Determine the creep compliance J(t) of a material that responds like:
a) an elastic spring with Young's modulus E
J(t):
b) a viscous dashpot with viscosity η as a function of time t)
J(t):
c) the Maxwell model (E for spring, and η for dashpot as a function of time t)
J(t):
d) the Voigt model (E for spring, and η for dashpot as a function of time t)
J(t):
To determine the creep compliance J(t) of different material models, we need to understand the behavior of each model and the equations that describe them. Let's break down each case:
a) Elastic spring model:
In this model, the material behaves like an idealized elastic spring governed by Hooke's Law. The equation for the creep compliance J(t) is given by J(t) = 1 / (E * t), where E is the Young's modulus of the material and t is the time.
b) Viscous dashpot model:
In this model, the material behaves like a viscous fluid, exhibiting a time-dependent deformation. The equation for the creep compliance J(t) is given by J(t) = η * t, where η is the viscosity of the material.
c) Maxwell model:
The Maxwell model is a combination of an elastic spring and a viscous dashpot in series. It represents materials with both elastic and viscous properties. In this model, the creep compliance J(t) is given by J(t) = (1 / E) + (η * t).
d) Voigt model:
The Voigt model is a combination of an elastic spring and a viscous dashpot in parallel. It represents materials with both elastic and viscous properties. In this model, the creep compliance J(t) is given by J(t) = (1 / E) * (1 + (η * t)).
To determine the creep compliance J(t) for any given time t, you need to know the values of the material properties: Young's modulus (E) for the spring component and viscosity (η) for the dashpot component if applicable. Once you have these values, you can plug them into the relevant equation for the material model you are considering.