Material Properties: Viscoelasticity 1. Maxwell model of viscoelastic materials 2. Kelvin-Voigt mod…
Автор: Numerade Mathematics
Загружено: 2025-03-29
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Material Properties: Viscoelasticity 1. Maxwell model of viscoelastic materials 2. Kelvin-Voigt model of viscoelastic materials (solid-type) 3. Standard-Linear-Solid (SLS) model of viscoelastic materials In viscoelastic materials, the behavior is a combination of both elastic and viscous properties. The Maxwell model represents the viscoelastic behavior by combining an elastic element (spring) and a viscous element (dashpot) in series. The strain in the material, de(t), is given by the equation: de(t) = Et + n * dt where E is the elastic modulus (Young #x27;s modulus) and n is the viscous modulus. The Kelvin-Voigt model represents the viscoelastic behavior by combining an elastic element (spring) and a viscous element (dashpot) in parallel. The strain in the material, de(t), is given by the equation: de(t) = E * creep + E * stress relaxation where creep is the creep compliance and stress relaxation is the relaxation modulus. The Standard-Linear-Solid (SLS) model is a more complex model that combines multiple elements to represent the viscoelastic behavior. It consists of an elastic element (spring) in parallel with a series combination of a dashpot and an elastic element. The strain in the material, de(t), is given by the equation: de(t) = E * stress + L * stress relaxation + E * creep where L is a constant. It is important to note that each viscoelastic model has its advantages and disadvantages. The Maxwell model is simple and easy to understand, but it does not accurately represent the behavior of many viscoelastic materials. The Kelvin-Voigt model is more accurate, but it requires more parameters to describe the material behavior. The SLS model is the most complex, but it can accurately represent a wide range of viscoelastic behaviors. To derive the constitutive equations for these viscoelastic models, one must consider the relationships between stress, strain, and time. Creep compliance and relaxation modulus are important parameters in characterizing the viscoelastic behavior of materials. References: - [Insert relevant references here]
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