Recent content by Klaus3

But it can if both are non symmetric

###T##is going to be symmetric per the first derivation. It is not necessarily symmetric per the second derivation. The character of ##T_1## here doesnt matter. The only thing it does is, in the second derivation, making ##T## asymmetric if it is asymmetric. The results are conflicting because...

Microscopically speaking the distinction doesnt exist. ##T## is supposed to account for contact forces. So forces between particles that are touching each other. On the micro scale, atoms and molecules never touch each other, the interaction they have is long range (i.e, body force). And these...

I mean, electromagnetic force is the example. You can always use the maxwell equations to transform it into a divergence. if you go onto the truesdell reference I said above. You will see that he makes this transformation and uses the maxwell stress tensor to reformulate the body forces as a...

I am ok with the Total stress tensor being symmetric, however, the sum ##T+T_1## being symmetric doesn't imply that ##T## and ##T_1## are each symmetric. However, if you keep the tensors separated, one of the derivations implies that ##T## is symmetric no matter what. assuming ## k = 0## $$...

Local balance is simply the statement that results when you drop the integral signs, by saying that the integral equation is valid for arbitrary volumes in the body, which leaves an equation relating the forces/torques densities. When you drop the integral signs in the angular momentum...

I am aware of the controversy, there is no (at least to my knowing) a general specific form of the maxwell stress tensor without disagreements. However, my issue isn't with the exact for of it, rather, with how it mathematically functions in the overall balances. Let's forget we are talking...

This expression for the maxwell stress tensor only works for linear dielectrics or monopolar bodies. It is not necessarily symmetric for polarizable materials/ferromagnetic and so on, you can see alternate versions of it in Truesdell and Toupin "The classical field theories" . Sect 284, Page...

Consider the balance of momentum and angular momentum on a continuum body $$ \int \frac{dp}{dt}dV = \int TndA + \int bdV $$ $$ div(T) + b = \frac{dp}{dt}$$ $$ \int r \times \frac{dp}{dt}dV = \int r \times TndA + \int r \times bdV $$ ##p## is the volumetric momentum density ##T## is the stress...

They are external to a particular system you choose, you can choose either the entire body, as such the forces would be fully external or to a particular volume inside the entire body, where the forces would be both internal and external. Isn't this still a decomposition of the contact force...

I am not aware of any force diagram that includes the couples in that case, and have no idea how would they appear, the texts only lay down the equations. ##t## are represented by contact forces which you have plenty of examples here https://en.wikipedia.org/wiki/Cauchy_stress_tensor and ##f##...

In books that deal with continuum modelling of materials that include the presence of internal rotations/torques in the microstructure, the torque is defined as follows: $$ \tau = \int ((r \times t + m) dA) + \int ( (r \times f + l) dV )$$ From this definition, the stress tensor and couple...

I just couldn't find an explicit mention of work in the textbook (its always power), but its still the same definition found in other places, such as: https://en.wikipedia.org/wiki/Virtual_work#Proof_of_equivalence_between_the_principle_of_virtual_work_and_the_equilibrium_equation i know the...

It does not, they just define it that way.

##\frac{dT}{dt}## and ##\frac{db}{dt}## are generally not zero. For example, imagine ##T## is a pressure, pressure is not necessarily constant on a general process. Also, the product rule isn't straightforward for volume and area integrals, because generally they also vary with time (which is...