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Mathematical Modelling of Continuum Physics

Part of the Modeling and Simulation in Science, Engineering and Technology Book Series

DOI: 10.1007/978-3-031-20814-0

ISBN: 978-3-031-20813-3

Publisher: Springer International Publishing - Springer Journals

Mar 19, 2023

1 - 10 of 16 Chapters

Available

Kinematics

Morro, Angelo; Giorgi, Claudio

Pages: 3 –71

[This chapter deals with the kinematics of deformable bodies. Both deformation and motion of a body are developed by using the reference configuration. Attention is addressed to the topics of objectivity and objective time derivatives, thus establishing a general framework that proves remarkable...
Available

Balance Equations

Morro, Angelo; Giorgi, Claudio

Pages: 73 –174

[Borrowing from the mechanics of systems of particles, the balance equations for mass, linear momentum, and angular momentum are established. Next, the balance of energy is obtained after having realized that energy in general requires a more general framework including quantities of...
Available

Generalities on Constitutive Models

Morro, Angelo; Giorgi, Claudio

Pages: 177 –201

[The balance equations of a body form an under-determined differential system, insufficient to yield specific results unless further relations are supplied. The balance equations for a continuum (free from internal structures) are the continuity equation, the equation of motion, and the balance...
Available

Solids

Morro, Angelo; Giorgi, Claudio

Pages: 203 –262

[Solids are described as simple materials namely materials modelled by first-order gradients of deformation, velocity, and temperature. Hence the chapter develops linear and non-linear thermoelastic solids along with corresponding discontinuity waves and time-harmonic waves, thus arriving at the...
Available

Fluids

Morro, Angelo; Giorgi, Claudio

Pages: 263 –318

[Fluids include liquid and gas phases. Here fluids are characterized by the constitutive properties. Some models are examined in detail: elastic fluids (along with water wave theories), thermoelastic fluids, the ideal gas and some real gases, heat-conducting viscous fluids, Newtonian fluids,...
Available

Rate-Type Models

Morro, Angelo; Giorgi, Claudio

Pages: 321 –380

[Spatial interaction and memory effects are among the possible features of non-simple materials. As to memory effects in fluids, the inadequacy of the classical Navier-Stokes theory to describe rheological complex fluids, such as geological materials, liquid foams, and polymeric fluids, has led...
Available

Materials with Memory

Morro, Angelo; Giorgi, Claudio

Pages: 381 –495

[Real materials exhibit a continuing strain rate(creep) under persistent constant stress and decay of stress (relaxation) under constant strain. The analogue occurs for electric current or electric polarization and electric field. In this connection, here the mathematical framework of materials...
Available

Aging and Higher-Order Grade Materials

Morro, Angelo; Giorgi, Claudio

Pages: 497 –544

[This chapter investigates some aspects of non-simple materials. First, aging materials are examined. Aging is a general problem of the modelling of materials. Mathematically the problem is made formal by letting constitutive parameters depend on time. It is pointed out that the second law of...
Available

Mixtures

Morro, Angelo; Giorgi, Claudio

Pages: 545 –610

[Mixtures consist of different substances which keep their own properties. The individual molecules enjoy being near to each other so that, in the mathematical model, each point in the mixture may be occupied by all of the substances simultaneously. If the chemical structure of a substance...
Available

Micropolar Media

Morro, Angelo; Giorgi, Claudio

Pages: 611 –658

[There are materials with internal structure (e.g. composites, polymers, liquid crystals, soil, and bone) for which a reasonable model should view the points no longer as purely geometric in character but as rigid-body particles or even deformable continua. Models accounting for rigid-body...

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