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feynman1
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What's the derivative of deformation gradient F w.r.t cauchy green tensor C, where C=F'F and ' denotes the transpose?
very helpful but it doesn't answer my question directlyfresh_42 said:Open https://de.wikipedia.org/wiki/Verzerrungstensor with Chrome and let Google translate it into a language of your choice.
no, but of F w.r.t CChestermiller said:Are you trying to find the derivative of the CG tensor with respect to time in terms of the time derivatives of the deformation gradient tensor and its transpose?
The derivative of the deformation gradient with respect to the Cauchy green tensor is a mathematical concept that describes the rate of change of the deformation gradient with respect to changes in the Cauchy green tensor. It is essentially a measure of how the deformation gradient responds to changes in the Cauchy green tensor.
The derivative of the deformation gradient with respect to the Cauchy green tensor is important in mechanics because it helps us understand how materials deform and behave under different conditions. It is a key component in the study of elasticity and plasticity of materials.
The derivative of the deformation gradient with respect to the Cauchy green tensor is calculated using mathematical techniques such as the chain rule and tensor calculus. It involves taking partial derivatives of the deformation gradient components with respect to the Cauchy green tensor components.
The derivative of the deformation gradient with respect to the Cauchy green tensor has many applications in fields such as solid mechanics, material science, and engineering. It is used in the analysis and design of structures, predicting material behavior under different loading conditions, and developing constitutive models for materials.
Yes, there are some limitations and assumptions when using the derivative of the deformation gradient with respect to the Cauchy green tensor. It assumes that the material is homogeneous, isotropic, and undergoes small deformations. It also assumes that the material is in a state of mechanical equilibrium.