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Direct ink writing (DIW) process is a facile additive manufacturing technology to fabricate three-dimensional (3D) objects with various materials. Its versatility has attracted considerable interest in academia and industry in recent years. As such, upsurging endeavors are invested in advancing the ink flow behaviors in order to optimize the process resolution and the printing quality. However, so far, the physical phenomena during the DIW process are not revealed in detail, leaving a research gap between the physical experiments and its underlying theories. Here, we present a comprehensive analytical study of non-Newtonian ink flow behavior during the DIW process. Different syringe-nozzle geometries are modeled for the comparative case studies. By using the computational fluid dynamics (CFD) simulation method, we reveal the shear-thinning property during the ink extrusion process. Besides, we study the viscosity, shear stress, and velocity fields, and analyze the advantages and drawbacks of each syringe-nozzle model. On the basis of these investigations and analyses, we propose an improved syringe-nozzle geometry for stable extrusion and high printing quality. A set of DIW printing experiments and rheological characterizations are carried out to verify the simulation studies. The results developed in this work offer an in-depth understanding of the ink flow behavior in the DIW process, providing valuable guidelines for optimizing the physical DIW configuration toward high-resolution printing and, consequently, improving the performance of DIW-printed objects.

 

Abstract The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models. 

As a facile and versatile additive manufacturing technology, direct ink writing (DIW) has attracted considerable interest in academia and industry to fabricate three-dimensional structures with unique properties and functionalities. However, so far, the physical phenomena during the DIW process are not revealed in detail, leaving a research gap between the physical experiments and the underlying theories. Here, we presented a comprehensive simulation study of non-Newtonian ink flow during the DIW process. We used the computational fluid dynamics (CFD) method and revealed the shear-thinning behavior during the extrusion process. Different nozzle geometry models were adopted in the simulation. The advantages and drawbacks of each syringe-nozzle geometry were analyzed. In addition, the ink shear stress and velocity fields were investigated and compared in the case studies. Based on these investigations and analysis, we proposed an improved syringe-nozzle geometry towards high-resolution DIW. Consequently, the high-resolution and high shape fidelity DIW could enhance the DIW product performance. The results developed in this work offer valuable guidelines and could accelerate further advancement of DIW.

 

Many geo‐engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase‐field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase‐field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy‐based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase‐field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase‐field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. The comparison of numerical results for two‐dimensional test cases with existing analytical solutions demonstrates that the proposed phase‐field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three‐dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

 

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off‐fault damage over a wide range of spatial and temporal scales. Here, we develop a phase‐field model for quasi‐dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off‐fault damage processes with a single formulation. Built on a recently developed phase‐field framework for shear fractures with frictional contact, the proposed formulation incorporates rate‐ and state‐dependent friction, radiation damping, and their impacts on fault mechanics and off‐fault damage. We show that the numerical results of the phase‐field model are consistent with those obtained from well‐verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase‐field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.