Stress and strain are fundamental concepts in physics that describe how materials respond to forces. They help us understand why buildings stand, bridges don't collapse, and materials bend or break under pressure.

Knowing how to calculate stress and strain is crucial for engineers and designers. It allows them to predict how materials will behave under different loads, ensuring structures are safe and durable in real-world applications.

Stress and Strain Fundamentals

Stress and strain relationship

• Stress measures force per unit area quantified in pascals (Pa) or N/m² using formula $\sigma = F/A$
• Strain quantifies deformation as dimensionless ratio calculated by $\varepsilon = \Delta L / L_0$
• Hooke's law connects stress and strain for elastic materials $\sigma = E\varepsilon$ within elastic limit

Types of stress

• Compressive stress pushes inward causing shortening (weight on building foundation)
• Tensile stress pulls outward resulting in elongation (elevator cable under load)
• Shear stress acts parallel to surface creating angular deformation (bolt holding plates)

Elastic moduli calculations

• Young's modulus (E) measures stiffness under tensile or compressive stress $E = \sigma / \varepsilon$ in Pa
• Shear modulus (G) quantifies resistance to shear deformation $G = \tau / \gamma$ in Pa
• Bulk modulus (K) indicates resistance to uniform compression $K = -V(\Delta P / \Delta V)$ in Pa

Applications of elastic deformation

• Identify variables and given information in problem
• Select appropriate formulas based on stress or strain type
• Convert units and apply Hooke's law within elastic limit
• Consider safety factors for engineering applications (bridge design, material selection)

Material behavior under loading

• Stress-strain curve shows elastic region, yield point, plastic region, ultimate strength, and fracture point
• Ductile materials exhibit large plastic region (copper) while brittle materials show sudden failure (ceramics)
• Fatigue from cyclic loading leads to failure at lower stress levels (airplane wings, bicycle frames)
• Creep causes time-dependent deformation under constant stress, more pronounced at high temps (turbine blades)