Understanding Constitutive Definitions in Cont. Mech.: What Does It Mean?

In summary, a constitutive definition in continuum mechanics is a mathematical representation of the relationship between different variables that govern the behavior of a continuous material or system. The key components of a constitutive definition are the dependent and independent variables, parameters or coefficients, and mathematical equations. It is different from a material property, which is an intrinsic characteristic of a material. Understanding constitutive definitions is important in continuum mechanics for predicting the behavior of materials and solving engineering problems. Examples of constitutive definitions include Hooke's law, Fourier's law, and Navier-Stokes equations.
  • #1
mohammed El-Kady
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while I study in cont. mech. I found this equation and in the index he mention that "the difference between the volume supply and the production phi can be recognized only in relation to the constitutive definition of the material"
what does it mean?

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What's cont. mech.?
 
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berkeman said:
What's cont. mech.?
Continuum Mechanics
 
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1. What is the definition of constitutive behavior in continuum mechanics?

Constitutive behavior refers to the response of a material to external forces or stimuli, such as stress, strain, and temperature. It is described by a set of equations that relate the material's internal state to its external behavior.

2. How is constitutive behavior different from material properties?

Material properties are intrinsic characteristics of a material, such as density, elasticity, and strength, while constitutive behavior describes how a material responds to external forces. Material properties are used to define constitutive behavior equations.

3. What is the significance of understanding constitutive definitions in continuum mechanics?

Understanding constitutive definitions allows scientists and engineers to accurately predict the behavior of materials under different conditions, which is crucial for designing and analyzing structures and systems.

4. How are constitutive definitions determined experimentally?

Constitutive definitions can be determined experimentally by subjecting a material to different external forces and measuring its response. These data points are then used to develop equations that describe the material's behavior.

5. Can constitutive definitions change for a material?

Yes, constitutive definitions can change for a material depending on factors such as temperature, strain rate, and microstructural changes. This is why it is important to understand and account for these variations in material behavior when using constitutive definitions in continuum mechanics.

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