Space-Time Gauge Theories for Continuum Modelling of Viscoplasticity, Damage And Electro-Magneto-Mechanical Phenomena in Solids

Abstract

Over the years, sustained research efforts have aimed to understand the material behaviour under a broad range of response regimes, especially from micromechanical or phenomenological perspectives — via both continuum modeling and experiments conducted at different scales. However, a review of the relevant literature has revealed that physics-based models that can replicate experimental results are very few, and models depicting consistent coupling phenomena observed in solids beyond elasticity are elusive. Symmetry-driven approaches to continuum mechanics of solids typically have a unifying nature, combining the prediction of diverse observed phenomena under a single umbrella. This thesis attempts to derive a unified field theory for various physical phenomena in solids by exploring local symmetry, which offers a framework to consistently arrive at the relations among polarization vector, temperature, scalar potential, vector potential, and the electric and magnetic field for multiphysics phenomena. Furthermore, this approach enables a consistent and robust coupling among flow stress, strain rate, and other variables describing the kinematics of plasticity and damage. This thesis draws upon continuous and local symmetry-based principles of gauge theory to arrive at continuum models for various electro-magneto-mechanical coupling phenomena and inelastic responses involving plasticity and damage in solids. The specific local symmetries we exploit in the process are conformal (scaling) and translational in space-time. The work presented may thus be classed in two parts – one focusing on a unified continuum description of multi-physics phenomena such as piezoelectricity, piezo-magnetism, coupled thermoelasticity and flexoelectricity and the other on dissipative phenomena such as plasticity and damage. Under an inhomogeneous (local) action of the symmetry (gauge) group, invariance of the energy density is lost. Minimal replacement is used to restore gauge invariance of the energy density; this requires the definition of a gauge covariant operator in place of the ordinary partial derivative. Minimal replacement introduces a non-trivial gauge compensating 1-form field. The 1-form field is decomposed into an anti-exact part and the exact differential of a scalar-valued function. The other essential ingredient of gauge theory is minimal coupling