Author name: GULSHAN SHAFI

Wagner’s theorem predicts composite material stiffness distribution in laminates.The formula is given by: Where: Ec​ is the effective modulus of elasticity of the composite. Vf​ is the volume fraction of the fiber (or reinforcing phase). Ef​ is the modulus of elasticity of the fiber. Vm​ is the volume fraction of the matrix. Em​ is the modulus […]

Lamé’s equation predicts composite material deformation under applied stress.The formula is given by: Where: σ is the stress tensor ε₁, ε₂, ε₃ are the principal strains λ and μ are Lamé’s first and second parameters, respectively, which are material constants.

Composite material’s maximum stress equals sum of principal stresses.The formula is given by: where: σmax​ is the maximum normal stress that the composite material can withstand before failure. σ1​ and σ2​ are the principal stresses acting on the composite material.

Adjusts predicted stiffness to match experimental results in composites.The formula is given by: ​​ Where: Eexperiment​ represents the experimentally determined modulus of elasticity of the composite. Emicromechanical​ represents the modulus of elasticity predicted by the micromechanical model.

Material failure based on cohesion, friction, and stress components.The formula is given by: Where: τ is the shear stress on the plane of failure, c is the cohesion intercept (a measure of the material’s shear strength when the normal stress is zero), σ is the normal stress acting on the plane of failure, ϕ is the

Haigh-Westergaard Stress Space: graphical representation for multiaxial stress states.The formula is given by: where: σH​ is the Haigh-Westergaard stress, σx​ is the normal stress in the x-direction, and σy​ is the normal stress in the y-direction.

Loading distant from region, stress independent of loading details nearby.The formula is given by: Where: σ is the stress at a distance z from the applied load. σ0​ is the stress due to any initial loading or boundary conditions. M is the bending moment at the location of interest. I is the second moment of area

Predicts fatigue failure in composites under cyclic loading conditions graphically.The formula is given by: Where: Sut is the ultimate tensile strength of the material. Se​ is the endurance limit of the material (or fatigue strength). σm​ is the mean stress acting on the material.

Love’s stress function describes stress distribution in composite materials.The formula is given by: Where: r is the radial distance from the origin, θ is the angular coordinate, A and B are constants determined by the boundary conditions of the specific problem.

Rayleigh’s Method in composites is a technique used to estimate the effective properties of composite materials based on the properties of individual constituents.The formula is given by: Where: Ec​ is the effective elastic modulus of the composite material. Vm​ and Vf​ are the volume fractions of the matrix and fiber phases, respectively. Em​ and Ef​ are