12.8
Strain and Elastic Modulus
The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume…
The amount of deformation experienced by an object under stress, divided by its initial dimensions, is called strain. Strain is a dimensionless quantity.
If the deformation due to the applied force results in an increase in the length of an object, it is called tensile strain. Whereas, if the length decreases due to stress, it is called compressive strain.
The change in the volume of an object due to the applied force in all directions is known as bulk strain. If the direction of the force is parallel to the object's plane, it undergoes deformation along that plane, and this is known as shear strain.
For small deformations, the elastic modulus is defined as the ratio of the stress exerted on the object to the resultant strain.
Young's modulus is the ratio of tensile stress to tensile strain. The ratio of volumetric stress to volumetric strain is known as bulk modulus, whereas the ratio of shear stress to shear strain corresponds to shear modulus.
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Q1: What is strain and how does it differ from stress?
Strain is the fractional deformation of an object under stress, expressed as the change in dimension divided by the initial dimension. Unlike stress, which is the applied force per unit area, strain is dimensionless and describes the object's response to that force. Strain quantifies how much an object actually deforms when stress is applied.
Q2: What are the main types of strain?
The four main types of strain are tensile strain (length increase), compressive strain (length decrease), bulk strain (volume change from all-direction forces), and shear strain (deformation along a plane when force is parallel to the surface). Each type corresponds to different stress applications and describes distinct deformation patterns in materials.
Q3: How does elastic modulus relate to stress and strain?
Elastic modulus is the proportionality constant between stress and strain for small deformations, calculated as the ratio of stress to strain. Materials with large elastic moduli resist deformation, while those with small moduli deform easily under the same stress. For example, steel has a much larger elastic modulus than rubber, so rubber deforms more under identical stress.
Q4: What is Young's modulus and when is it used?
Young's modulus is the elastic modulus for tensile or compressive stress, measuring a material's resistance to length changes. It is calculated as the ratio of tensile stress to tensile strain and applies when forces pull or push along the object's length. Young's modulus is commonly used to characterize how stiff materials are under tension or compression.
Q5: What is the difference between bulk modulus and shear modulus?
Bulk modulus measures resistance to volume change under pressure from all directions, calculated as volumetric stress divided by volumetric strain. Shear modulus measures resistance to shape change when force is parallel to a surface, calculated as shear stress divided by shear strain. Both are elastic moduli but apply to different types of deformation.
Q6: Why is elastic modulus measured in pascals?
Elastic modulus is measured in pascals because strain is dimensionless. Since elastic modulus equals stress divided by strain, and stress is measured in pascals, the unit of elastic modulus is also pascals. This allows direct comparison of elastic moduli across different materials and stress types.
Q7: How does the relationship between stress and strain change for large deformations?
For small deformations, stress and strain are directly proportional, with elastic modulus as the constant of proportionality. However, for larger deformations, this linear relationship breaks down. The proportionality only holds when stress is sufficiently low; beyond that threshold, the relationship becomes nonlinear and problem solving on stress and strain requires more complex analysis.