Volume Jacobian and scale
Use detF for finite deformation; sigma is the small-strain density term. The second part is an isotropic frame with linear matching sigma=-3varphi; do not conflate general anisotropy, density energy kernels and independent stretch actions.
Based on the final manuscript · Chapters 4 and 5
Use detF for finite deformation; sigma is the small-strain density term. The second part is an isotropic frame with linear matching sigma=-3varphi; do not conflate general anisotropy, density energy kernels and independent stretch actions.
Chapter reference: Ch. 4 (4.14)–(4.15); Ch. 5 (5.4.5) and isotropic-frame discussion · ASD-BOOK-ddbade997b45
Source and ID
ASD-WEB-SD-034 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.
Return to premises and derivationAdopted source, conditions and previous versions
Ch. 4 (4.14)–(4.15); Ch. 5 (5.4.5) and isotropic-frame discussion
Registered formula checked individually against the final manuscript; semantic potential phi→varphi; finite-density Jacobian vs linear small-strain density made explicit; source-grounded scope note synchronized
Conditions retained in this adoption
- Use detF for finite deformation; sigma is the small-strain density term. The second part is an isotropic frame with linear matching sigma=-3varphi; do not conflate general anisotropy, density energy kernels and independent stretch actions.
Source locators: p1342–1348 · p2028 · p2041
Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e
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Previous source, retained as history
SD-51779505a476 · Ch. 4 (4.15); Ch. 5 (5.4.5), §4.2
Dependencies
algebraCompression-positive densityASD-WEB-SD-003