• Manuel DoblaréEmail author
  • Mohamed H. Doweidar
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 262)


In this chapter, we review the fundamental concepts and formulation of the thermomechanics of continuous media. First, we revise the expressions of the two first laws of thermodynamics for thermomechanical processes, that is, those with changes in temperature and strains as state-independent variables. These equations constitute the generalization of the energy balance equation that was presented, particularized for the isothermal case, in chapter “ Basic Equations of Continuum Mechanics” [10]. Next, we introduce different thermodynamic potentials such as the internal energy density, the Helmholtz free energy density, and the dissipation density. This latter is expressed in terms of additional independent internal state variables that take into account history-dependent changes in the material’s internal microstructure. The associated thermodynamic fluxes are then defined as derivatives of the dissipation density with respect to the corresponding thermodynamic drivers (internal variables). The next section introduces the fundamental principles for simple (local, nongraded) materials. These allow establishing the general constitutive equations for the rest of the state- dependent variables, stress and entropy, from the expression of the chosen thermodynamic potential and the fulfillment of the second law of thermodynamics. These expressions are finally applied to several examples: two types of non-dissipative materials, such as ideal fluids and elastic solids in thermomechanical processes, and two dissipative cases: damage mechanics and nonlinear viscoelastic solids. We finish with the formulation and results of a complex thermomechanical process, the extrusion forming process of an aluminum billet under high temperature and viscoplastic behavior.


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Authors and Affiliations

  1. 1.Aragón Institute of Engineering Research (I3A)University of ZaragozaZaragozaSpain
  2. 2.Aragón Institute of Engineering Research (I3A)University of ZaragozaZaragozaSpain

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