English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain. It is shown that the derivatives of the strain volume variables with respect to the stresses are reduced to conventional well known isothermal, elastic, and crystallographic compliances and crystallographic thermal expansion coefficients. The formulism is extended to all third order derivatives which establish 77 new thermodynamic identities: 27 are thermal and 50 are among selected stress components of elastic compliances. The stress dependence of heat capacity is typically coupled into the crystallographic thermal expansion coefficient's temperature dependence; the temperature dependence of the elastic compliances is related to the stress dependence of the thermal expansion coefficients; stress dependent relationships among elastic compliances are also found. This paper emphasizes internal self-consistency. General triclinic identity relations which are of academic interest are applied to specific higher symmetries including orthorhombic, tetragonal, and cubic; identities in higher symmetry crystals are very useful. A new generalized, constitutive law is found and applied to isotropic polycrystalline materials; the concept is based on shear thermal expansion coefficients. The constitutive modulus relation describes thermal and pressure properties only through an isochoric modulus.Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain. It is shown that the derivatives of the strain volume variables with respect to the stresses are reduced to conventional well known isothermal, elastic, and crystallographic compliances and crystallographic thermal expansion coefficients. The formulism is extended to all third order derivatives which establish 77 new thermodynamic identities: 27 are thermal and 50 are among selected stress components of elastic compliances. The stress dependence of heat capacity is typically coupled into the crystallographic thermal expansion coefficient's temperature dependence; the temperature dependence of the elastic compliances is related to the stress dependence of the thermal expansion coefficients; stress dependent relationships among elastic compliances are also found. This paper emphasizes internal self-consistency. General tricl...

77 new thermodynamic identities among crystalline elastic material properties leading to a shear modulus constitutive law in isotropic solids