Mussel adhesion is a problem of great interest to scientists and engineers. Recent microscopic imaging suggests that the mussel material is porous with patterned void distributions. In this paper, we study the effect of the pore distribution on the interfacial-to-the overall response of an elastic porous plate, inspired from mussel plaque, glued to a rigid substrate by a cohesive interface. We show using a semi-analytical approach that the existence of pores in the vicinity of the crack reduces the driving force for crack growth and increases the effective ductility and fracture toughness of the system. We also demonstrate how the failure mode may switch between edge crack propagation and inner crack nucleation depending on the geometric characteristics of the bulk in the vicinity of the interface. Numerically, we investigate using the finite element method two different void patterns; uniform and graded. Each case is analyzed under displacement-controlled loading. We show that by changing the void size, gradation, or volume fraction, we may control the peak pulling force, maximum elongation at failure, as well as the total energy dissipated at complete separation. We discuss the implications of our results on design of bulk heterogeneities for enhanced interfacial behavior.

Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are intrinsically multiscale, and it is computationally prohibitive to adopt a fully discrete approach for large scale systems. To overcome such a challenge, we introduce an adaptive numerical algorithm for modeling fracture in this class of materials, with a primary application to polymer networks, using an extended version of the Quasi-Continuum method that accounts for both material and geometric nonlinearities. In regions of high interest, for example near crack tips, explicit representation of the local topology is retained where each polymer chain is idealized using the worm like chain model. Away from these imperfections, the degrees of freedom are limited to a fraction of the network nodes and the network structure is computationally homogenized, using the micromacro energy consistency condition, to yield an anisotropic material tensor consistent with the underlying network structure. A nonlinear finite element framework including both material and geometric nonlinearities is used to solve the system where dynamic adaptivity allows transition between the continuum and discrete scales. The method enables accurate modelling of crack propagation without a priori constraint on the fracture energy while maintaining the influence of large-scale elastic loading in the bulk. We demonstrate the accuracy and efficiency of the method by applying it to study the fracture in different examples of network structures. We further use the method to investigate the effects of network topology and disorder on its fracture characteristics. We discuss the implications of our method for multiscale analysis of fracture in networked material as they arise in different applications in biology and engineering.

Peeling of thin films is a problem of great interest to scientists and engineers. Here, we study the peeling response of thin films with nonuniform thickness profile attached to a rigid substrate through a planar homogeneous interface. We show both analytically and using finite element analysis that patterning the film thickness may lead to direction-dependent adhesion such that the force required to peel the film in one direction is different from the force required in the other direction, without any change to the film material, the substrate interfacial geometry, or the adhesive material properties. Furthermore, we show that this asymmetry is tunable through modifying the geometric characteristics of the thin film to obtain higher asymmetry ratios than reported previously in the literature. We discuss our findings in the broader context of enhancing interfacial response by modulating the bulk geometric or compositional properties.

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Soft materials, such as rubber and gels, exhibit rate-dependent response where the stiffness, strength and fracture patterns depend largely on loading rates. Thus, accurate modeling of the mechanical behavior requires accounting for different sources of rate-dependence such as the intrinsic viscoelastic behavior of the polymer chains and the dynamic bond breakage and formation mechanism. In this chapter, we extend the QC approach presented in Ghareeb and Elbanna [Journal of the Mechanics and Physics of Solids, 137, 103819 (2020)] to include ratedependent behavior of polymer networks. We propose a homogenization rule for the viscous forces in the polymer chains and update the adaptive mesh refinement algorithm to account for dynamic bond breakage. Then, we use nonlinear finite element framework with predictorcorrector scheme to solve for the nodal displacements and velocities. We demonstrate the accuracy of the method by verifying it against fully discrete simulations for different examples of network structures and loading conditions. We further use the method to investigate the effects of the loading rates on the fracture characteristics of networks with different ratedependent parameters. Finally, We discuss the implications of the extended method for multiscale analysis of fracture in rate-dependent polymer networks.