| The microplane model is a versatile and powerful approach to constitutive modeling in which the stress-strain relations are defined in terms of vectors rather than tensors on planes of all possible orientations. Such planes are called the microplanes and are representative of the microstructure of the material. The microplane model with kinematic constraint has been successfully employed in the past in the modeling of concrete, soils, ice, rocks, fiber composites and other quasibrittle materials. The microplane model provides a powerful and efficient numerical and theoretical framework for the development and implementation of constitutive models for any kind of material. The dissertation presents a review of the background from which the microplane model stems, highlighting differences and similarities with other approaches. The basic structure of the microplane model is then presented, together with its extension to finite strain deformation. To show the effectiveness of the microplane model approach, some examples are given demonstrating applications of microplane models in structural analysis with the finite element method. Some new constitutive models are also introduced for materials characterized by very different properties and microstructures, showing that the approach is indeed very versatile and provides a robust basis for the study of a broad range of problems. New models are introduced for metal plasticity, shape memory alloys and cellular materials. The new models are compared quantitatively with the existing models and experimental data. In particular, the newly introduced microplane models for metal plasticity are compared with the classical J2-flow theory for incremental plasticity. An existing microplane model for concrete is employed in finite element analysis of the 'tube-squash' test, in which concrete undergoes very large deviatoric deformation, and of the size effect in compressive failure of concrete columns. The microplane model for shape memory alloys is shown to accurately reproduce the behavior observed experimentally in uniaxial and triaxial tests. Finally, the microplane model for cellular materials is successfully used to perform finite element analysis of failure of sandwich beams by core indentation. |
