The mechanical response of cellular materials with spinodal topologies

The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies are investigated: "solid models," where one of the two phases is modeled as a solid material and the remaining volume is void space; and "shell models," where the interface between the two phases is assumed to be a solid shell, with the rest of the volume modeled as void space. In both cases, a wide range of relative densities and spinodal characteristic feature sizes are investigated. The topology and morphology of all the numerically generated models are carefully characterized to extract key geometrical features and ensure that the distribution of curvatures and the aging law are consistent with the physics of spinodal decomposition. Finite element meshes are generated for each model, and the uniaxial compressive stiffness and strength are extracted. We show that while solid spinodal models in the density range of 30-70% are relatively inefficient (i.e., their strength and stiffness exhibit a high-power scaling with relative density), shell spinodal models in the density range of 0.01-1% are exceptionally stiff and strong. Spinodal shell materials are also shown to be remarkably imperfection insensitive. These findings are verified experimentally by in-situ uniaxial compression of polymeric samples printed at the microscale by Direct Laser Writing (DLW). At low relative densities, the strength and stiffness of shell spinodal models outperform those of most lattice materials and approach theoretical bounds for isotropic cellular materials. Most importantly, these materials can be produced by self-assembly techniques over a range of length scales, providing unique scalability

A versatile numerical approach for calculating the fracture toughness and R-curves of cellular materials

We develop a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and unveil the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices. The approach is based on finite element calculations of the J-integral on a single-edge-notch-bend (SENB) specimen, with individual bars modeled as beams having a linear elastic or a power-law elasto-plastic constitutive behavior and a maximum strain-based damage model. Results for three 2D isotropic lattice topologies (triangular, hexagonal and kagome) and two constituent materials (representative of a brittle ceramic (silicon carbide) and a strain hardening elasto-plastic metal (titanium alloy)) are presented. We extract initial fracture toughness and R-curves for all lattices and show that (i) elastic brittle triangular lattices exhibit toughening (rising R-curve), and (ii) elasto-plastic triangular lattices display significant toughening, while elasto-plastic hexagonal lattices fail in a brittle manner. We show that the difference in such failure behavior can be explained by the size of the plastic zone that grows upon crack propagation, and conclude that the nature of crack propagation in lattices (brittle vs ductile) depends both on the constituent material and the lattice architecture. While results are presented for 2D truss-lattices, the proposed approach can be easily applied to 3D truss and shell-lattices, as long as the crack tip lies within the empty space of a unit cell.Comment: 40 pages, 14 figure

Mechanical Performance of 3D Printed Interpenetrating Phase Composites with Spinodal Topologies

The mechanical response of interpenetrating phase composites (IPCs) with stochastic spinodal topologies is investigated experimentally and numerically. Model polymeric systems are fabricated by Polyjet multi-material printing, with the reinforcing phase taking the topology of a spinodal shell, and the remaining volume filled by a softer matrix. We show that spinodal shell IPCs have comparable compressive strength and stiffness to IPCs with two well-established periodic reinforcements, the Schwarz P triply periodic minimal surface (TPMS) and the octet truss-lattice, while exhibiting far less catastrophic failure and greater damage resistance, particularly at high volume fraction of reinforcing phase. The combination of high stiffness and strength and a long flat plateau after yielding makes spinodal shell IPCs a promising candidate for energy absorption and impact protection applications, where the lack of material softening upon large compressive strains can prevent sudden collapse. Importantly, in contrast with all IPCs with periodic reinforcements, spinodal shell IPCs are amenable to scalable manufacturing via self-assembly techniques

Catastrophic vs Gradual Collapse of Thin-Walled Nanocrystalline Ni Hollow Cylinders As Building Blocks of Microlattice Structures

