All Questions
Tagged with continuum-mechanicsthermodynamics
34 questions
2votes
0answers
50views
How can we calculate entropy produced by plastic deformation in this example?
Suppose we have a massless spring of spring constant $k$ attached to a mass $m$ at equilibrium position $x_{0}$ at temperature $T$. The mass may oscillate in one dimension only for simplicity. We ...
- 8,848
0votes
0answers
50views
What do we call a material property that has non-equal values when evaluated in opposite directions?
What do we call a material property that has non-equal values when evaluated in opposite directions? That is, if the material property $k_{ij}$ has a value of $X$ along the direction defined by the ...
- 1,475
1vote
0answers
50views
Not all anisotropic porous media can be associated with a symmetric permeability tensor $K_{ij}$?
My intuition tells me that permeability $K_{ij}$ of Darcy's Law is symmetric, $K_{ij}=K_{ji}$, and I am looking for an answer to show me why this is not the case. When measuring the permeability of a ...
- 1,475
6votes
2answers
234views
What's the difference between constitutive laws and equation of state?
While defining material properties in finite element modeling, when should we opt for constitutive models, such as Linear Elastic or Neohookean (that relate stresses and strains) over Equation of ...
0votes
1answer
54views
Regelation, and melting ice with pressure
It is an experimental fact (regelation) that if two weights are hung on the ends of a rigid bar, which passes over a block of ice, then the bar gradually passes through the block of ice. Moreover, the ...
- 1,301
0votes
1answer
134views
In Landau & Lifshitz's 'Theory of elasticity' why $\sigma_{ik}=0$ on the surface for an infinite medium?
It is not clear to me why considering an infinite medium we can consider $\sigma_{ik}=0$. Herewith the section is attached:
-1votes
1answer
93views
How characteristic length scale affects continuum treatment of matter?
I understand that by choosing a particular system with a given characteristic length, the smaller the mean free path ($\lambda$) the greater will be the validity of continuum treatment. Thus, $$...
2votes
2answers
227views
Closure conditions in the form of equation of state
While reading the book "Riemann solvers and numerical methods for fluid dynamics" By E. Toro, the very first paragraph is: "In this chapter, we present the governing equations for the ...
- 123
1vote
0answers
428views
Why does the Navier-Stokes energy equation neglect the pressure-volume work?
A strictly conservative form of the Navier-Stokes energy equation reads (Schlichting, Gersten: Boundary Layer Theory 2017, eq. 3.57) $$\frac{\partial \rho e_t}{\partial t} + \mathrm{div}\left(\rho e_t ...
- 141
3votes
0answers
93views
Differential geometry and the $P \vec A= \vec F$ equation?
How does one write $$\vec F = P \vec A$$ (where $\vec F$ is the force. $P$ is the pressure and $\vec A$ is the area) in the language of differential forms? I'm confused cause $\vec F$ is a one form ...
- 1,401
5votes
3answers
153views
How could we estimate the number of molecules below which a fluid cannot be adequately modeled by the Navier-Stokes equations?
As is known, the Navier-Stokes equations are an approximation in the continuum mechanics to model an aggregate of independent molecules, which, although they can move freely, interact strongly with ...
- 1,700
0votes
1answer
28views
How could we have a non-isothermal deformation without any heat source or heat flux?
I don't understand what does it mean that "no time remains for isothermal removal of heat"? The term "isothermal" means temperature is constant, so how does isothermal removal of ...
2votes
2answers
349views
Why does entropy decreases with the increase of helmholtz free energy?
I came across the following constitutive equation relating entropy with the change of Helmholtz free energy with respect to change in temperature while holding deformation tensor fixed. Source of ...
1vote
0answers
340views
"Bogus Axioms of Continuum Mechanics"
In this very interesting IMA Journal of Applied Mathematics article on the sources of irreversibility in thermodynamics [1] L.C. Woods writes This author has latterly published two articles on the &...
3votes
2answers
579views
Work conjugate pair of stress and strain and $pV$
I am trying to understand the role that the work conjugate pair of stress and strain plays in the enthalpy: $H = U - V_0\mathbf{P}:\mathbf{F}$, where $\mathbf{P} = J\sigma\mathbf{F}^{-T}$ is the 1st ...
- 31
