In material selection and design, questions like “Is this material strong enough?” “Will this structure bend?” “Will changing this steel be effective?”… all rely on the evaluation of several core performance indicators.

Today, from the perspective of material mechanics, we’ll systematically review eight common performance parameters, including stiffness, strength, hardness, toughness, and elasticity, to help you better understand material selection and design!

Stiffness—Resistance to Elastic Deformation

• Definition: The ability to resist elastic deformation describes how easily a material or structure moves under a certain load.
• Formula: k = F / δ
• Stiffness: Determined by the elastic modulus E (E = σ/ε)
• Structural stiffness: Determined in conjunction with E, geometric characteristics, and boundary conditions

Directional stiffness:

• Axial stiffness (e.g., tension spring)
• bending stiffness (e.g., beam)
• torsional stiffness (e.g., drive shaft)

▶ Example: A steel bar is more resistant to compression and deformation than a plastic rod of the same length and diameter, and therefore has greater stiffness; the elastic moduli of the two materials differ significantly.

Strength—The ultimate resistance to failure.

Definition: The maximum stress a material can withstand before failure. Common forms include:

• Yield strength (σ_y): The starting point of plastic deformation
• Tensile strength (σ_u): The maximum tensile stress a material can withstand
• Compressive strength: The ultimate resistance to compressive failure (e.g., concrete)

▶ Examples: A rubber band can be stretched very long without breaking easily; a steel wire is difficult to stretch but will suddenly break when the stress reaches its limit.

Strength ≠ stiffness. High-strength materials are not necessarily high in stiffness; the key lies in the modulus!

Hardness—Resistance to localized plastic deformation

Definition: Refers to a material’s ability to resist indentation or scratching. It is a local mechanical property.

Common testing methods:

• Brinell hardness (HB): Applicable to soft metals
• Rockwell hardness (HRC): Applicable to steel products
• Vickers hardness (HV): Applicable to micro-regions or thin films

▶ Misconception: High hardness does not equal high strength. Ceramics are hard but brittle and have low impact resistance.

Deflection—The lateral deformation of a structure under load.

Definition: The maximum elastic displacement of a structural member (such as a beam or slab) under a lateral load.

Common calculation (for simply supported beams with central load): δ = (F·L³)/(48·E·I)

• E: Elastic modulus
• I: Section moment of inertia
• L: Span

Standard control:

• Building slabs: δ ≤ L/360
• Bridge structures: δ ≤ L/80

▶ Examples: Wind sway control of buildings and mid-span deflection testing of bridges are typical deflection control scenarios.

Elasticity—Recoverable deformation capacity

Definition: The ability of a material to return to its original shape after loading and unloading.

Hooke’s law: σ = E⋅ε

• σ: Stress
• ε: Strain
• E: Elastic modulus, reflecting the material’s resistance to deformation.

▶ Example: Plucking a guitar string and seeing it quickly return to its original shape after deformation—typical elastic behavior.

Toughness—Energy Absorption Capacity + Crack Resistance

Definition: The amount of energy a material can absorb before actually breaking or destroying. It measures the material’s ability to withstand both elastic and plastic deformation.

Common Indicators:

• Impact Toughness AKV (unit: J)
• Fracture Toughness KIC (unit: MPa·√m)

▶ Example: Safety glass and polycarbonate do not shatter instantly under impact like ordinary glass. Instead, cracks propagate slowly, demonstrating excellent toughness.

Rigidity—Qualitatively describes the feeling of “toughness”

Definition: A non-quantitative indicator used to describe a state characterized by minimal overall deformation and a “hard” feel.

▶ Example: “Strong rigidity” is often a perceptual judgment, while “high stiffness” can be calculated using a formula. In practical engineering, the concept of “stiffness” should be prioritized.

Plasticity—Deformability + Formability

Definition: The ability of a material to undergo permanent deformation without breaking even after stress exceeds its yield strength.

Key Properties:

• Ductility: e.g., elongation after fracture
• Forgeability: the ability to maintain plasticity after undergoing compressive stress

▶ Example: Pure copper and low-carbon steel have good plasticity and excellent formability, making them suitable for processes like forging and rolling.

In engineering material selection and structural design, there is no “universal material,” only the “optimal property combination.” Achieving structural stability, reasonable cost, and manufacturability requires a balance between key properties such as stiffness, strength, hardness, toughness, elasticity, and plasticity. Understanding the significance and applicable scenarios of each property is the foundation for informed material selection and design optimization.