DATA-DRIVEN COMPUTATIONAL HOMOGENIZATION OF POLYMER NETWORKS TO HYPERELASTIC MATERIAL MODELS

Accurate constitutive relations relating stress and strain for continuum mechanical models of materials with complex, heterogeneous microstructures are difficult to formulate, but valuable for computer aided design and testing for industrial and commercial applications. In particular, continuum descriptions of the actin cytoskeleton would facilitate numerical simulations to complement the investigation of mechanobiological phenomena such as cell motility, embryonic development and morphogenesis, cancer metastasis, mechanically-regulated biological signal transduction. This thesis proposes a framework for the derivation of constitutive equations for actin polymer networks by computational or numerical means. Detailed simulations of a microscale model of crosslinked actin networks resolving microsctructural heterogeneity are performed, and continuum mechanical variables are extracted from these data. Measures of stress, strain, and strain energy are extracted and utilized to produce hyperelastic constitutive laws in the form of strain energy functions to model the mechanical response of the cytoskeleton as a continuum material. Strain energy functions are produced by least-squares fitting to known analytical forms and by training feed-forward or deep neural networks to learn the strain energy as a function of strain measures. The parameter-fitted constitutive models are employed in finite volume simulations of red blood cells in Poiseuille flow, and the quality of fit between the parameter-fitted model and the deep neural networks is compared and discussed.Doctor of Philosoph

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Multibody Systems with Flexible Elements

Multibody systems with flexible elements represent mechanical systems composed of many elastic (and rigid) interconnected bodies meeting a functional, technical, or biological assembly. The displacement of each or some of the elements of the system is generally large and cannot be neglected in mechanical modeling. The study of these multibody systems covers many industrial fields, but also has applications in medicine, sports, and art. The systematic treatment of the dynamic behavior of interconnected bodies has led to an important number of formalisms for multibody systems within mechanics. At present, this formalism is used in large engineering fields, especially robotics and vehicle dynamics. The formalism of multibody systems offers a means of algorithmic analysis, assisted by computers, and a means of simulating and optimizing an arbitrary movement of a possibly high number of elastic bodies in the connection. The domain where researchers apply these methods are robotics, simulations of the dynamics of vehicles, biomechanics, aerospace engineering (helicopters and the behavior of cars in a gravitational field), internal combustion engines, gearboxes, transmissions, mechanisms, the cellulose industry, simulation of particle behavior (granulated particles and molecules), dynamic simulation, military applications, computer games, medicine, and rehabilitation