In CLT, which matrix is associated with bending stiffness and relates curvature to bending moments?

• A. D is the bending stiffness relating curvature to bending moments.
• B. A is the extensional stiffness relating strains to in-plane forces.
• C. B is the extensional coupling.
• D. A is the through-thickness coupling matrix.

Answer: (A)

In Classical Laminate Theory, bending stiffness is captured by the bending stiffness matrix D. It is the matrix that links the midplane curvatures to the bending moment resultants, through the relation M = D · kappa. The full CLT constitutive relation for a laminate is {N; M} = [A B; B D] {epsilon0; kappa}, where A is the extensional stiffness relating in-plane strains to in-plane forces, B is the extensional–bending coupling (zero for symmetric laminates), and D is the bending stiffness relating curvatures to bending moments. If the laminate is symmetric, B = 0 and bending decouples from in-plane behavior. Thus, the matrix associated with bending stiffness and curvature-to-moment relation is the D matrix.