Mathematical modelling of continuum physics This monograph provides a comprehensive and self contained treatment of continuum physics illustrating a systematic approach to the constitutive equations for wide ranging classes of materials. Derivations of results are detailed through careful proofs and the contents have been developed to ensure a self contained and consistent presentation. Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics – such as reference and current configurations transport relations singular surfaces objectivity and objective time derivatives – are covered in detail. A chapter on balance equations then develops the balance laws of mass linear momentum angular momentum energy and entropy as well as the balance laws in electromagnetism. Part II is devoted to the general requirements on constitutive models emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed and in this framework detailed descriptions are given of solids (thermoelastic elastic and dissipative) and fluids (elastic thermoelastic viscous and Newtonian). A wide of variety of constitutive models are investigated in Part III which consists of separate chapters focused on several types of non simple materials: materials with memory aging and higher order grade materials mixtures micropolar media and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity magnetoelasticity and plasma theory. Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena such as those occurring in hysteretic continua (e.g. plasticity electromagnetism and the physics of shape memory alloys). Mathematical Modelling of Continuum Physics will be an important reference for mathematicians engineers physicists and other scientists interested in research or applications of continuum mechanics. .