In the field of materials science and engineering, stiffness, strength, hardness, deflection, elasticity, toughness, rigidity and plasticity are important concepts that describe the mechanical properties of materials. These concepts are interrelated, but each has a unique definition and practical applications.

I. Stiffness

Definition: Stiffness refers to the ability of a material or structure to resist elastic deformation when subjected to force. It is a reflection of the material's inherent deformation characteristics, the core indicator is the modulus of elasticity (Young's modulus, E), calculated as stiffness = stress / strain (E = σ / ε).

Example: Take steel and rubber for example, if you stretch them with the same force, the steel will hardly deform, while the rubber will be significantly elongated. This is because steel has a much higher stiffness than rubber, i.e. steel is more able to resist elastic deformation when a force is applied.

Difference with other concepts: Stiffness is a material property and is directly related to the modulus of elasticity of a material, whereas it is not directly related to other concepts such as strength and hardness. Stiffness describes the performance of a material within the range of elastic deformation, while strength is concerned with the ability of a material to resist plastic deformation or fracture.

II. Strength

Definition: Strength is the ability of a material to resist permanent deformation or fracture. According to the different stages of resistance to deformation, strength can be divided into yield strength (the beginning of plastic deformation of the stress) and tensile strength (the maximum stress that can be withstood before fracture) and so on.

Example: Reinforcing bars have high strength and can withstand large tensile forces without breaking, so they are often used as load-bearing materials in building structures; while chalk has low strength and will break when gently broken.

Difference with other concepts: Strength is concerned with the ability of a material to resist damage during stress, unlike stiffness, which is not limited to the elastic deformation range. Although hardness is also related to the material's ability to resist deformation, but hardness is more focused on the material surface resistance to local indentation or scratch ability.

III. Hardness

Definition: Hardness is the ability of a material surface to resist localised indentation or scratching. It is an important indicator of the material's ability to resist wear and tear, test methods include Brinell hardness (HB), Rockwell hardness (HRC), Vickers hardness (HV) and so on.

Example: Diamond is one of the hardest substances in nature and can easily scratch other materials; rubber, on the other hand, has very low hardness and is easily scratched.

Difference with other concepts: Hardness is a comprehensive mechanical property index, with the material's elasticity, strength, plasticity, etc. are related. However, compared with the stiffness, hardness is more focused on the local resistance of the material surface; compared with the strength, hardness is more concerned about the performance of the material in resistance to local indentation or scratches.

IV. Deflection

Definition: Deflection is the amount of elastic deformation displacement produced by the structure when it is subjected to force. It is related to the size of the load, material stiffness (E) and structural geometry.

Example: When a plank is built on two ends and a person stands in the middle, the plank will bend downward by a certain amount, and this amount is the deflection.

Difference with other concepts: Deflection describes the overall deformation of a structure when subjected to a force and is directly related to the stiffness of the material. The greater the stiffness, the smaller the deflection of the structure when subjected to a force. In contrast to strength, deflection is more concerned with the deformation of the structure within the elastic deformation range and does not involve the destruction of the material.

V. Elasticity

Definition: Elasticity is the ability of a material to recover its original shape after unloading. It is a property inherent in the material, the elastic limit is the maximum stress value of the material can completely restore the deformation.

Example: rubber bands can spring back to their original length after being stretched and released, and springs can be restored to their original length after being compressed, all of which are manifestations of material elasticity.

Difference with other concepts: elasticity and stiffness are closely related, because the stiffness is to describe the ability of the material to resist elastic deformation. However, elasticity focuses more on describing the ability of a material to recover after unloading, whereas stiffness is more concerned with the ability of a material to resist deformation when subjected to a force. In contrast to plasticity, elasticity describes the property of a material that can be fully recovered after deformation, whereas plasticity refers to the property of a material that cannot be fully recovered after deformation.

VI. Toughness

Definition: Toughness refers to the ability of the material to absorb energy before fracture. It is a combination of material strength and plasticity, indicators include impact toughness (energy absorbed per unit volume) and fracture toughness (resistance to crack expansion) and so on.

Example: bulletproof glass high toughness, in the impact can absorb a lot of energy and not broken; and ceramic toughness is low, easy to be directly broken by the impact.

Difference with other concepts: toughness is a comprehensive performance indicators, it is both with the strength of the material (because the strength of the material determines the ability to resist damage), but also with the plasticity of the material (because the plasticity of the material determines how much energy can be absorbed in the deformation process). Compared with the stiffness, toughness is more concerned about the energy absorption capacity of the material before fracture, rather than the ability to resist elastic deformation.

VII. Rigidity

Definition: Rigidity is the ability of the structure as a whole to resist deformation. It is related to both the stiffness of the material and the geometry of the structure (e.g. section size).

Example: two beams of the same length and material, if the cross-section size is different, then the beam with the larger cross-section size is more rigid, i.e., the ability to resist deformation is stronger.

Difference with other concepts: Stiffness is a structural property, not a material property. It describes the ability of the entire structure to resist deformation when subjected to a force, not just the properties of the material itself. Compared with stiffness, rigidity is more focused on describing the overall performance of the structure, rather than the local performance of the material.

VIII. Plasticity

Definition: plasticity refers to the material in excess of the elastic limit of permanent deformation without breaking the ability. It is a material in the force process of plastic deformation of a property, the indicators include elongation (stretching length change percentage) and section shrinkage.

Examples: Metals can deform plastically without breaking during stamping and thus be worked into various shapes; clay can also deform plastically and retain its shape during kneading and moulding.

Differences from other concepts: Plasticity, as opposed to elasticity, describes the inability of a material to recover completely after deformation. In contrast to strength, plasticity is more concerned with how a material behaves during deformation than with its ability to resist damage. In contrast to toughness, which also describes the nature of a material during deformation, toughness focuses more on the ability of a material to absorb energy before fracture, whereas plasticity is more concerned with the ability of a material to deform permanently during deformation.