Problems related to the constitutive relation

[cuicw]

I'm trying to understand the derivation of the formula in the image. I'm unfamiliar with this particular form of constitutive relationship and would appreciate any explanation.

[mou3adb]

Hi cuicw, I took it from the references, you can check Landau and Lifschitz, Theory of Elasticity. The derivation is lengthy and cannot be summarized in an email, but it starts from the energy formula, coming from the bending energy of a rod per unit length.

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On Mon, Jan 6, 2025 at 6:58 PM cuicw ***@***.***> wrote: I'm trying to understand the derivation of the formula in the image. I'm unfamiliar with this particular form of constitutive relationship and would appreciate any explanation. image.png (view on web) <https://github.com/user-attachments/assets/7701cfab-be9e-4a7b-a197-fdc81bd5bc68> — Reply to this email directly, view it on GitHub <#2>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AOEQCDJAP7ZELKSCRIF22ED2JM7CXAVCNFSM6AAAAABUWZM36SVHI2DSMVQWIX3LMV43ASLTON2WKOZSG43TCNZYHE4DAMQ> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[cuicw]

Thank you, I 've deduced that

[cuicw]

Excuse me again, I want to know how to derive the formula of variational principle.

[mou3adb]

Hi cui. Each term is basically a product of a governing equation multiplied by the corresponding test function. For example, the first term comes from equation 7.1, which says that the derivative of the position vector is exactly the tangent vector. And so forth.

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On Wed, Jan 15, 2025 at 12:09 AM cuicw ***@***.***> wrote: Excuse me again, I want to know how to derive the formula of variational principle. image.png (view on web) <https://github.com/user-attachments/assets/6152e47f-7d9f-405b-b876-5be9aa83ac4e> — Reply to this email directly, view it on GitHub <#2 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AOEQCDONSVY5VTZEBQ4IG432KYJRZAVCNFSM6AAAAABUWZM36SVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKOJRHA4TANBVGU> . You are receiving this because you commented.Message ID: ***@***.***>