety of subjects are examined, the contents are developed so as to get a self-contained and consistent presentation of the various topics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
