Advanced computational models for the analysis of adhesive friction

Dry adhesion and friction play an important role in various natural and technical applications. These include the remarkable characteristics of both bio-adhesive systems (like adhesion of insects and lizards) and synthetic materials like bio-inspired tapes.In this work we propose several computational models to analyze physical problems that are dominated by combined adhesion and friction. To this end, we consider the interacting bodies as deformable or rigid continua; in order to improve efficiency, we additionally use special structural elements like beams and membranes. We further account for finite deformations during contact as well as different types of material behavior.We first develop a computational contact model for dry adhesion and dynamic friction of biological and bio-inspired adhesives. This model is based on a general framework to include different phenomenological laws for the frictional resistance during sliding. We start with modeling adhesion and repulsion due to van der Waals interactions by means of an integrated Lennard-Jones potential. We then discuss several phenomenological friction laws that are motivated by theoretical and experimental studies. In particular, our model may yield frictional sliding also if the contact pressure is zero (i.e., in equilibrium) or even negative (i.e., tensile). This is motivated by experimental observations for soft and compliant bio-adhesive pads; even though their resistance to bending is negligible, these are able to generate non-negligible sliding friction under zero normal load. Afterwards, we discretize the underlying model equations in terms of the finite element (FE) method, and discuss the algorithmic treatment of frictional sticking and sliding. We finally investigate our models by means of various numerical examples in both 2D and 3D. As we will demonstrate, our model is applicable to both structures with a high stiffness and extremelysoft, compliant tapes.In addition, we propose an efficient model for thin and beam-like adhesive fibrils. To this end, we develop a reduced finite beam element formulation, which captures different types of adhesive contact and friction. This beam model is applicable to complex geometries with varying cross section or hierarchical structure. As our numerical results show, the reduced model captures the physical behavior of the solid body accurately, while being remarkably more efficient.We finally use our beam model to efficiently improve the adhesion properties of a system according to specific design criteria. For this purpose, we develop a general framework for computational optimization of adhesive strips (or fibrils) that undergo finite deformations during peeling. We then address numerous potential optimization criteria, which can be considered either separately or in a combined manner. Our framework is suitable to design the shape and material properties of thin structures at both the macroscopic and microscopic scale