# Elastizität von Materialien - Interaktive Visualisierung

Interaktive Simulation demonstrierend das Hookesche Gesetz, Spannungs-Dehnungs-Beziehungen und Materialeigenschaften

> Kanonische Seite: https://elysiatools.com/de/visualizations/elasticity-materials

- **Kategorie:** Physics

## Überblick

Interactive elasticity simulation demonstrating Hooke's Law, stress-strain relationships, and material properties with real-time visualization. Features spring-mass system with animated extension showing Hooke's Law F = k·x behavior, force-displacement (F-x) curve plotting with elastic region (linear green, Hooke's Law), plastic region (non-linear orange), and fracture point (red X). Physics equations: Hooke's Law F = k·x (within elastic limit), Stress σ = F/A, Strain ε = ΔL/L₀, Young's Modulus E = σ/ε, Elastic Potential Energy Eₚ = ½kx². Interactive parameter controls: Applied force F (0-100 N), Spring constant k (10-200 N/m), Material selection with three presets. Material properties comparison: Steel (E ≈ 200 GPa, high modulus, ductile with large linear range, yield strength ~250 MPa, blue curve), Rubber (E ≈ 0.01-0.1 GPa, low modulus, hyperelastic behavior with large strain capability, red curve), Concrete (E ≈ 30 GPa, medium modulus, brittle with sudden fracture at low strain, weak in tension strong in compression, gray curve). Real-time visualizations: (1) Spring animation showing coil stretching under applied load with dimensional lines displaying original length L₀ and current length L, weight/mass at bottom with force value in Newtons, energy indicator showing stored elastic potential energy Eₚ as colored spring area. (2) Force-displacement curve with current operating point (red dot), elastic limit marker, plastic deformation onset, fracture point indicator, grid with force (y-axis) and displacement (x-axis) labels. (3) Stress-strain comparison chart superimposing all three material curves showing different behaviors: Steel shows linear region followed by yield plateau and strain hardening, Rubber shows non-linear hyperelastic curve with large strains, Concrete shows linear region ending in abrupt fracture. Material properties display: Young's Modulus E in GPa, Elastic limit in MPa, Yield strength in MPa. Animation controls: Load button (gradually increase force to 100N), Unload button (decrease force to 0N), Reset button (return to initial state). Quick material presets: Steel (k = 50 N/m, blue), Rubber (k = 10 N/m, red), Concrete (k = 100 N/m, gray). Real-time measurements: Original length L₀ (100 mm), Current length L (calculated from F = kx), Elongation ΔL = L - L₀, Elastic potential energy Eₚ = ½kx² in Joules. Educational content: Mathematical foundation with six key formulas, stress-strain curve regions explanation (elastic region with reversible deformation following Hooke's Law σ = E·ε, plastic region with permanent non-linear deformation, fracture point representing ultimate tensile strength), material properties comparison table showing steel (high E, ductile, construction tools), rubber (low E, very elastic large strain, seals tires), concrete (medium E, brittle sudden fracture, weak tension strong compression), real-world applications including mechanical springs (vehicle suspensions, watches, mechanisms with k determining force per displacement), structural engineering (buildings bridges operating in elastic range, steel for tension, concrete for compression), material testing (tensile tests measuring stress-strain curves for Young's Modulus, yield strength, ultimate tensile strength), biomaterials (implants prosthetics matching mechanical properties of biological tissues), nanotechnology (carbon nanotubes with E ~ 1 TPa for reinforcing composites). Experiment guide: Start with small forces under 20N to observe linear Hooke's Law, compare materials to see stiffness effects on elongation (steel minimal stretch, rubber significant stretch), observe energy storage quadratic relationship Eₚ = ½kx² with area under F-x curve representing stored energy. Responsive design with synchronized canvas rendering. Multi-language support (zh, en, fr, de, es, pt, ru).

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