The term modulus originates from Latin, broadly meaning a ‘measure’ or ‘form of expression’ of something. In mathematics, physics, and engineering, multiple physical quantities are called modulus (plural: moduli). One important category is known as elastic modulus.
So what is elastic modulus?
You can understand it this way: elastic modulus is a general term referring to an object’s ability to resist elastic deformation when subjected to stress. Since stress can be classified into different types, the corresponding elastic moduli have their own specific definitions.
In engineering, we commonly encounter four types of modulus: tensile modulus, shear modulus, bulk modulus, and flexural modulus.
This article organizes the basic concepts of these four common moduli.
I. Tensile Modulus
Tensile modulus, also known as Young’s modulus, symbol E, is the most commonly used modulus. It is primarily used to describe the tensile and compressive elasticity of materials—that is, the tendency of an object to deform along the axis when subjected to force in the axial direction.
It is defined as the ratio of tensile stress to tensile strain, representing the slope of the linear portion in the stress-strain curve, as shown below:
Application Scenarios:
1. Rods, beams, cables, and other components primarily subjected to axial tension/compression
2. Basic mechanical property characterization for most metals, plastics, and composite materials
3. The most commonly used elastic modulus parameter in finite element analysis
II. Shear Modulus
Shear modulus, also known as modulus of rigidity, symbol G, primarily describes the tendency of an object to undergo shear deformation (shape change without volume change) when subjected to opposing forces.
It is defined as the ratio of shear stress to shear strain. It can be calculated by dividing the shear force per unit area by the displacement of the material edge.
Relationship with Young’s modulus (for isotropic materials): G = E / [2(1 + ν)], where ν is Poisson’s ratio.
Application Scenarios:
1. Torsion shafts, springs, shear pins
2. Thin-walled structures, sandwich panels, adhesive layers
3. Polymer, rubber, and viscoelastic material property characterization
4. Used when inputting shear stiffness in finite element analysis
III. Bulk Modulus
Bulk modulus, symbol K, primarily describes the volume elasticity of a material—that is, the tendency of an object to deform in all directions when subjected to uniform loading from all sides.
It is defined as the ratio of volumetric stress to volumetric strain, and is the reciprocal of compressibility. Bulk modulus is the extension of Young’s modulus into three-dimensional space, as shown below.
Application Scenarios:
1. High-pressure environments (such as deep sea, oil drilling)
2. Hydrostatic forming, explosive forming
3. Characterization of nearly incompressible materials such as rubber, liquids, and soft tissue
4. Geophysics, geomechanics
IV. Flexural Modulus
Flexural modulus, symbol E_flex, primarily describes the tendency of an object to undergo bending deformation under the action of a moment. Also known as the modulus of rupture, it reflects the material’s ability to resist bending.
Characteristics and Notes:
1. For isotropic homogeneous materials, flexural modulus ≈ tensile modulus
2. For fiber-reinforced composite materials, flexural modulus is typically higher than tensile modulus (because fibers are mainly distributed on the surface, and surface fibers bear more load during bending)
3. Commonly used for plastics, composite materials, wood, ceramics, and other plate/rod materials
4. Very sensitive to surface defects, fiber orientation, and interlaminar properties
V. Summary Comparison Table
VI. Setting Material Modulus in ANSYS Workbench
ANSYS Mechanical allows users to input Young’s modulus, shear modulus, and bulk modulus. The following shows how to find the modulus input options in the ANSYS Workbench engineering data module.
Do you now understand these four moduli?
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