Abstract
We present new general relationships among the material properties of an isotropic material kept in homogeneous stress conditions with hydrostatic pressure and plane shear. The derivation is not limited to the proximity of the zero shear-stress and -strain condition, which allows us to identify the relationship between adiabatic and isothermal shear compliances (inverse of the moduli of rigidity) along with new links, among others, between isobaric and isochoric shear thermal expansion coefficients and heat capacities at constant stress and constant shear strain. Such relationships are important for a variety of applications, including the determination of constitutive equations, the characterization of nanomaterials, and the identification of properties related to earthquakes precursors and complex media (e.g., soil) behavior. The results may be useful to investigate the behavior of materials during phase transitions involving shear or in non-homogeneous conditions within a local thermodynamic equilibrium framework.
Highlights
Since Gibbs’ fundamental contribution in 1876 [1], the thermodynamic theory of solids under different stress conditions has remained an active field of inquiry, with a recent intensification spurred by interest in amorphous states and glass transition, high pressure physics, and the development of artificial materials [2,3,4,5,6,7]
Continuum mechanics and thermoelasticity have focused more on finite deformations and field theories, traditionally shifting away from homogeneous thermodynamics [8,9]
One of the great utilities of equilibrium thermodynamics lies in its theoretical structure, which provides fundamental links among material properties through the Hessian matrix of the Gibbs free energy, while ensuring feasible reversible transformations
Summary
Since Gibbs’ fundamental contribution in 1876 [1], the thermodynamic theory of solids under different stress conditions has remained an active field of inquiry, with a recent intensification spurred by interest in amorphous states and glass transition, high pressure physics, and the development of artificial materials [2,3,4,5,6,7]. We focus on the case of plane shear, which is intermediate between the hydrostatic and the fully-anisotropic one, and derive new relations between the material properties in general shear-stress and -strain conditions. While it represents a highly idealized state compared to the heterogeneous and anisotropic stress configurations typical of real-life conditions, this homogeneous stress condition remains an important benchmark for the averaged properties of polycrystals and amorphous materials. The case of homogeneous and isotropic, but non-hydrostatic stress is dealt with in classic texts [2,17,19] Their thermodynamic analysis, is essentially limited to the case of small deformations around the state of zero shear stress and deformation. An application to the thermodynamic properties of clay is used to illustrate the new relationships
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