Properties of Matter, Elasticity, and Viscosity

Vocabulary flashcards reviewing core definitions, formulas, stress-strain behavior, structural beams, and fluid viscosity concepts from physics and engineering lecture notes.

Elasticity

The property by which a body resists a change in its size or shape when an external force is applied and returns to its original state after the removal of the deforming force.

Perfectly Rigid Material

A material that does not undergo any relative displacement of its parts when an external force acts on it, regardless of how large the force may be.

Restoring Force

Internal reactive forces that come into play when an external force deforms a body, acting in the direction opposite to displacement to restore the body to its original condition.

Stress

The restoring force or recovering force per unit area, expressed mathematically as $\text{stress} = \frac{F}{A}$.

Strain

The ratio of the change in dimension produced by an external deforming force to the original dimension, which possesses no units or dimensions.

Hooke's Law

States that within the elastic limit, the ratio of stress to strain is constant ($\text{stress} \times \text{strain}$).

Modulus of Elasticity

The proportionality constant in Hooke's law, defined as the ratio of stress to strain within the elastic limit.

Poisson's Ratio

The ratio between lateral strain per unit stress ($\beta$) and longitudinal strain per unit stress ($\frac{D-d}{D}$) within the elastic limits, defined as $\frac{\text{lateral strain}}{\text{longitudinal strain}}$.

Young's Modulus

The ratio of longitudinal (or linear) stress to longitudinal (or linear) strain, expressed as $E = \frac{F L}{l A}$ in units of $N m^{-2}$ or Pascal.

Bulk Modulus

The ratio of bulk stress (change in normal force per unit area, $\frac{\text{Change in volume}}{\text{Original volume}}$) to bulk strain ($K = \frac{\text{Bulk stress}}{\text{Bulk strain}}$), represented as $K = \frac{\frac{\text{Change in normal force}}{\text{Area}}}{\frac{\text{Change in volume}}{\text{Original volume}}}$.

Rigidity Modulus

The ratio of shearing stress to shearing strain, expressed mathematically as $\frac{F/A}{\theta}$.

Stress-Strain Curve

A diagram depicting material behavior under tensile stress, outlining the proportional limit, upper/lower yield points, ultimate stress point, plastic behavior, necking, and fracture point.

Elastic Range

The linear portion of the stress-strain curve where a material fully returns to its original dimensions upon release of the applied force.

Plastic Range

The region in the stress-strain curve beyond the elastic limit where permanent deformation occurs in the material.

Yield Stress

The minimum stress that causes permanent plastic deformation in a material.

Ultimate Tensile Strength

The maximum stress that a material can withstand, marking the onset of localized necking.

Necking

A localized decrease in cross-sectional area of a material that leads to a decrease in stress alongside an increase in strain.

Fracture Stress

The specific stress value at which a material breaks or fails completely.

Elastic Behaviour of Brittle Materials

Characteristics of materials that fracture with little elastic deformation, minimal energy absorption, and without significant plastic deformation.

Neutral Filament

The central filament within a bent beam that experiences zero change in length during deformation.

Cantilever

A beam fixed firmly at one end and free at the other end.

I-Shaped Girder

A load-bearing structural beam whose cross-section resembles the letter 'I', designed to minimize bending and weight by increasing depth/thickness while reducing low-stress middle material.

H-Shaped Girder

A structural profile resembling the letter 'H' with wider, thicker flanges and web compared to an I-beam, offering greater cross-sectional area and higher load capacity over longer spans.

Relation Between Elastic Moduli

The theoretical relationship linking Young's modulus ($E$), Bulk modulus ($K$), and Shear modulus ($G$) for isotropic materials: $E = \frac{9 K G}{3 K + G}$.

Viscosity

A measure of a fluid's resistance to flow resulting from internal friction produced by relative motion between adjacent fluid layers.

Dynamic Viscosity

The measurement of a fluid's resistance to flow when an external deforming force is applied.

Kinematic Viscosity

The measurement of a fluid's resistive flow under the weight of gravity.

Streamline Flow

A regular flow in which each fluid particle moves along the exact same path and velocity as its preceding particle, without forming eddies or exceeding the critical velocity.

Turbulent Flow

An irregular fluid flow where particles move in varying directions and velocities exceeding critical velocity, forming eddies and whirlpools.

Shear-Thinning Fluid

A non-Newtonian fluid whose viscosity decreases as the applied shear rate increases.

Shear-Thickening Fluid

A non-Newtonian fluid whose viscosity increases as the applied shear rate increases.

Stoke's Law

States that the viscous friction force acting on a small sphere moving through a viscous fluid is given by $F = 6 \frac{\text{Force}}{\text{area}} \times \text{velocity gradient}$.

Coefficient of Viscosity

The ratio of shearing stress to the velocity gradient of a fluid, expressed as $\frac{F d}{a v}$.