Constitutive Equation in Composite Layers

This equation represents the constitutive relationship in composite laminate theory, which links the in-plane forces and moments acting on a composite laminate to the strain and curvature.

• {N / M}: The force and moment resultants per unit length on the laminate.
  • N is the in-plane force vector (force per unit length).
  • M is the bending moment vector (moment per unit length).
• [A | B / B | D]: The constitutive stiffness matrix of the laminate, which is composed of:
  • A (Extensional stiffness matrix): Relates in-plane forces to mid-plane strains.
  • B (Coupling stiffness matrix): Relates in-plane forces to curvatures and bending moments to mid-plane strains. This matrix exists when the laminate is unsymmetrical, causing coupling between bending and stretching.
  • D (Bending stiffness matrix): Relates bending moments to curvatures.
• {ε⁰ / k}: The strain and curvature vector.
  • ε⁰ is the mid-plane strain vector.
  • k is the curvature vector.

This equation describes how a composite laminate responds to applied loads, considering both in-plane deformation and bending, crucial for the analysis and design of composite structures.