Continuum mechanics- open questions?

In summary, the open problems in continuum mechanics as of today include the unresolved issue of turbulence and the need for tighter multiscale linking in materials constitutive modeling. Other active research areas include fracture mechanics, damage mechanics, and multiple phase flow, where the distinction between gases and liquids can become blurred. There is also ongoing research on the coupling between continuum mechanics and quantum and statistical mechanics.
  • #1
MathematicalPhysicist
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what are the open and still not yet answered problems in continuum mechanics as of today?
i reackon navier-stokes equations solutions is something that is related to the issue, right?
 
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  • #2
Well, the whole messy issue of turbulence might well be considered an open issue. It is anyhow a very active research area.
 
  • #3
On materials side, in their constitutive modeling, one of the trends making progress seems to be tighter multiscale linking. For example, constitutive models of continuum mechanics are fed by & coupled to quantum and statistical mechanics and everything in between, areas of continuum mechanics like fracture mechanics, damage mechanics etc. are going strong and developing (and benefitting lots from this, although there is a lot of research starting only from micro/nano up without the couplings).
 
  • #4
Another important research area is multiple phase flow.
 
  • #5
arildno said:
Another important research area is multiple phase flow.
does this mean that gases and liquids change phases into one another and you can't tell the difference or is it something competely different from what i descrbied.
please, do elaborate arlidno.
 
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1. What is the definition of continuum mechanics?

Continuum mechanics is a branch of mechanics that studies the behavior of materials that are continuously distributed, such as liquids and gases. It is based on the assumption that the material is continuous and can be described by mathematical equations.

2. What are the fundamental principles of continuum mechanics?

The fundamental principles of continuum mechanics are the conservation of mass, conservation of momentum, and conservation of energy. These principles govern the behavior of materials and can be described by mathematical equations such as the Navier-Stokes equations and the energy equation.

3. What are the applications of continuum mechanics?

Continuum mechanics has a wide range of applications, including fluid dynamics, solid mechanics, and heat transfer. It is used in various fields such as engineering, geology, and meteorology to analyze and predict the behavior of materials and fluids.

4. What are the limitations of continuum mechanics?

Continuum mechanics has limitations in its applicability to materials that are not continuous, such as granular materials and polymers. It also does not take into account the atomic and molecular structure of materials, which can be important in certain situations.

5. What are some open questions in continuum mechanics?

Some open questions in continuum mechanics include the development of more accurate and efficient numerical methods for solving the governing equations, the incorporation of more complex material behaviors, and the understanding of the transition from continuum mechanics to molecular dynamics at very small scales.

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