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What is the phenomenon called when a body is suddenly strained, and the strain is maintained constant afterward, causing the stresses induced in the body to decrease with time?
What is the phenomenon called when a body is suddenly strained, and the strain is maintained constant afterward, causing the stresses induced in the body to decrease with time?
Stress relaxation
What is the phenomenon called when a body is suddenly stressed and the stress is maintained constant afterward, causing the body to continue to deform?
What is the phenomenon called when a body is suddenly stressed and the stress is maintained constant afterward, causing the body to continue to deform?
Creep
What is the phenomenon called when the stress-strain relationship in the loading process is different from the unloading process?
What is the phenomenon called when the stress-strain relationship in the loading process is different from the unloading process?
Hysteresis
Which of the following are features of viscoelasticity? (Select all that apply)
Which of the following are features of viscoelasticity? (Select all that apply)
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What are the three mechanical models commonly used to discuss the viscoelastic behavior of materials?
What are the three mechanical models commonly used to discuss the viscoelastic behavior of materials?
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A dashpot is a device that represents a viscous component in a viscoelastic model. It produces instantaneously a deformation proportional to the load.
A dashpot is a device that represents a viscous component in a viscoelastic model. It produces instantaneously a deformation proportional to the load.
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A linear spring is a device that represents an elastic component in a viscoelastic model, producing instantaneously a deformation proportional to the load.
A linear spring is a device that represents an elastic component in a viscoelastic model, producing instantaneously a deformation proportional to the load.
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In a Maxwell model the same force is transmitted from the spring to the dashpot, resulting in the dashpot having a velocity of F/η and the spring having a displacement of F/μ .
In a Maxwell model the same force is transmitted from the spring to the dashpot, resulting in the dashpot having a velocity of F/η and the spring having a displacement of F/μ .
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In a Voigt model, the spring and the dashpot have the same displacement producing a total force F = μu + ηu.
In a Voigt model, the spring and the dashpot have the same displacement producing a total force F = μu + ηu.
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The Kelvin model, also known as the standard linear solid, incorporates a spring and a dashpot in series, with the force being the sum of the force from the dashpot and the force from the spring.
The Kelvin model, also known as the standard linear solid, incorporates a spring and a dashpot in series, with the force being the sum of the force from the dashpot and the force from the spring.
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What is the name of the function that describes the elongation produced by a sudden application of a constant force at t=0?
What is the name of the function that describes the elongation produced by a sudden application of a constant force at t=0?
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What is the name of the function that describes the force required to maintain a constant elongation, and changes from zero to unity at t=0 and remains unity thereafter?
What is the name of the function that describes the force required to maintain a constant elongation, and changes from zero to unity at t=0 and remains unity thereafter?
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The Boltzmann formulation generalizes the relaxation function by representing it with a series of exponential terms with varying amplitudes and characteristic frequencies in the form: k(t) = Σ (a_n) exp[-t/τn].
The Boltzmann formulation generalizes the relaxation function by representing it with a series of exponential terms with varying amplitudes and characteristic frequencies in the form: k(t) = Σ (a_n) exp[-t/τn].
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What is the term used to describe the set of amplitudes an associated with each characteristic frequency vn for the relaxation functions, when plotted on a frequency axis?
What is the term used to describe the set of amplitudes an associated with each characteristic frequency vn for the relaxation functions, when plotted on a frequency axis?
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The Boltzmann formulation provides a linear explanation of the relationship between stress and strain in a viscoelastic material, meaning a doubling of the load will double the elongation.
The Boltzmann formulation provides a linear explanation of the relationship between stress and strain in a viscoelastic material, meaning a doubling of the load will double the elongation.
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The time derivatives of stress and strain are important considerations in the Boltzmann formulation, especially when dealing with small, infinitesimal displacements, strains, and velocities.
The time derivatives of stress and strain are important considerations in the Boltzmann formulation, especially when dealing with small, infinitesimal displacements, strains, and velocities.
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Study Notes
Viscoelasticity
- Viscoelasticity describes materials that exhibit both viscous and elastic properties.
- Stress relaxation: When a material is strained and then the strain is held constant, the stress decreases over time.
- Creep: When a material is stressed and then the stress is held constant, the material continues to deform over time.
- Hysteresis: When a material is subjected to cyclic loading, the stress-strain relationship during loading is different from the relationship during unloading.
- These three characteristics (hysteresis, relaxation, creep) are features of viscoelasticity found in many materials.
Models of Viscoelastic Materials
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Mechanical models describe the viscoelastic behavior of materials.
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Maxwell model: Composed of a spring and a dashpot in series. The force is equal to the sum of the force in the spring and the dashpot. The velocity of the spring extension is denoted by a dot.
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Voigt model: Composed of a spring and a dashpot in parallel. The force is shared by both elements. The displacement is the same for both.
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Kelvin model (standard linear solid): Composed of a spring and a dashpot in series with a spring. The force is shared by all three elements.
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All viscoelastic models involve combinations of linear springs and dashpots.
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Springs produce instantaneous deformations proportional to load.
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Dashpots produce velocities proportional to load instantaneously.
Initial Conditions
- If a force is suddenly applied at time t=0, the spring will immediately deform, while the dashpot will take time to deform (its initial deflection is zero).
- Initial conditions for each model are stated.
Voigt Model
- In the Voigt model, spring and dashpot share the same displacement. The total force is the sum of the forces exerted by the spring and the dashpot, accounting for their individual deformations/velocities.
Kelvin Model
- The Kelvin (standard linear solid) model breaks down displacement into two parts (u₁ and u'₁).
- The total force is the sum of the forces of the elements.
- The equations relating the elements are summarised.
Boltzmann Formulation
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The Maxwell, Voigt, and Kelvin models are special cases of the more general Boltzmann formulation.
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The relaxation function describes how a material responds to a sudden step change in strain.
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The function is expressed as a sum of exponential terms, and the constants represent time for relaxation.
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A plot of an(νn) is called a spectrum of relaxation functions.
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Generalization to a continuous spectrum is sometimes required, such as in the case of living tissue like mesentery.
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Equations have been generalized to tensors for situations involving the more complex situations of stress and strain tensors.
Simplifications and Additional Considerations
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Finite deformations are more mathematically challenging than infinitesimal deformations.
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For simpler analyses, infinitesimal displacements, strains, and velocities are generally assumed.
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Special consideration might be given to the effects of stress rates and the initial conditions given by the jumps in the strain history. Stress rate is complex and more difficult to handle mathematically.
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The equations shown express the relationships between force, strain, and time.
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Description
Explore the fascinating world of viscoelastic materials, which showcase both viscous and elastic properties. This quiz covers key concepts such as stress relaxation, creep, hysteresis, and the mechanical models used to describe these behaviors, including the Maxwell and Voigt models.
