This is one of the most lucid explanations of continuum mechanics' foundational principles, i.e., finite deformation theory. This topic is often taught so poorly that it confounds first-year graduate students. This video is simply outstanding from an instructional perspective.
I have had my YT account for 10 years now but this is the first comment I will ever leave under a video. Mr. Pettit, your explanations are very incredibly well thought out with nice and simple visuals that help a lot. It is clear to me that you have spent a great deal of time preparing this material in "easy-to-follow" manner and as an academic I know that this takes a lot of effort. I would really appreciate if you could provide me with a list of materials (books, papers, notes) that you have used to prepare your Solid Mechanics playlist. Thank you from a PhD student trying to learn Advanced Solid Mechanics.
absolutely understandable and clear explanation, you are genies , hope you are a lecturer in order to make simplicity the solid mechanics for students. Thank you so much , you make clear my doubt and my knowledge in this topic !
Great videos man! Well explained and displayed. Only comment i would have is on the volume of the video itsself. Its relatively low and every time commercials interrupt the yt video it blows up my headphones 😂.
Your explanation is simple and clear. Can you also make some videos which dig deeper into the theory of continuum mechanic(all those Finger strain,Piola strain, Almansi strain, left Cauchy-Green strain........ a zoo of Greek and English alphabets)? You will be a Salvator of many graduate students
hello and thank you very much. please can you explain to me why the deformation equal to the derivative of the displacement vector (we did that in the finite element method and I couldn't imagine the situation)
In the slide for the position gradient (22:21) I understand why du1/dX1 + 1= dx1/dX1, but what happens with the off-diagonal terms? why du1/dX2= dx1/dX2? and not du1/dX2= dx1/dX2 - dX1/dX2, is it dX1/dX2=0, why? Can someone explain it ? is it because for the reference frame?
Ciao! Penso che sia perché u1 = x1-X1 e di conseguenza quando andiamo a derivare rispetto a X2 o X3 usiamo la regola di derivazione della somma e abbiamo la derivata parziale di x1 rispetto a X2, meno la derivata parziale di X1 rispetto a X2 che è nulla( dal momento che abbiamo scelto una base ortonormale e la componente di X1 relativa alla direzione di X2 è costantemente uguale a 0).
the off diagonal terms vanish. Take for example, du1/dX2 = dx1/dX2 - dX1/dX2 = dx1/dX2 since dX1/dX2 = 0. The X1, X2, X3 directions are orthogonal to each other. dX1/dX2 means what is the infinitesimal change in X1 if we change X2 by an infinitesimal amount dX2, and the answer is zero due to orthogonality. In terms of Cartesian notation, think of dx/dy... that is just zero
Actually, here dx^2 is being obtained. In vector form we can do this like dot product= dx . dx= (dx^t)(dx). So, dx^t will be (Fd X)^t= dX^t F^t. Now we can write dx . dx= dX^t F^t F dX = dX . (F^t F) dX. See, a dot is written after the term dX and before F^t F dX.
This is one of the most lucid explanations of continuum mechanics' foundational principles, i.e., finite deformation theory. This topic is often taught so poorly that it confounds first-year graduate students. This video is simply outstanding from an instructional perspective.
I have had my YT account for 10 years now but this is the first comment I will ever leave under a video. Mr. Pettit, your explanations are very incredibly well thought out with nice and simple visuals that help a lot. It is clear to me that you have spent a great deal of time preparing this material in "easy-to-follow" manner and as an academic I know that this takes a lot of effort.
I would really appreciate if you could provide me with a list of materials (books, papers, notes) that you have used to prepare your Solid Mechanics playlist.
Thank you from a PhD student trying to learn Advanced Solid Mechanics.
As clear as it can ever be! Incredible video. Thank you.
Amazing video that genuinely makes you appreciate knowing how mathematical tools are constructed and derived.
Great video. Easy to understand for someone who is new to the topic. Thanks!
Just what im lookin for. Simple and clear. Thank you. Can wait to next video clip.
I can't believe this. Clear, intuitive explanation. Thank you so much!
absolutely understandable and clear explanation, you are genies , hope you are a lecturer in order to make simplicity the solid mechanics for students. Thank you so much , you make clear my doubt and my knowledge in this topic !
Incredible video, easy explained, never thogth i will understand contnuum mechanics, thanks alot
Great videos man! Well explained and displayed. Only comment i would have is on the volume of the video itsself. Its relatively low and every time commercials interrupt the yt video it blows up my headphones 😂.
Your explanation is simple and clear. Can you also make some videos which dig deeper into the theory of continuum mechanic(all those Finger strain,Piola strain, Almansi strain, left Cauchy-Green strain........ a zoo of Greek and English alphabets)? You will be a Salvator of many graduate students
Greatest explanation on strain tensor ever. Can Believe the that no of subscribers though
This lecture is greatly appreciated.
why I haven,t find you yet , brilliant man
Excellent explanation
Brilliant explanation!
you saved my life thank you
Awesome video. I tried reading about this, but couldn't follow the text. This video just made it click for some reason. Thanks.
Why finite strain is defined using the square of the norms and not just the norms themselves?
Awesome amazing lecture! 💥
Amazing lecture :)
Excellent explaination, Thanks
Very helpful video
hello and thank you very much. please can you explain to me why the deformation equal to the derivative of the displacement vector (we did that in the finite element method and I couldn't imagine the situation)
In the slide for the position gradient (22:21) I understand why du1/dX1 + 1= dx1/dX1, but what happens with the off-diagonal terms? why du1/dX2= dx1/dX2? and not du1/dX2= dx1/dX2 - dX1/dX2, is it dX1/dX2=0, why?
Can someone explain it ? is it because for the reference frame?
Ciao! Penso che sia perché u1 = x1-X1 e di conseguenza quando andiamo a derivare rispetto a X2 o X3 usiamo la regola di derivazione della somma e abbiamo la derivata parziale di x1 rispetto a X2, meno la derivata parziale di X1 rispetto a X2 che è nulla( dal momento che abbiamo scelto una base ortonormale e la componente di X1 relativa alla direzione di X2 è costantemente uguale a 0).
the off diagonal terms vanish. Take for example, du1/dX2 = dx1/dX2 - dX1/dX2 = dx1/dX2 since dX1/dX2 = 0. The X1, X2, X3 directions are orthogonal to each other. dX1/dX2 means what is the infinitesimal change in X1 if we change X2 by an infinitesimal amount dX2, and the answer is zero due to orthogonality. In terms of Cartesian notation, think of dx/dy... that is just zero
Can you please explain this?
(F.dX).(F.dX) = dX.(F^T.F).dX -------> How did we get this?
@@physicsanimated1623 Thanks you so much.
can you share your slides?
Why there is no "metric tensor"(g, G) explanation
Can anyone please explain this?
(F.dX).(F.dX) = dX.(F^T.F).dX -------> How did we get this?
Actually, here dx^2 is being obtained. In vector form we can do this like dot product= dx . dx= (dx^t)(dx). So, dx^t will be (Fd X)^t= dX^t F^t. Now we can write dx . dx= dX^t F^t F dX = dX . (F^t F) dX. See, a dot is written after the term dX and before F^t F dX.
Audio is tooo low