What is the definition of a viscoelastic material?
Viscoelastic materials are those for which the relationship between stress and strain depends on time
Name three viscoelastic phenomena.
Creep
stress relaxation
sinusoidal strain
How is the time dependency of stress in viscoelastic materials expressed?
How is creep compliance and creep modulus described?
How is relaxation modulus and compliance described?
How does the creep mechanism look like for different mechanics?
Describe the mechanism of creep.
Creep is the deformation due to a constant stress sigma0 as a function of time. The strain is monitored.
What are the classifications of materials for creep.
rheological solid: deformation increase until limit.
rheological liquid: deformation until fracture.
Describe the shape of the creep compliance function.
sigmodial with Dr (r=relaxed) and Du (u=unrelaxed) limiters (epsilon=sig)
Describe the mechanism of relaxation.
At t0 a strain is applied, and the stress variation is monitored.
How does the relaxation mechanism look like for different mechanics?
Describe the shape of the relaxation modulus function.
anti sigmodial with Er (r=relaxed) and Eu (u=unrelaxed) limiters (epsilon=sig)
What are the conversion rules between creep and relaxation compliance?
How is an information about linear and non linear viscoelastic behaviour obtained?
By plotting isochronic (the same time) stress strain curves.
How is non linear viscoelasticity described?
D = D(t, sigma(t))
E = E(t, epsilon(t))
Which two laws can be combined to describe viscoelastic behaviour?
Combination of spring element (pure elastic behaviour) and dashpot element (pure viscous behaviour).
How can viscoelasticity be described, using the Maxwell model?
How does the Maxwell model apply specifically for the creep and relaxation behaviour?
How can viscoelasticity be described, using the Voigt model?
What does recovery describe in viscoelastic models?
The spontanious removal of the initial elongation or stress.
How does the Voigt model apply specifically for the creep and relaxation behaviour? How does it behave for recovery?
creep:
relaxation:
How can the recovery of the voigt model be described?
What are the drawbacks of the Maxwell model?
It doesnt dexcribe creep and recovery behaviour correctly.
What are drawbacks of the Voigt model?
relaxation behaviour is not adequately described
How can viscoelasticity be described, using the Maxwell-Wiechert model?
Maxwell models in series:
How does the Maxwell-Wiechert model apply for relaxation?
How is the retardation time defined?
How can viscoelasticity be described, using the Voigt-Kelvin model?
How does the Voigt-Kelvin model apply to creep?
How can viscoelasticity be described, using the standard linear solid (or Zener) model? What is the consitutive equation?
How is the compliance calculated in the Voigt Kelvin model?
What is the solution of the constitutive differential equation for creep in the Zener model? What is the boundary equation?
boundary equation: (dashpot element doesnt deform at t=0)
What is the solution of the constitutive differential equation for relaxation in the Zener model? What is the boundary equation?
boundary condition:
What is the solution of the constitutive differential equation for recovery for creep in the Zener model? What is the boundary equation?
Boundary condition:
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