Finite Element Analysis for Composite Materials

A Python-based finite element analysis tool for simulating mechanical behavior of composite materials with periodic boundary conditions.

Features

• 2D linear elastic analysis
• Periodic boundary conditions
• Multi-phase material support
• Adaptive mesh generation
• Numerical stability handling
• Visualization of results

Environment Setup

Prerequisites

• Python 3.8+
• Rye package manager

Installation

Clone repository git clone https://github.com/yourusername/finite-element-composite.git cd finite-element-composite Install dependencies rye sync Structure

Project Structure

├── src/
│   ├── mechanics/          # Material properties and constitutive models
│   │   └── material.py
│   ├── mesh/               # Mesh generation and processing
│   │   └── mesh_generator.py
│   └── solver/             # Finite element solver implementation
│       └── fem_solver.py
├── main.py                 # Main simulation workflow
├── CONFIG                  # Simulation parameters
└── requirements.txt        # Dependency list

Configuration

Edit main.py to modify simulation parameters:

CONFIG = {
    "length": 1.0,         # Domain size (meters)
    "nx": 60,              # Mesh density (elements per side)
    "inclusions": 2,       # Number of inclusions
    "radius": 0.2,         # Inclusion radius (meters)
    "material_props": {
        "E": [1e9, 50e9],  # Young's modulus values (Pa)
        "nu": [0.25, 0.3]  # Poisson's ratios
    },
    "applied_force": 5e4,  # Applied tensile force (N)
    "plane_stress": True   # Analysis type
}

Running the Simulation

# Run main simulation
python main.py

# Expected output:
# - Material phase visualization
# - Displacement contour plot
# - Deformed mesh visualization
# - Console output with numerical diagnostics

Key Components

Material Model (src/mechanics/material.py)

• Implements plane stress/strain constitutive laws
• Validates material properties
• Calculates Lame parameters
• Generates constitutive matrices

Mesh Generator (src/mesh/mesh_generator.py)

• Generates structured quadrilateral meshes
• Calculates element areas and centroids
• Identifies boundary nodes
• Creates degree-of-freedom mapping

FEM Solver (src/solver/fem_solver.py)

• Assembles global stiffness matrix
• Implements periodic boundary conditions
• Solves linear systems with regularization
• Handles numerical stability issues

Visualization

The simulation generates three plots:

1. Material phase distribution
2. Displacement magnitude contour
3. Deformed mesh configuration

Troubleshooting

Common issues and solutions:

Q: Getting NaN values in displacement results

• Verify material properties are physically valid
• Check boundary condition constraints
• Reduce applied load magnitude

Q: Mesh quality warnings

• Increase mesh density (nx in CONFIG)
• Check inclusion radius vs domain size

Q: Singular matrix errors

• Confirm proper boundary constraints
• Enable plane stress condition
• Increase regularization in solver

License

MIT License - See LICENSE for details.