| The study focuses on two of the main causes leading to failure of composite materials: loss of stability and progressive damage followed by softening. The differences among various stability theories for homogenized soft-in-shear orthotropic composites are reviewed. These theories, energetically associated with different finite strain measures, are equivalent if the tangent moduli are transformed as a function of the stress. However, they can differ greatly if the material is in small strain and constant elastic moduli are used. Only one theory can then be correct. In particular, variational energy analysis shows that, for sandwich columns and elastomeric bearings, respectively, the correct theories are Engesser's and Haringx's, associated with Green's and Almansi's Lagrangian strain tensors. This result is confirmed by experimental evidence. In case of multiaxially loaded homogenized composites, the correct stability theory is associated with a general Doyle-Ericksen finite strain tensor of exponent m depending on the principal stress ratio. Implications of the variational analysis for commercial finite element software are explored. The energetic variational analysis is then extended to the initial postcritical behavior. For this purpose, consideration of transverse deformation is found to be essential. For a certain range of stiffness and geometric parameters, a homogenized soft-in-shear orthotropic column exhibits imperfection sensitivity, which causes failure for a load lower than the critical one. The analysis is supported by finite element simulations of practical cases. The problem of failure of composites caused by progressive damage followed by softening is analyzed by modelling the non-linear constitutive behavior using the microplane model, which is based on a vectorial rather than a tensorial description of the material constitutive relations. First, a novel microplane model based on the spectral decomposition of the elastic stiffness tensor is developed for unidirectional laminates. Later, the microplane model is applied to describe the non-linear triaxial behavior of fiber reinforced concrete. The models developed show close match with the published test data for uniaxial and multiaxial stress-strain curves, and multiaxial failure envelopes. |
