A Lagrangian approach for thermomechanics towards damage and deterioration of structures
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Theoretical advances in earthquake engineering and the experience gained from recent earthquakes have led to a re-characterization of the seismic hazard. As a result, updated performance demands for new structures are defined in a socio-economic context. At the same time, a necessity for evaluation and retrofit of existing infrastructure is established. All of the above have created an increased interest in analytical and computational tools that can reliably assess the different performance levels of a structure under rare loadings. The present dissertation will attempt to set the analytical and computational basis for coping with these analyses and challenges. In this direction, a unified theory for elasticity and plasticity is developed based on thermomechanical principles. A weak formulation using Hamilton’s principle is introduced for thermoelasticity and thermoplasticity. The proposed formalism is a mixed Lagrangian formulation considering displacements, temperatures, forces, heat fluxes and other state variables as primary unknowns. In order to integrate in time and space the governing thermomechanical equations a variational discrete scheme is developed. The variational scheme is symplectic and possesses momentum and energy conserving characteristics. The thermoelasticity formulation can be postulated as a minimization problem at each time-step. This is not the case for the thermoplasticity formulation where the discrete nonlinear equations can not be solved as a minimization problem for any selection of state variables. The Lagrangian formalism is extended to the three-dimensional continuum and thermoelastic and thermoplastic elements are formulated using variational principles. The spatial discretization in the developed elements is consisted with the developed Lagrangian formalism. Computer programs are developed and the thermoelasticity/plasticity formulation is verified with a series of numerical applications, including second sound in solids, elastic/plastic wave propagation in solids, and material softening under thermal field.