FPC Neutral Axis Calculator: Bend Stress & Stackup Visualization

How to use the FPC Neutral Axis & Bend Stress Calculator

This FPC neutral-axis calculator goes beyond a simple bend-radius check by combining formula steps, draggable stack-up ordering and dynamic visualization. It uses layer thickness, elastic modulus and Poisson ratio to estimate neutral-axis location, copper surface strain and layer tension or compression stress, with coverlay opening and air-gap bend-zone modes for design comparison.

Composite neutral axis, strain and layer stress

Formula: Neutral axis = sum(Ei x ti x yi) / sum(Ei x ti); strain = y / (R + y0); stress = E x strain

• Ei: effective modulus of each included material layer.
• ti: layer thickness.
• yi: layer centroid measured through the stack-up.
• R: inside bend radius.
• y0: distance from the bend inner side to the neutral axis.
• Air-gap layer: keeps spacing in the stack geometry but contributes zero stiffness.
• Layer stress sign: positive and negative values identify tensile or compressive side behavior.

Formula Basis

• Formula basis: mechanics-of-materials composite beam / transformed-section theory. The neutral axis is treated as the stiffness-weighted centroid, yNA = sum(Ei x Ai x yi) / sum(Ei x Ai); for a unit-width FPC stack-up, Ai is represented by layer thickness ti.
• Formula basis: Euler-Bernoulli bending theory. Normal strain varies approximately linearly with distance from the neutral axis, epsilon = y / rho; this tool uses rho = inside bend radius + neutral-axis distance from the bend inner side.
• Formula basis: Hooke's-law stress estimate, sigma = Eeff x epsilon. When plane-strain mode is enabled, Eeff = E / (1 - nu^2).
• Reference: University of Illinois MechRef, Bending of Beams and composite / transformed beam notes. https://mechref.engr.illinois.edu/sol/bending.html
• Reference: D. Roylance / LibreTexts, Stresses in Beams. https://eng.libretexts.org/Bookshelves/Mechanical_Engineering/Mechanics_of_Materials_(Roylance)/04%3A_Bending/4.02%3A_Stresses_in_Beams
• Reference: PMC open-access mechanics reference for plane-strain modulus E / (1 - nu^2). https://pmc.ncbi.nlm.nih.gov/articles/PMC2391012/
• Engineering note: this neutral-axis page is based on composite beam mechanics, not IPC-2221. Air-gap zero-stiffness treatment is an engineering modeling assumption for local FPC bend-zone comparison before detailed simulation, material testing or bend-life validation.

Example

A coverlay-open or air-gap bend zone can shift the stiffness balance of the FPC stack-up. By changing the layer order or bend-zone mode, the drawing and stress table update together so the tensile and compressive layers can be reviewed before layout release.

Related Manufacturing Process

• Stack-up Design - Total thickness, dielectric spacing, symmetry, controlled impedance
• Circuit Layout - Trace width, spacing, bend-zone routing, differential pair spacing
• Reliability Validation - Bending test, thermal shock, peel strength, solder float, ionic contamination

Related Calculators

• FPC Bend Radius Calculator - Estimate minimum bend radius and flex strain for RA or ED copper.
• Stiffener Setback Calculator - Estimate the minimum setback between stiffener edge and bend tangent for flex reliability review.

FAQ