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Relation between strain and velocity

your question: "Is it right to identify $\frac{\partial u_i}{\partial t}$ with the velocity vi of the particles of the material,.." The correct formula implies material derivatives (as ...
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What is the physical meaning of the third invariant of the strain deviatoric?

For a general $3\times 3$ matrix $\mathbf{A, you have: $$I_3 = \frac{1}{3!}[\mbox{tr}(\mathbf{A})^3 - 3\mbox{tr}(\mathbf{A}^2)\mbox{tr}(\mathbf{A}) + 2\mbox{tr}(\mathbf{A}^3)]$$ If you have $\text{tr}(...
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Decomposition of deformation into bend, stretch and twist?

Yes, there is a way to decompose strain (ie: deformation) into six components. The components are the three amounts of stretching along (x,y,z) and the 3 amounts of parallelepipeding in the planes ...
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Decomposition of deformation into bend, stretch and twist?

There is no such general decomposition, simply because bending and twist can only be defined for rods (where there is a longitudinal direction of reference). So it makes no sense to talk about "...
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Axial Force and Normal Stress in Mechanics

The normal stress is identical at any section you consider as long as the beam is in static equilibrium. Consider any section of some finite thickness. The force on each face must be equal, ...
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Is a stress tensor still symmetric when the object is rotating?

I will answer your questions below. Yes. The Cauchy stress is still symmetric. The thing is that this stress measure is not energy conjugate with the strain measure that you picked. This means that ...
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