  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.
