Architecture of Matter

NODE 01

Matter as Structure

• Interatomic/intermolecular forces.
• Fixed average positions.
• Rigid object vs Deformable body.

NODE 02

Deformation

◀▶

• External force changes shape/dimensions.
• Stretching, Compression, Bending, Twisting, Shearing.

NODE 03

Elasticity

• Tends to return to original configuration.
• After deforming force is removed.
• Elastic ≠ "Soft".

NODE 04

Plasticity

• Deformation remains after removing force.
• Permanent deformation.
• Crucial for metal forming/manufacturing.

NODE 05

Force Distribution

• Force transmitted through material.
• Internal vs External forces.
• Distributed loading over an area.

NODE 06

Stress

σ =FORCEAREA

• Force distributed over area.
• SI Unit: Pascal (Pa).
• Same force = diff stress based on area.

NODE 07

Tensile Stress

◀▶

• When a body is pulled.
• Pull → elongation.
• Wires, cables, ropes.

NODE 08

Compressive Stress

▼▲

• When a body is pushed/compressed.
• Shortening, load-bearing.
• Building columns, pillars.

NODE 09

Shear Stress

▶

• Forces act tangentially to surface.
• Shape change (parallelogram).
• Cutting, rivets, bolts.

NODE 10

Strain

Δ DEFORMATIONORIGINAL SIZE

• Deformation relative to original size.
• Dimensionless quantity.

NODE 11

Longitudinal Strain

L

L+ΔL

• ε = ΔL / L.
• Tensile or compressive.
• Relative to original length.

NODE 12

Lateral Strain

• Change in dimensions perpendicular to force.
• Stretch → typically thinner.
• Compress → typically wider.

NODE 13

Poisson's Ratio

ν =LATERAL STRAINLONGITUDINAL STRAIN

• Ratio of lateral to longitudinal strain.
• Relates to material volume preservation.

NODE 14

Hooke's Law

STRESS=E× STRAIN

• Within elastic region: stress ∝ strain.
• Stress = elastic modulus × strain.
• Connects to spring law F = kx.

NODE 15

Young's Modulus (Y)

Y =LONG. STRESSLONG. STRAIN

• Resistance to longitudinal deformation.
• Y = (F/A) / (ΔL/L).
• Higher Y = stiffer material.

NODE 16

Bulk Modulus (K)

K =- ΔPΔV / V

• Resistance to volume deformation.
• Pressure vs Volume change.
• Connects to fluids/gases.

NODE 17

Shear Modulus (G)

G =SHEAR STRESSSHEAR STRAIN

• Resistance to shear deformation.
• Tangential deformation (rigidity).

NODE 18

Elastic Moduli Map

YOUNG'SLENGTH

BULKVOLUME

SHEARSHAPE

• How materials resist different deformations.
• Complete modulus family.

NODE 19

Stress-Strain Curve

σε

• Visual chamber of material behavior.
• Elastic → Yield → Plastic → Ultimate → Fracture.

NODE 20

Elastic Limit

• Max stress for recoverable deformation.
• Beyond this, permanent deformation occurs.

NODE 21

Yielding

• Yield point / Yield stress.
• Onset of plastic flow (permanent deformation).

NODE 22

Ultimate Strength

• Max engineering stress reached before weakening.
• Precedes necking and fracture.

NODE 23

Fracture

⚡

• Loss of structural integrity (breaking).
• Ductile vs Brittle fracture.

NODE 24

Ductility

▶

• Substantial plastic deformation before fracture.
• E.g., Copper drawn into wire.

NODE 25

Brittleness

• Little plastic deformation before fracture.
• E.g., Glass, ceramics. Sudden failure.

NODE 26

Malleability

▼

• Plastic deformation under compressive load.
• Formed into sheets. Malleable ≠ Ductile.

NODE 27

Toughness

• Ability to absorb energy before fracture.
• Area under the stress-strain curve.
• Impact resistance.

NODE 28

Hardness

• Resistance to scratching/indentation.
• Hardness ≠ Strength ≠ Toughness.

NODE 29

Resilience

• Absorb elastic energy and release during unloading.
• Prepares for springs and oscillations.

NODE 30

Elastic Potential Eng

U=½kx²

• Work required to deform material.
• Connects to Realm 06 (Force → Work → Energy).

NODE 31

Springs

• Natural length, extension, compression.
• Spring constant (k). Restoring force F = -kx.

NODE 32

Series Springs

• 1/keq = 1/k₁ + 1/k₂ + ...
• Same force, shared extension.

NODE 33

Parallel Springs

• keq = k₁ + k₂ + ...
• Shared extension, combined restoring force.

NODE 34

Material Selection

STIFF

STRNG

TOUGH

DUCT

• Not just "Which is strongest?"
• Depends on load, environment, cost. Bridge to engineering.

NODE 35

Thermal Effects

🔥

• Heating → Expansion/Contraction.
• Thermal stress. Connects to Realm 10.

NODE 36

Structures

• Bridges, buildings, dams, cables.
• How much deformation can a structure safely tolerate?

NODE 37

Buckling

• Slender member fails by bending under compression.
• Rather than simple crushing.

NODE 38

Material Fatigue

▼

• Repeated cyclic loading causes damage.
• Even if loads are below static failure strength.

NODE 39

Creep

• Slow permanent deformation under sustained load.
• Especially at elevated temperatures.

NODE 40

Experiment Lab

▼

• Stretch wire: load → extension.
• Determine spring constant (k).
• Compare material stiffness.

NODE 41

Graph Chamber

• Force vs extension, Stress vs strain.
• Extract gradient, moduli, elastic region, energy.

NODE 42

Misconceptions

X

• "Elastic = easy to stretch" → No, can be stiff.
• "Stress & strain have same units" → Strain is unitless.
• "Thicker wire stretches more" → Area matters.

NODE 43

Solving Engine

• ID MAT/LOAD/GEOM → CALC STRESS/STRAIN.
• SELECT MODULUS → DEFORMATION → CHECK LIMITS.

NODE 44

Master Map

FORCESTRAINELASTICMAT

• Force → Load → Stress → Strain.
• Deformation → Elastic Response → Energy Storage.
• Material Limit → Failure.