Spectral Stiffness Microplane Model for Quasibrittle Textile Composites

Abstract

The present contribution proposes a general constitutive model to simulate the orthotropic stiffness, pre-peak nonlinearity, failure envelopes, and the post-peak softening and fracture of textile composites. Following the microplane model framework, the constitutive laws are formulated in terms of stress and strain vectors acting on planes of several orientations within the material meso-structure. The model exploits the spectral decomposition of the orthotropic stiffness tensor to define orthogonal strain modes at the microplane level. These are associated to the various constituents at the mesoscale and to the material response to different types of deformation. Strain-dependent constitutive equations are used to relate the microplane eigenstresses and eigenstrains while a variational principle is applied to relate the microplane stresses at the mesoscale to the continuum tensor at the macroscale. Thanks to these features, the resulting spectral stiffness microplane formulation can easily capture various physical inelastic phenomena typical of fiber and textile composites such as: matrix microcracking, micro-delamination, crack bridging, pullout, and debonding. The application of the model to a twill 2$\times$2 shows that it can realistically predict its uniaxial as well as multi-axial behavior. Furthermore, the model shows excellent agreement with experiments on the axial crushing of composite tubes, this capability making it a valuable design tool for crashworthiness applications. The formulation is computationally efficient, easy to calibrate and adaptable to other kinds of composite architectures of great current interest such as 2D and 3D braids or 3D woven textiles.