Dipanjan Sen

Meso-origami: Folding multilayer graphene sheets

Graphene features unique electronic, thermal, and mechanical properties, and the flexibility and strong attraction between graphene layers promotes the formation of self-folded nanostructures. Here we study the self-folding of mono- and multilayer graphene sheets, utilizing a coarse-grained hierarchical multiscale model derived directly from atomistic simulation. Our model, developed by enforcing assertion of energy conservation, enables the simulation of graphene folding across a range of length scales from nanometers to micrometers. Through theoretical and simulation analysis we show that the critical self-folded length is πC/γ, where C and γ are the bending stiffness per unit length and the surface energy per unit length.

Tearing Graphene Sheets From Adhesive Substrates Produces Tapered Nanoribbons

Graphene is a truly two-dimensional atomic crystal with exceptional electronic and mechanical properties. Whereas conventional bulk and thin-film materials have been studied extensively, the key mechanical properties of graphene, such as tearing and cracking, remain unknown, partly due to its two-dimensional nature and ultimate single-atom-layer thickness, which result in the breakdown of conventional material models. By combining first-principles ReaxFF molecular dynamics and experimental studies, a bottom-up investigation of the tearing of graphene sheets from adhesive substrates is reported, including the discovery of the formation of tapered graphene nanoribbons. Through a careful analysis of the underlying molecular rupture mechanisms, it is shown that the resulting nanoribbon geometry is controlled by both the graphene-substrate adhesion energy and by the number of torn graphene layers. By considering graphene as a model material for a broader class of two-dimensional atomic crystals, these results provide fundamental insights into the tearing and cracking mechanisms of highly confined nanomaterials.

Structural hierarchies define toughness and defect-tolerance despite simple and mechanically inferior brittle building blocks

Mineralized biological materials such as bone, sea sponges or diatoms provide load-bearing and armor functions and universally feature structural hierarchies from nano to macro. Here we report a systematic investigation of the effect of hierarchical structures on toughness and defect-tolerance based on a single and mechanically inferior brittle base material, silica, using a bottom-up approach rooted in atomistic modeling. Our analysis reveals drastic changes in the material crack-propagation resistance (R-curve) solely due to the introduction of hierarchical structures that also result in a vastly increased toughness and defect-tolerance, enabling stable crack propagation over an extensive range of crack sizes. Over a range of up to four hierarchy levels, we find an exponential increase in the defect-tolerance approaching hundred micrometers without introducing additional mechanisms or materials. This presents a significant departure from the defect-tolerance of the base material, silica, which is brittle and highly sensitive even to extremely small nanometer-scale defects.

Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant

Alpha-helix based protein networks as they appear in intermediate filaments in the cell’s cytoskeleton and the nuclear membrane robustly withstand large deformation of up to several hundred percent strain, despite the presence of structural imperfections or flaws. This performance is not achieved by most synthetic materials, which typically fail at much smaller deformation and show a great sensitivity to the existence of structural flaws. Here we report a series of molecular dynamics simulations with a simple coarse-grained multi-scale model of alpha-helical protein domains, explaining the structural and mechanistic basis for this observed behavior. We find that the characteristic properties of alpha-helix based protein networks are due to the particular nanomechanical properties of their protein constituents, enabling the formation of large dissipative yield regions around structural flaws, effectively protecting the protein network against catastrophic failure. We show that the key for these self protecting properties is a geometric transformation of the crack shape that significantly reduces the stress concentration at corners. Specifically, our analysis demonstrates that the failure strain of alpha-helix based protein networks is insensitive to the presence of structural flaws in the protein network, only marginally affecting their overall strength. Our findings may help to explain the ability of cells to undergo large deformation without catastrophic failure while providing significant mechanical resistance.

ATOMISTICALLY-INFORMED MESOSCALE MODEL OF DEFORMATION AND FAILURE OF BIOINSPIRED HIERARCHICAL SILICA NANOCOMPOSITES

Structural hierarchies are universal design paradigms of biological materials, e.g., several materials in nature used for carrying mechanical load or impact protection such as bone, nacre, dentin show structural design at multiple length scales from the nanoscale to the macroscale. Another example is the case of diatoms, microscopic mineralized algae with intricately patterned silica-based exoskeletons, with substructure from the nanometer to micrometer length scale. Previous studies on silica nano-honeycomb structures inspired from these diatom substructures at the nanoscale have shown a great improvement in plasticity, ductility and toughness through these designs over macroscopic silica, though along with a substantial reduction in stiffness. Here, we extend the study of these structural designs to the micron length scale by introducing additional hierarchy levels to implement a multilevel composite design. To facilitate our computational experiments we first develop a mesoscale particle-spring model description of the mechanics of bulk silica/nano-honeycomb silica composites. Our mesoscale description is directly derived from constitutive material behavior found through atomistic simulations at the nanoscale with the first principles-based ReaxFF force field, but is capable of describing deformation and failure of silica materials at tens of micrometer length scales. We create several models of randomly-dispersed fiber-composite materials with a small volume fraction of the nano-honeycomb phase, and analyze the fracture mechanics using J-integral and R-curve studies. Our simulations show a dominance of quasi-brittle fracture behavior in all cases considered. For particular materials with a small volume fraction of the nano-honeycomb phase dispersed as fibers within a bulk silica matrix, we find a large improvement (≈4.4 times) in toughness over bulk silica, while retaining the high stiffness (to 70%) of the material. The increase in toughness is observed to arise primarily from crack path deflection and crack bridging by the nano-honeycomb fibers. The first structural hierarchy at the nanometer scale (nano-honeycomb silica) provides large improvements in ductility and toughness at the cost of a large reduction in stiffness. The second structural hierarchy at the micron length scale (bulk silica/nano-honeycomb composite) recovers the stiffness of bulk silica while substantially improving its toughness. The results reported here provide direct evidence that structural hierarchies present a powerful design paradigm to obtain heightened levels of stiffness and toughness from multiscale engineering a single brittle — and by itself a functionally inferior material — without the need to introduce organic (e.g., protein) phases. Our model sets the stage for the direct simulation of multiple hierarchical levels to describe deformation and failure of complex biological composites.