Lightweight yet stiff and strong lattice structures are attractive for various engineering applications, such as cores of sandwich shells and components designed for impact mitigation. Recent breakthroughs in manufacturing enable efficient fabrication of hierarchically architected microlattices, with dimensional control spanning seven orders of magnitude in length scale. These materials have the potential to exploit desirable nanoscale-size effects in a macroscopic structure, as long as their mechanical behavior at each appropriate scale – nano, micro, and macro levels – is properly understood. In this letter, we report the nanomechanical response of individual microlattice members. We show that hollow nanocrystalline Ni cylinders differing only in wall thicknesses, 500 and 150 nm, exhibit strikingly different collapse modes: the 500 nm sample collapses in a brittle manner, via a single strain burst, while the 150 nm sample shows a gradual collapse, via a series of small and discrete strain bursts. Further, compressive strength in 150 nm sample is 99.2% lower than predicted by shell buckling theory, likely due to localized buckling and fracture events observed during in situ compression experiments. We attribute this difference to the size-induced transition in deformation behavior, unique to nanoscale, and discuss it in the framework of “size effects” in crystalline strength

Emergence of film-thickness- and grain-size-dependent elastic properties in nanocrystalline thin films

Molecular dynamics simulations of nanocrystalline Ni revealed that the in-plane Young’s modulus of 2.2 nm grained Ni film with ∼10 grains across its thickness was only 0.64% smaller than that of bulk, while it dropped to 24.1% below bulk value for ∼1 grain across film. This size dependence arises from the increased number of more compliant grains adjacent to the free surface. Simulations of nanocrystalline diamond revealed that the anharmonicity of the potential curve determined the sensitivity of the Young’s modulus to variations in the sample size

Concentration Independent Modulation of Local Micromechanics in a Fibrin Gel

Methods for tuning extracellular matrix (ECM) mechanics in 3D cell culture that rely on increasing the concentration of either protein or cross-linking molecules fail to control important parameters such as pore size, ligand density, and molecular diffusivity. Alternatively, ECM stiffness can be modulated independently from protein concentration by mechanically loading the ECM. We have developed a novel device for generating stiffness gradients in naturally derived ECMs, where stiffness is tuned by inducing strain, while local mechanical properties are directly determined by laser tweezers based active microrheology (AMR). Hydrogel substrates polymerized within 35 mm diameter Petri dishes are strained non-uniformly by the precise rotation of an embedded cylindrical post, and exhibit a position-dependent stiffness with little to no modulation of local mesh geometry. Here we present the device in the context of fibrin hydrogels. First AMR is used to directly measure local micromechanics in unstrained hydrogels of increasing fibrin concentration. Changes in stiffness are then mapped within our device, where fibrin concentration is held constant. Fluorescence confocal imaging and orbital particle tracking are used to quantify structural changes in fibrin on the micro and nano levels respectively. The micromechanical strain stiffening measured by microrheology is not accompanied by ECM microstructural changes under our applied loads, as measured by confocal microscopy. However, super-resolution orbital tracking reveals nanostructural straightening, lengthening, and reduced movement of fibrin fibers. Furthermore, we show that aortic smooth muscle cells cultured within our device are morphologically sensitive to the induced mechanical gradient. Our results demonstrate a powerful cell culture tool that can be used in the study of mechanical effects on cellular physiology in naturally derived 3D ECM tissues

Self calibrating micro-fabricated load cells

Self calibrating micro-fabricated load cells are disclosed. According to one embodiment, a self calibrating load cell comprises a resonant double ended tuning fork force sensor and a phase locked loop circuit for detection of frequency changes upon external load application to the resonant double ended tuning fork force sensor

Update (2.0) to MiniSurf—A minimal surface generator for finite element modeling and additive manufacturing

This is an update to PII: S2665963820300178.We present an updated version v2.0 of our minimal surface generator MiniSurf v1.0, that creates triply periodic minimal surface (TPMS) computer-aided design (CAD) files for both finite element modeling and additive manufacturing. Besides making the GUI more user-friendly, in this new version we significantly improve the mesh quality of the generated CAD files by incorporating a mesh smoothing feature. With this new smoothing feature, MiniSurf v2.0 can now produce high quality CAD files for more accurate finite element modeling and more precise additive manufacturing