Author name: GULSHAN SHAFI

Maximum Principal Strain Theory is a Material failure predicted when maximum strain exceeds critical value.The formula is given by:   Where: σ_1 and σ_2 are the maximum and minimum principal stresses, respectively. E is the Young’s modulus of the material.  

Energy method for calculating deflections in elastic structures.The formula is given by: Where: δ is the displacement at the point of application of the load. U is the strain energy of the structure. P is the applied load.

Flexing beam theory describes bending in slender structures mathematically.The formula is given by: Where: σ is the bending stress at a point on the beam, M is the bending moment at that point, y is the perpendicular distance from the neutral axis to the point where the stress is being calculated (the distance from the centroid

Ductility Index is a Measure of material’s deformation capability before rupture.The formula is given by: Where: DI = Ductility Index. εult​ = Ultimate elongation (or other measure of elongation). L0​ = Original length of the material.    

Brittleness Index is a Ratio of tensile strength to hardness.The formula is given by: Where: BI = Brittleness Index. σt​ = Tensile strength of the material. H = Hardness of the material.

Neutral axis is a Line of zero bending stress in structures.The formula is given by: Where: yn​ = distance from the centroid to the neutral axis (in the direction perpendicular to the axis of bending). Ic​ = moment of inertia of the entire cross-section about its neutral axis A = cross-sectional area. yc​ = distance from

Dielectric constant is a material’s ability to store electrical energy in fields.The formula is given by: Where: C = capacitance of the capacitor. ε = dielectric constant of the material between the plates. ε0​ = permittivity of free space (approximately 8.854×10−12 F/m8.854×10−12F/m) A = area of the plates. d = distance between the plates.

Material’s ability to allow substances through; varies with conditions.The formula is given by: Where: μ is the magnetic permeability of the material, B is the magnetic flux density (in teslas), and H is the magnetic field strength (in amperes per meter).

Material’s resistance to electric current flow.The formula is given by: Where: ρ is the electrical resistivity (in ohm-meters, Ω⋅m), R is the electrical resistance (in ohms, Ω), A is the cross-sectional area of the material through which the current flows (in square meters, m²), L is the length of the material through which the current flows

Heat conduction speed relative to storage.The formula is given by: Where: α is the thermal diffusivity. k is the thermal conductivity of the material. ρ is the mass density of the material. cp​ is the specific heat capacity of the material.