How Do Maxwell Elements in Parallel Derive Force Elongation Relationships?

Click For Summary
SUMMARY

The discussion focuses on deriving the force elongation relationship for Maxwell elements in parallel, specifically in relation to Kelvin-Voigt elements in series. The key equation referenced is Equation 2.93, which states F = D * Delta^n. The user expresses confusion over the derivation of the powers of the differentials on the right-hand side of the equation, indicating that they can derive the left-hand side but struggle with the right-hand side's complexity. Clarification on this derivation is sought from the forum community.

PREREQUISITES
  • Understanding of Maxwell elements and their behavior in viscoelastic materials.
  • Familiarity with Kelvin-Voigt model mechanics.
  • Knowledge of differential equations and their applications in material science.
  • Ability to interpret and manipulate mathematical equations in the context of physics.
NEXT STEPS
  • Research the derivation of force elongation relationships in viscoelastic materials.
  • Study the mathematical principles behind differential equations in material mechanics.
  • Explore the differences between Maxwell and Kelvin-Voigt models in viscoelasticity.
  • Examine practical applications of these models in engineering and material science.
USEFUL FOR

Students and professionals in materials science, mechanical engineering, and physics who are working with viscoelastic materials and require a deeper understanding of force elongation relationships in complex systems.

La82
Messages
5
Reaction score
0

Homework Statement


Not sure this is the right place for this but here it goes...
I am trying to figure out the derivation of the force elongation relationship of the maxwell elements in parallel in order to derive it for the Kelvin Voigt elements in series.
I have attached the material that I am using, the derivation is on page 47 and I can't seem to figure out how they get the different powers of the Differentials in 2.93. The lefthand side I can easily derive, but as far as I can tell the right hand side should just be = D Delta.

It is probably really simple, but my mind is going blank at the moment.

Hope someone can help me
 

Attachments

Last edited:
Physics news on Phys.org
out here.Homework Equations 2.93F = D * Delta^nThe Attempt at a SolutionI have been trying to solve this for some time now, but I can't seem to figure out how they get the different powers of the Differentials in 2.93. The lefthand side I can easily derive, but as far as I can tell the right hand side should just be = D Delta.
 

Similar threads

Derive Fresnel's Equations for Parallel Incidence using Maxwell's BC's
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Magnetic field when the area of the plates of a capacitor increases
  • · Replies 7 ·
Replies
7
Views
2K
High School Applying the Gauss (1835) formula for force between 2 parallel DC currents
  • · Replies 6 ·
Replies
6
Views
1K
How to Derive Non-Linear Behaviour in Simpack's Force Element F042?
  • · Replies 1 ·
Replies
1
Views
1K
How Do Particles Leak from a Container and Reach a Spherical Cap?
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Force using the Maxwell Stress Tensor
  • · Replies 1 ·
Replies
1
Views
6K
Force between 2 parallel magnetic dipole moments
  • · Replies 1 ·
Replies
1
Views
5K
Evaluate the partial derivative of a matrix element
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Deriving Maxwell's Equations from Field Tensor (Griffith 4ed)
  • · Replies 6 ·
Replies
6
Views
3K
High School How Does Parallel Transport Affect Vector Components and Their Changes?
  • · Replies 24 ·
Replies
24
Views
3K