Stiffness, strength, hardness, deflection, elasticity, toughness, rigidity, and plasticity are all key indicators in materials mechanics and engineering that describe the properties or structural properties of materials, and they have clear definitions and application scenarios.

Here's a detailed comparison of them:

         1. Stiffness

Definition: The ability of a material or structure to resist elastic deformation.

Key points: The greater the stiffness, the smaller the deformation under the same external force. It is related to the modulus of elasticity (E), but the modulus of elasticity is a material property and stiffness is a structural property.

Applications: Spring design, building seismic resistance (e.g. lateral shift stiffness in high-rise buildings).

2. Strength

Definition: The ability of a material to resist permanent deformation or breakage.

Classification: Tensile strength: The maximum stress against tensile failure. Compressive strength: The ability to resist compressive failure. Yield strength: The critical stress at which the material begins to undergo plastic deformation.

Application: Bridge load-bearing design, mechanical parts selection.

3. Hardness

Definition: The ability of a material surface to resist local pressing or scratching.

Test methods: Brinell hardness (HB), Rockwell hardness (HRC), Vickers hardness (HV).

Relationship with strength: Materials with high hardness usually have higher strength, but there is no strict correspondence.

Application: Tool material selection (high hardness), bearing surface treatment.

4. Deflection

Definition: The amount of elastic displacement generated by a structure (such as beams and plates) when subjected to stress.

Key point: It is the embodiment of stiffness in the actual structure, and large deflection indicates low stiffness. The calculation formula is related to the load type and boundary conditions (such as the deflection formula of the simply supported beam).

Applications: bridge deformation monitoring, robotic arm end precision control.

5. Elasticity

Definition: The ability of a material to regain its original shape after being undone by an external force.

Elastic limit: The maximum stress value at which a material maintains elasticity.

Application: Rubber products, spring design.

6. Toughness

Definition: The ability of a material to absorb energy (including elastic and plastic deformation) before breaking.

Difference from strength: high-strength materials may be brittle (such as ceramic) and have low toughness; Materials with good toughness, such as rubber, are not necessarily strong.

Test method: impact test (such as Charpy impact test).

Application: Bulletproof material, car bumper.

7. Rigidity

Note: In the Chinese context, it is often used interchangeably with "stiffness".

Rigidity: Emphasizes the overall properties of a material or structure that is not prone to deformation (qualitative description).

Stiffness: is a quantitative indicator of rigidity (such as N/m).

Application: Machine bed (high rigidity reduces machining vibrations).

8. Plasticity

Definition: The ability of a material to permanently deform after exceeding its elastic limit.

Key point: Materials with good plasticity (such as copper) can be malleable and formed. In contrast to brittleness, brittle materials such as glass are virtually plastic.

Application: metal stamping forming, plastic processing technology.

Comparison summary

Common misconceptions

Stiffness vs. strength: High stiffness does not necessarily mean high strength (e.g., carbon fiber has high stiffness but may be lower than steel).

Hardness vs. toughness: Diamonds have extremely high hardness but poor toughness and are prone to chipping.

Elastic vs plasticity: elastic deformation is reversible, plastic deformation is irreversible.