Abstract
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.
Highlights
Mechanical modeling plays a crucial role in understanding organisms’ physiological responses from the cellular level[1] to the whole-body level[2] under complicated in vivo environments
We take an example of the mechanical simulation of a 2D proximal femur, whose deformation and fracture have been the benchmarks to examine modeling methods including the image-based finite element simulations.[43−45] Here, we present a method of maintaining uniform meshes in the majority of the structure, with nonuniform polygonal meshes limited near the boundaries
Similar to the quadrilateral lattice model, we show that the polygonal lattice model can be established by applying the technique of computing the lattice spring constant from the shape functions in polygon element methods,[72−76] known as virtual elements
Summary
Mechanical modeling plays a crucial role in understanding organisms’ physiological responses from the cellular level[1] to the whole-body level[2] under complicated in vivo environments. One of the prominent complexities is the complicated anatomy with heterogeneous material phases in various organs and tissues, such as bones,[6−10] brains,[11] and cartilages.[12] It has been well documented that structure heterogeneity plays a critical role in determining the mechanical properties of biological materials.[13,14] The significance of heterogeneity shows in biomimetic materials with similar heterogeneous structures.[15−17] The interaction between different phases requires coupling across materials with distinctive rheological properties through interfaces Handling these complexities in modeling poses great challenges for computational science and engineering and has attracted attention to developing more efficient modeling algorithms and simulation platforms.[18−23]. The simplicity of the polygonal lattice model makes it a very promising candidate to be integrated with existing simulation methods to tackle multiphysics problems, such as coupling fluid and structure such as the lattice Boltzmann method for fluid−structure interactions.[70]
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