Mechanics of Nano-Honeycomb Silica Structures: Size-Dependent Brittle-to-Ductile Transition

Porous silica structures with intricate design patterns form the exoskeleton of diatoms, a large class of microscopic mineralized algae, whose structural features have been observed to exist down to nanoscale dimensions. Nanoscale patterned porous silica structures have also been manufactured for the use in optical systems, catalysts, and semiconductor nanolithography. The mechanical properties of these porous structures at the nanoscale are a subject of great interest for potential technological and biomimetic applications in the context of new classes of multifunctional materials. Previous studies have established the emergence of enhanced toughness and ductility in nanoporous crystalline silica structures over bulk silica. The authors undertake molecular dynamics simulations and theoretical size-scaling studies of elasticity and strength of a simple model of generic nanoporous silica structures, used to establish a theoretical model for the detailed mechanisms behind their improved properties, and show...

Direct atomistic simulation of brittle-to-ductile transition in silicon single crystals

Silicon is an important material not only for semiconductor applications, but also for the development of novel bioinspired and biomimicking materials and structures or drug delivery systems in the context of nanomedicine. For these applications, a thorough understanding of the fracture behavior of the material is critical. In this paper we address this issue by investigating a fundamental issue of the mechanical properties of silicon, its behavior under extreme mechanical loading. Earlier experimental work has shown that at low temperatures, silicon is a brittle material that fractures catastrophically like glass once the applied load exceeds a threshold value. At elevated temperatures, however, the behavior of silicon is ductile. This brittle-to-ductile transition (BDT) has been observed in many experimental studies of single crystals of silicon. However, the mechanisms that lead to this change in behavior remain questionable, and the atomic-scale phenomena are unknown. Here we report for the first time the direct atomistic simulation of the nucleation of dislocations from a crack tip in silicon only due to an increase of the temperature, using large-scale atomistic simulation with the first principles based ReaxFF force field. By raising the temperature in a computational experiment with otherwise identical boundary conditions, we show that the material response changes from brittle cracking to emission of a dislocation at the crack tip, representing evidence for a potential mechanisms of dislocation mediated ductility in silicon.

Shock Loading of Bone-Inspired Metallic Nanocomposites

Nanostructured composites inspired by structural biomaterials such as bone and nacre form intriguing design templates for biomimetic materials. Here we use large scale molecular dynamics to study the shock response of nanocomposites with similar nanoscopic structural features as bone, to determine whether bioinspired nanostructures provide an improved shock mitigating performance. The utilization of these nanostructures is motivated by the toughness of bone under tensile load, which is far greater than its constituent phases and greater than most synthetic materials. To facilitate the computational experiments, we develop a modified version of an Embedded Atom Method (EAM) alloy multi-body interatomic potential to model the mechanical and physical properties of dissimilar phases of the biomimetic bone nanostructure. We find that the geometric arrangement and the specific length scales of design elements at nanoscale does not have a significant effect on shock dissipation, in contrast to the case of tensile loading where the nanostructural length scales strongly influence the mechanical properties. We find that interfacial sliding between the composite’s constituents is a major source of plasticity under shock loading. Based on this finding, we conclude that controlling the interfacial strength can be used to design a material with larger shock absorption. These observations provide valuable insight towards improving the design of nanostructures in shock-absorbing applications, and suggest that by tuning the interfacial properties in the nanocomposite may provide a path to design materials with enhanced shock absorbing capability.

Multi-paradigm modeling of fracture of a silicon single crystal under mode II shear loading

We report a novel multi-paradigm multi-scale approach based on a combination of the first principles ReaxFF force field with an empirical Tersoff potential. Our hybrid multi-scale simulation model is computationally efficient and capable of treating thousands of atoms with QM accuracy, extending our ability to simulate the dynamical behavior of a wider range of chemically complex materials such as silicon, silica and metal-organic compounds. It is implemented in the Python based Computational Materials Design Facility (CMDF). We exemplify our method in a study focused on a systematic comparison of the fracture dynamics in silicon under mode II shear versus mode I tensile loading. We find that the mode II crack tends to branch at an angle of approximately 45 degrees once the crack speed approaches 38% of the Rayleigh-wave speed. In contrast, the mode I crack continuously propagates in the direction of the initial crack, and only makes a slight change of direction towards 10 degrees once fracture instabilities occur. Our results reveal fundamental differences of fracture dynamics under mode I versus mode II loading.

Multiscale Modeling of Biological Protein Materials – Deformation and Failure

Multi-scale properties of biological protein materials have been the focal point of extensive investigations over the past decades, leading to formation of a research field that connects biology and materials science, referred to as materiomics. In this chapter we review atomistic based modeling approaches applied to study the scale-dependent mechanical behavior of biological protein materials, focused on mechanical deformation and failure properties. Specific examples are provided to illustrate the application of numerical methods that link atomistic to mesoscopic and larger continuum scales. The discussion includes the formulation of atomistic simulation methods, as well as examples that demonstrate their application in case studies focused on size effects of the fracture behavior of protein materials. The link of atomistic scale features of molecular structures to structural scales at length-scales of micrometers will be discussed in the analysis of the mechanics of a simple model of the nuclear lamin network, revealing how protein networks with structural flaws cope with mechanical load