In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.

/pdf/material-interpolation-schemes-in-topology-optimization-1ps0tr57ei.pdf

Material interpolation schemes in topology optimization

Multi-scale computational homogenization: Trends and challenges

We present a computational homogenization approach for linear and nonlinear solid mechanics problems, which is fully compatible with conventional finite element code architecture. A seamless implementation in ABAQUS is presented including Python script, validation problems and a web-link where script files, user-defined subroutines and input files can be accessed. For linear problems, we demonstrate how to utilize ABAQUS existing facilities to develop analysis attributes required for solving a unit cell problem. For nonlinear problems, a Python script invoked by a coarse scale stress update procedure is introduced to carry out the scale bridging. The purpose of this paper is twofold: (i) to motivate practitioners to adopt the computational homogenization as an integral part of their analysis and design process; and (ii) to encourage commercial code vendors to seamlessly integrate the architectures proposed in their legacy codes.

/pdf/toward-realization-of-computational-homogenization-in-1w0nzdfn8e.pdf

Toward realization of computational homogenization in practice

Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models

Computational models are often used as tools to study traumatic brain injury. The fidelity of such models depends on the incorporation of an appropriate level of structural detail, the accurate representation of the material behavior, and the use of an appropriate measure of injury. In this study, an axonal strain injury criterion is used to estimate the probability of diffuse axonal injury (DAI), which accounts for a large percentage of deaths due to brain trauma and is characterized by damage to neural axons in the deep white matter regions of the brain. We present an analytical and computational model that treats the white matter as an anisotropic, hyperelastic material. Diffusion tensor imaging is used to incorporate the structural orientation of the neural axons into the model. It is shown that the degree of injury that is predicted in a computational model of DAI is highly dependent on the incorporation of the axonal orientation information and the inclusion of anisotropy into the constitutive model for white matter.

An axonal strain injury criterion for traumatic brain injury

Two-scale finite element analysis of heterogeneous solids with periodic microstructures

The generalized layout optimization method is applied to nonlinear problems. The algorithm was originally invented by Bendsoe and Kikuchi (1988), where an admissible design domain is assumed to be composed of periodic microstructures with tiny cavities; the sizes and the rotational angle of the cavities are defined as design variables which are optimized to minimize the applied work. The macroscoic material tensor of the porous material is calculated by the homogenization method for the sensitivity analysis. In order to apply it to nonlinear problems, we present a 2-D database of the material tensor calculated by the elasto-plastic homogenization method and an interpolation technique of the database for the practical computation. Several numerical examples of 2-D structures and a thin shell are shown to demonstrate the effectiveness of our algorithms. The algorithm is also extended to the finite deformation problems, and a practical optimized design is exhibited.

/pdf/optimization-of-2-d-structures-subjected-to-nonlinear-47hm5txeq7.pdf

Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method

Numerical analysis of an ultrasonically levitated droplet with a free surface boundary is discussed. The droplet is known to change its shape from sphere to spheroid when it is suspended in a standing wave owing to the acoustic radiation force. However, few studies on numerical simulation have been reported in association with this phenomenon including fluid dynamics inside the droplet. In this paper, coupled analysis using the distributed point source method (DPSM) and the moving particle semi-implicit (MPS) method, both of which do not require grids or meshes to handle the moving boundary with ease, is suggested. A droplet levitated in a plane standing wave field between a piston-vibrating ultrasonic transducer and a reflector is simulated with the DPSM–MPS coupled method. The dynamic change in the spheroidal shape of the droplet is successfully reproduced numerically, and the gravitational center and the change in the spheroidal aspect ratio are discussed and compared with the previous literature.

http://iopscience.iop.org/article/10.7567/JJAP.54.07HE04/pdf

Dynamic analysis of ultrasonically levitated droplet with moving particle semi-implicit and distributed point source method

The brain is the most important organ for life activity and humanity and is also an organ that tends to have residual disabilities after an accident because neuron cells cannot repair themselves. Therefore, protecting the brain from serious damage should be one of the most important objectives in automotive safety design for both passengers and pedestrians. For this reason, the Seikei University Graduate School and others have examined head impacts and the subsequent responses.

Kohei Yuge

Papers

Two-scale finite element analysis of heterogeneous solids with periodic microstructures

Optimization of 2-D structures subjected to nonlinear deformations using the homogenization method

Dynamic analysis of ultrasonically levitated droplet with moving particle semi-implicit and distributed point source method

Impact Injury Analysis of the Human Head

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations