Discrete Micromechanics of Random Fibrous Architectures

Abstract

Fibrous micro-architectures are subscale motifs ubiquitously found in structures ranging from eukaryotic cells to laminated composites. The mechanics of such microstructures including their stiffness, strength and damage is enriched by the nonlinearities and stochastic effects arising from microstructural randomness coupled with constituent properties. In this dissertation, we investigate the mechanics of two types of fibrous architectures that span over several decades of stiffness and length-scales: (i) soft, filamentous networks mimicking bio-polymers, and (ii) stiff, fiber-reinforced polymers employed in many engineering applications. The focus is primarily on the role of microstructural discreteness in the evolution of elasticity and failure of the above-mentioned exemplars.

Computational tools are developed and algorithms are implemented in finite element (FE) methods to study model problems. In-house algorithms are developed for the generation of discrete microstructures (DM). In order to understand the correlation between the topological characteristics and mechanical response of microstructures, statistical parameters are identified that could characterize the microstructures. We investigated the influence of microstructural parameters on the elasticity of DM using FE methods. The model is further extended to study the stochastic rate dependent failure of biological networks like F-actin. The inherent variability seen in the response of DM is also studied. The effect of the random microstructural arrangement on the transport property and failure is investigated by considering fiber reinforced polymers as a model problem.