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 (N V E) ensemble-we explore the concept of structural thermalization in the canonical (N V T ) 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 It would be a criminal omission to open this section without paying homage to my compatriot Homer, legendary author of the Odyssey. Although I approach the milestone destination of my PhD conclusion, I am grateful for the journey. This journey is far from mine to claim, but rather a culmination of many steps that everyone in my life took with me. These steps started with the guidance of professor Demos Angelides, who introduced me to the interface between engineering and statistics: reliability analysis. Through his mentorship during my Master's thesis I developed a sound structural and probabilistic background, which proved immensely useful during my doctoral studies on resilience of structures. I truly regret that I was not able to finish my dissertation before he lost the battle with cancer in August 2022.Every step along the journey I was fortunate to work with my advisor, Franz-Josef Ulm. His infectious enthusiasm, all-round mentoring and the ability to integrate concepts from seemingly disparate fields through simple and robust analogies shaped my vision as a researcher. His humility and patience helped me develop a peoplefirst attitude in an exhausting and competitive academic environment. Along with Franz, I had the pleasure of working with many inspiring researchers like Roland Pellenq...