Constitutive models play an important role when characterizing structural materials in order to evaluate their thermomechanical behavior. The experimental characterization of materials (using techniques discussed in Part C of this Handbook) involves measuring and controlling macroscopic variables such as force, displacement and temperature. Concise models are also of great use when characterizing the continuous media used to create structural materials, because phenomenological modeling can be carried out regardless of the internal material structure. This continuum modeling usually successfully describes the behavior of various classes of material under complex boundary conditions.
This chapter presents phenomenological constitutive models from both macroscopic and microscopic viewpoints:
Starting from viscoplasticity models, model performance is reviewed in order to predict the mechanical response under creep–plasticity interaction conditions, taking into account internal state variables.
Material anisotropy is discussed; mathematical modeling of initial anisotropy and induced anisotropy based on the representation theorem for higher order isotropic tensors is presented.
Thermomechanical coupling phenomena involving phase transformations predominatein engineering applications of heat treatment and material processing. A continuum model is presented that takes into account the way structural rearrangement evolves in materials.
Finally, microscopic analysis based on crystal plasticity, which relates the resolved shear stress to crystal slip, is applied to describe the inhomogeneous deformation process in polycrystalline materials.