Developing a stochastic linear elastic material model and composite laminate theory including failures, using the fiber bundle–based approach—Part I: Stochastic Linear Elastic Material Model

This paper presents a novel theoretical statistical material model, which is a kind of extension of the usual 3D Hooke’s law and can take into account the damage process up to the final failure as well. This material model can provide the stress response also together with the damages to multiaxial short time alternating strain loads. It was developed by utilizing our earlier validated results of applying E-bundles for modelling stress-strain curve of different types of fibrous materials and fibre-reinforced composite sheets subjected to simple (uniaxial) mechanical loads. Based on the fiber bundle cells (FBC) theory, we introduced the so-called memory reliability functions to take into account the different changing strain loads including both the monotone, the pulsating and the alternating modes. We proved that the duplex compressive–tensile memory reliability function is the product of the compressive and the tensile memory reliability functions. Utilizing the generalized Hooke’s law and the memory reliability functions, we developed a stochastic linear elastic material law that also represents the damage and failure processes with normal and shear strain loads. This made it possible to calculate the expected value as the variance of the stress response process and determine its confidence interval at any strain load.