Kinetic temperature of structures for resilience, instability and failure analysis of building systems

Abstract

This thesis aims to address the urgent need for quantitative resilience assessment of buildings which, due to the perils of global warming, are expected to be subject to extreme hazards. To obtain the key input for resilience calculations in the form of structural fragility, we redefine structural mechanics within the context of statistical physics and atomistic simulations in the molecular dynamics (MD)--based framework. At the core of the approach, potentials of mean force for two-body, three-body and four-body interactions are derived to define the energy states between mass points discretizing structural members. An original potential parameter calibration procedure is proposed to link our methodology to classical continuum mechanics and experiments.

At the interface between structural mechanics and statistical physics lie the thermodynamic ensembles, which dictate the conservation of macroscopic properties in dynamic systems. Moving beyond the classical engineering ensemble of choice --the energy conserving microcanonical (NVE) ensemble-- we explore the concept of structural thermalization in the canonical (NVT) ensemble. To that end we evoke the equipartition theorem of statistical physics and introduce, by analogy to kinetic theory of gases, the kinetic temperature of structures. Structural thermalization manifests by connecting the momentum balance equations to an outside bath reservoir maintained at a reference temperature history through the Nosé-Hoover thermostat. Following the Zeroth Law of Thermodynamics, it is recognized that a structure is in (thermal) equilibrium as long as the structure's kinetic temperature attains the bath temperature; whereas it is out-of-equilibrium when the open system (structure plus bath) exhibits a sustained temperature difference. In this case, the structure has exhausted its fluctuation-dissipation capacity, which is indicative --for structures-- of a progressive failure and instability. The implementation of the kinetic temperature as an order parameter is illustrated for numerous applications, ranging from buckling of rods to wind and fire response of buildings, all the way to determining fragility curves required for the assessment of resilience of buildings. It is suggested that the proposed order parameter becomes an integral part of the structural engineering toolbox for resilience studies of buildings and structures.