The Mechanics and Thermodynamics of Continua

Abstract

The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Lazy zone bone remodeling theory and its relation to topology optimization

“…We then observe that this inequality resembles the well-known dissipation inequality of thermodynamics, stated for instance in Gurtin et al [7] or Frémond [6]. In fact, the logical status of these two inequalities are the same: we are to find a dynamical system that satisfies the inequality for all possible evolutions.…”

“…In fact, the logical status of these two inequalities are the same: we are to find a dynamical system that satisfies the inequality for all possible evolutions. In thermodynamics, this particular modeling step is known as the Coleman-Noll procedure, [7,6]. Following this procedure we derive a general dynamical system that when specialized takes the form of a lazy zone bone remodeling theory.…”

On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

“…Their unimodular parts are defined as C = J −2/3 C and b = J −2/3 b. For an elaborate treatment see, e.g., Truesdell and Noll [36], Holzapfel [15] and Gurtin et al [13]. Next, we exploit the representation theorem of invariants according to Spencer [34] and Holzapfel [15], and define the three irreducible isotropic invariants…”

“…Therefore, all volumetric responses essentially emerge on an element level instead of a constitutive level. It is also worth mentioning that all three formulations (Q1P0, Q1P0+AL, Q1P0+WAS) assume the same expressions for their volumetric and isotropic stress responses, as stated in (13). The mere difference originates from their distinct anisotropic constitutive forms.…”

Metaphysical Foundations of Neoclassical Mechanics

“…And, the rigid body is the preferred ontology of analytic mechanics, which I have set aside for now, as I explained above. 3 Sections 1 and 2 are synoptic capsules that rely variously on Hamel 1909, Joos 1934, Malvern 1969, Truesdell 1991, Gurtin, Fried & Anand 2010, and Wilson 2013 'Neoclassical' denotes a certain presentation of mechanics, more rigorous than the partial and often implicit 'classical' version of Newton and Kant, but less formal than the 'post-classical' axiomatizations of Noll and his school.…”