A Monte Carlo simulation of paper deformation and failure

A computer program was developed to solve for the modulus and strength of a sheet of paper using a Monte Carlo simulation. The simulation can deal with elastic-plastic fibres with varying length and strength, and with sheets with varying degrees of local bonding. It can account for both fibre failure and pull-out, and provides a means of solving problems which would be intractable using closed-from solution techniques. The program works by generating a file of up to 10 000 fibres which cross the rupture line, and applying shear lag analysis to determine the stress along the fibre, the bond stress, etc. The modulus and strength are computed by summing the force at the scan line and dividing by the appropriate cross-sectional area. A number of trials are performed using the same fibre parameters, but different randomly generated values, to yield a set of ''experimental'' data with a mean and standard deviation. The simulation was found to agree with theory for simple sheets.