Elastic and isotropic constitutive relationship

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SUMMARY

The discussion centers on the necessity of incorporating an indeterminate hydrostatic term in the stress tensor for incompressible materials, applicable to both solids and fluids. Incompressibility implies that hydrostatic stress, or constant pressure, results in zero strain, making it impossible to derive hydrostatic stress from the strain tensor alone. Participants emphasize that hydrostatic pressure acts as a mean normal stress and cannot be eliminated from Hooke's law in indeterminate situations, highlighting its critical role in load transmission through materials.

PREREQUISITES
  • Understanding of stress tensors in continuum mechanics
  • Familiarity with Hooke's law and its applications
  • Knowledge of incompressible material behavior
  • Basic principles of fluid mechanics and solid mechanics
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  • Research the mathematical formulation of stress tensors in elastic materials
  • Study the implications of incompressibility in solid and fluid mechanics
  • Explore advanced topics in continuum mechanics related to indeterminate structures
  • Learn about the role of hydrostatic pressure in various engineering applications
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Mechanical engineers, materials scientists, and students studying continuum mechanics who seek to deepen their understanding of elastic and isotropic constitutive relationships in incompressible materials.

ftarak
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Hi everybody,
I have just a question about elastic and isotropic constitutive relationship

Why does the stress tensor need an indeterminate hydrostatic term for an incompressible material? for both solids and fluids.
 
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"Incompressible" means that if you have a hydrostatic stress (or a constant pressure, which is the same thing), the strain is zero.

So you can't get the hydrostatic stress by multiplying the strain tensor by something.

But it is a phsyically real stress, that transmits loads through the solid or fluid, so you have to include it in the model some other way.
 
AlephZero said:
"Incompressible" means that if you have a hydrostatic stress (or a constant pressure, which is the same thing), the strain is zero.

So you can't get the hydrostatic stress by multiplying the strain tensor by something.

But it is a phsyically real stress, that transmits loads through the solid or fluid, so you have to include it in the model some other way.

thank you for your answer. that was helpful. I got the point, the point is that the hydrostatic pressure is mean normal stress. and we cannot cancel out the hydrostatic term in the Hooke's law in the situation, which is indeterminate.
 

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