Computational Framework to Predict Failure and Performance of Bone-Inspired Materials

Mechanical and Crack Propagating Behavior of Sierpiński Carpet Composites

Fractals, mathematically defined as "self-similar subsets at different scales", are ubiquitous in nature despite their complexity in assembly and formulation. Fractal geometry formed by simple components has long been applied to many fields, from physics and chemistry to electronics and architecture. The Sierpiński carpet (SC), a fractal with a Hausdorff dimension of approximately 1.8933, has two-dimensional space-filling abilities and therefore provides many structural applications. However, few studies have investigated its mechanical properties and fracture behaviors. Here, utilizing the lattice spring model (LSM), we constructed SC composites with two base materials and simulated tensile tests to show how fractal iterations affect their mechanical properties and crack propagation. From observing the stress-strain responses, we find that, for either the soft-base or stiff-base SC composites, the second iteration has the optimal mechanical performance in the terms of stiffness, strength, and toughness compared to the composites with higher hierarchies. The reason behind this surprising result is that the largest stress intensities occur at the corners of the smallest squares in the middle zone, which consequently induces crack nucleation. We also find that the main crack tends to deflect locally in SC composites with a soft matrix, but in global main crack behavior, SC composites with a stiff matrix have a large equivalent crack deflection. Furthermore, considering the inherent anisotropy of SC composites, we rotated the samples by 45°. The results show that the tensile strength and toughness of rotated SC composites are inferior and the crack propagating behaviors are distinct from the standard SC composites. This finding infers advanced engineering for crack control and deflection by adjusting the orientation of SC composites. Overall, our study opens the door for future engineering applications in stretchable devices, seismic metamaterials, and structural materials with tunable properties and hierarchies.

Predicting pullout strength of pedicle screws in broken bones from X-ray images

Pedicle screw fixation is one of the most common procedures used in spinal fusion surgery. The screw loosening is a major concern, which may be caused by broken pedicles. In vitro pullout tests or insertion torque are the main approaches for assessing the stability of the screw; however, direct evidence was lacking for clinical human spines. Here, we aim to provide a model that can predict the pullout strengths of pedicle screws in various pedicle conditions from X-ray images. A weighted embedded bone volume (EBV) model is proposed for pullout strengths prediction by considering the bone heterogeneity and confinement of the screw. We showed that the pullout strength is proportional to the EBV for homogeneous bone and the weighted EBV for layered composite bone. The proposed weighted EBV model is validated with in vitro Sawbones® pullout experiments. The results show that the model has better accuracy than the simple EBV model, with a coefficient of determination of 0.94. The proposed weighted EBV model can help assess the stability of a pedicle screw in a broken pedicle by simply examining 2D X-ray images.

Down to the Bone: A Novel Bio-Inspired Design Concept

The solutions provided through natural evolution of living creatures serve as an ingenious source of inspiration for many technological and applicative fields. Along these lines, bone-inspired concepts lead to fascinating advances in product design, architecture and garments, thanks to the bone’s exceptional combination of strength, toughness and lightness. Structural applications are inspired by the bone’s ability to resist fracture under a large spectrum of forces, while the high surface area and pore connectivity of bone architecture present exciting opportunities from an aesthetic point of view. Behind these inspirations, a disruptive common belief emerges: “down to the bone”, a journey in search of equality, universality and substantiality. Herein, we explore the current state of the art in bone-inspired applications in these fields, considering the two major categories of structural and aesthetic inspirations and discussing further technological developments.

3D-Printed Architected Materials Inspired by Cubic Bravais Lattices

Learning from Nature and leveraging 3D printing, mechanical testing, and numerical modeling, this study aims to provide a deeper understanding of the structure-property relationship of crystal-lattice-inspired materials, starting from the study of single unit cells inspired by the cubic Bravais crystal lattices. In particular, here we study the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattices. Mechanical testing of 3D-printed structures is used to investigate the influence of different printing parameters. Numerical models, validated based on experimental testing carried out on single unit cells and embedding manufacturing-induced defects, are used to derive the scaling laws for each studied topology, thus providing guidelines for materials selection and design, and the basis for future homogenization and optimization studies. We observe no clear effect of the layer thickness on the mechanical properties of both bulk material and lattice structures. Instead, the printing direction effect, negligible in solid samples, becomes relevant in lattice structures, yielding different stiffnesses of struts and nodes. This phenomenon is accounted for in the proposed simulation framework. The numerical models of large arrays, used to define the scaling laws, suggest that the chosen topologies have a mainly stretching-dominated behavior-a hallmark of structurally efficient structures-where the modulus scales linearly with the relative density. By looking ahead, mimicking the characteristic microscale structure of crystalline materials will allow replicating the typical behavior of crystals at a larger scale, combining the hardening traits of metallurgy with the characteristic behavior of polymers and the advantage of lightweight architected structures, leading to novel materials with multiple functions.

Understanding Plant Biomass via Computational Modeling

Plant biomass, especially wood, has been used for structural materials since ancient times. It is also showing great potential for new structural materials and it is the major feedstock for the emerging biorefineries for building a sustainable society. The plant cell wall is a hierarchical matrix of mainly cellulose, hemicellulose, and lignin. Herein, the structure, properties, and reactions of cellulose, lignin, and wood cell walls, studied using density functional theory (DFT) and molecular dynamics (MD), which are the widely used computational modeling approaches, are reviewed. Computational modeling, which has played a crucial role in understanding the structure and properties of plant biomass and its nanomaterials, may serve a leading role on developing new hierarchical materials from biomass in the future.

Image-Based Polygonal Lattices for Mechanical Modeling of Biological Materials: 2D Demonstrations

Understanding the structure-property relationship of biological materials, such as bones, teeth, cells, and biofilms, is critical for diagnosing diseases and developing bioinspired materials and structures. The intrinsic multiphase heterogeneity with interfaces places great challenges for mechanical modeling. Here, we develop an image-based polygonal lattice model for simulating the mechanical deformation of biological materials with complicated shapes and interfaces. The proposed lattice model maintains the uniform meshes inside the homogeneous phases and restricts the irregular polygonal meshes near the boundaries or interfaces. This approach significantly simplifies the mesh generation from images of biological structures with complicated geometries. The conventional finite element simulations validate this polygonal lattice model. We further demonstrate that the image-based polygonal lattices generate meshes from images of composite structures with multiple inclusions and capture the nonlinear mechanical deformation. We conclude the paper by highlighting a few future research directions that will benefit from the functionalities of polygonal lattice modeling.

Role of porosity and matrix behavior on compressive fracture of Haversian bone using random spring network model

Haversian remodeling is known to result in improved resistance to compressive fracture in healthy cortical bone. Here, we examine the individual roles of the mean porosity, structure of the network of pores and remodeled bone matrix properties in the fracture behavior of Haversian bone. The detailed structure of porosity network is obtained both pre- and post-testing of dry cubical bone samples using micro-Computed Tomography. Based on the periodicity in the features of porosity along tangential direction, we develop a two dimensional porosity-based random spring network model for Haversian bone. The model is shown to capture well the macroscopic response and reproduce the avalanche statistics similar to recently reported experiments on porcine bone. The predictions suggest that at the millimeter scale, the remodeled bone matrix of Haversian bone is less stiff but tougher than that of plexiform/primary bone.