Finite element mapping for spring network representations of the mechanics of solids

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.

Modeling multiscale evolution of numerous voids in shocked brittle material

The influence of the evolution of numerous voids on macroscopic properties of materials is a multiscale problem that challenges computational research. A shock-wave compression model for brittle material, which can obtain both microscopic evolution and macroscopic shock properties, was developed using discrete element methods (lattice model). Using a model interaction-parameter-mapping procedure, qualitative features, as well as trends in the calculated shock-wave profiles, are shown to agree with experimental results. The shock wave splits into an elastic wave and a deformation wave in porous brittle materials, indicating significant shock plasticity. Void collapses in the deformation wave were the natural reason for volume shrinkage and deformation. However, media slippage and rotation deformations indicated by complex vortex patterns composed of relative velocity vectors were also confirmed as an important source of shock plasticity. With increasing pressure, the contribution from slippage deformation to the final plastic strain increased. Porosity was found to determine the amplitude of the elastic wave; porosity and shock stress together determine propagation speed of the deformation wave, as well as stress and strain on the final equilibrium state. Thus, shock behaviors of porous brittle material can be systematically designed for specific applications.

General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models

We integrate the lattice Boltzmann model (LBM) and lattice spring model (LSM) to capture the coupling between a compliant bounding surface and the hydrodynamic response of an enclosed fluid. We focus on an elastic, spherical shell filled with a Newtonian fluid where no-slip boundary conditions induce the interaction. We calculate the "breathing mode" oscillations for this system and find good agreement with analytical solutions. Furthermore, we simulate the impact of the fluid-filled, elastic shell on a hard wall and on an adhesive surface. Understanding the dynamics of fluid-filled shells, especially near adhesive surfaces, can be particularly important in the design of microcapsules for pharmaceutical and other technological applications. Our studies reveal that the binding of these capsules to specific surfaces can be sensitive to the physical properties of both the outer shell and the enclosed fluid. The integrated LBM-LSM methodology opens up the possibility of accurately and efficiently capturing the dynamic coupling between fluid flow and a compliant bounding surface in a broad variety of systems.