Calculation of the Wöhler (S-N) Curve Using a Two-Scale Model

This chapter deals with the initiation of a short crack and subsequent growth of the long crack in a carbon steel under cyclic loading, concluded with the estimation of the complete lifetime represented by the Wöhler (S-N) curve. A micro-model containing the microstructure of the material is generated using the Finite Element Method and the according non-uniform stress distribution is calculated afterwards. The number of cycles needed for crack initiation is estimated on the basis of the stress distribution in the microstructural model and by applying the physically-based Tanaka-Mura model. The long crack growth is handled using the Paris law. The analysis yields good agreement with experimental results from literature.

Derivation of continuum models from discrete models of mechanical forces in cell populations

In certain discrete models of populations of biological cells, the mechanical forces between the cells are center based or vertex based on the microscopic level where each cell is individually represented. The cells are circular or spherical in a center based model and polygonal or polyhedral in a vertex based model. On a higher, macroscopic level, the time evolution of the density of the cells is described by partial differential equations (PDEs). We derive relations between the modelling on the micro and macro levels in one, two, and three dimensions by regarding the micro model as a discretization of a PDE for conservation of mass on the macro level. The forces in the micro model correspond on the macro level to a gradient of the pressure scaled by quantities depending on the cell geometry. The two levels of modelling are compared in numerical experiments in one and two dimensions.

Mechanism of crack initiation and propagation of re-entrant auxetic honeycombs under thermal shock

Thermal shock multiple cracking behaviors of re-entrant auxetic honeycombs with a negative Poisson's ratio are investigated, and the crack initiation and propagation behavior are discussed. An effective macro continuum model is developed to detect the effects of cracking density and microstructures of auxetic honeycombs on the thermal stress and intensity. The microscale tensile stresses in the struts ahead of the crack as functions of the corresponding thermal stress intensity factor (SIF) at the macroscale are evaluated by employing a macro-micro model. Then, a lower-bound method is proposed to assess the critical thermal load of auxetic honeycombs by combining the macro-micro model and the macro continuum model. A significant increase in both transient thermal stress and intensity as the growing cell-wall angle is demonstrated. Results for the maximum thermal SIF as well as the maximum tensile stress in the middle of cracks are calculated as functions of crack density and length. With the identical SIF, the microscale tensile stresses ahead of the crack in honeycombs with smaller cell-wall angles are greater than that in mediums with larger angles due to the more significant crack tip opening displacement. Critical thermal load prediction reveals that the honeycombs with smaller cell-wall angles generally possess more excellent thermal shock resistance. Also, the varying failure modes of different auxetic honeycomb strips under specific thermal load are predicted. The corresponding crack initiation and propagation mechanisms are revealed.

Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts

The Covid-19 disease has caused a world-wide pandemic with more than 60 million positive cases and more than 1.4 million deaths by the end of November 2020. As long as effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, self-isolation and quarantine as well as far-reaching shutdowns of economic activity and public life are the only available strategies to prevent the virus from spreading. These interventions must meet conflicting requirements where some objectives, like the minimization of disease-related deaths or the impact on health systems, demand for stronger counter-measures, while others, such as social and economic costs, call for weaker counter-measures. Therefore, finding the optimal compromise of counter-measures requires the solution of a multi-objective optimization problem that is based on accurate prediction of future infection spreading for all combinations of counter-measures under consideration. We present a strategy for construction and solution of such a multi-objective optimization problem with real-world applicability. The strategy is based on a micro-model allowing for accurate prediction via a realistic combination of person-centric data-driven human mobility and behavior, stochastic infection models and disease progression models including micro-level inclusion of governmental intervention strategies. For this micro-model, a surrogate macro-model is constructed and validated that is much less computationally expensive and can therefore be used in the core of a numerical solver for the multi-objective optimization problem. The resulting set of optimal compromises between counter-measures (Pareto front) is discussed and its meaning for policy decisions is outlined.

Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts

The Covid-19 disease has caused a world-wide pandemic with more than 60 million positive cases and more than 1.4 million deaths by the end of November 2020. As long as effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, self-isolation and quarantine as well as far-reaching shutdowns of economic activity and public life are the only available strategies to prevent the virus from spreading. These interventions must meet conflicting requirements where some objectives, like the minimization of disease-related deaths or the impact on health systems, demand for stronger counter-measures, while others, such as social and economic costs, call for weaker counter-measures. Therefore, finding the optimal compromise of counter-measures requires the solution of a multi-objective optimization problem that is based on accurate prediction of future infection spreading for all combinations of counter-measures under consideration. We present a strategy for construction and solution of such a multi-objective optimization problem with real-world applicability. The strategy is based on a micro-model allowing for accurate prediction via a realistic combination of person-centric data-driven human mobility and behavior, stochastic infection models and disease progression models including micro-level inclusion of governmental intervention strategies. For this micro-model, a surrogate macro-model is constructed and validated that is much less computationally expensive and can therefore be used in the core of a numerical solver for the multi-objective optimization problem. The resulting set of optimal compromises between counter-measures (Pareto front) is discussed and its meaning for policy decisions is outlined.