• Zschocke, Selina

Abstract

Traditional computational mechanics are based on constitutive models representing materialbehavior. In case of solid mechanics, these result from assuming a class of material behavior and fitting the corresponding parameters to experimentally obtained stress-strain data. In contrast to that, by the method of data-driven computing, numerical simulations can be executed directly based on stress-strain data. Therefore, the step of material modeling is bypassed and the analysis is performed through minimizing the distance between the data set and the subspace of stress-strain states which are compatible in terms of kinematic compatibility and equilibrium. <br/><br/>Uncertainty needs to be taken into account to provide realistic assessments of structural responses. Aleatoric uncertainty, describing variability, and epistemic uncertainty, caused by inaccuracy and incompleteness, are distinguished. The modeling of polymorphic uncertainty, enabling simultaneous consideration of aleatoric and epistemic uncertainty, in the context of structural analysis is a current research field. <br/><br/>The material behavior of composite materials is strongly affected by the heterogeneities occurring as a result of the combination of individual constituents. Based on numerical homogenization methods the problem is divided into different length scales and the mechanical behavior on the mesoscale, representing heterogeneities, is considered within the structural analysis of the homogeneous macroscopic replacement continuum. <br/><br/>In this thesis, a workflow for the quantification of polymorphic uncertain stress-strain databased on different types of available information is established. Based on this, a decoupled numerical homogenization scheme with the purpose of taking mesoscale uncertainties into account utilizing the method of data-driven computing is developed and introduced. In order to demonstrate the workflow and characteristics of the proposed framework, deterministic and uncertain structural analyses are executed.

Topics

• impedance spectroscopy
• simulation
• composite
• homogenization