Article
Materials Science, Multidisciplinary
Sriram Ganesan, Iman Javaheri, Veera Sundararaghavan
Summary: Measurement and analysis of microstructures are crucial for materials design and structural performance. By using a generalized inverse Voronoi problem to approximate 3D microstructures from surface EBSD images, the study was able to compare predicted surface strains to experimentally measured data, finding that surface strains were qualitatively similar among different reconstructions but subsurface grains influenced the choice of activated slip systems. The results highlight the importance of performing a full 3D crystal plasticity analysis for accurate interpretation of measured surface data.
MECHANICS OF MATERIALS
(2021)
Article
Engineering, Multidisciplinary
Wenlong Tian, Lehua Qi
Summary: This work focuses on the use of Periodic Boundary Condition (PBC) in the Finite Element Homogenization (FEH) method to numerically determine the Thermo-mechanical (T-M) properties of composites. Unified numerical implementation algorithms of PBC are proposed and detailed for accurate prediction of the elastic properties, coefficients of thermal expansion, and elasto-plastic behaviors of composites. The algorithms are verified to accurately predict the T-M properties of composites, including thermo-elastic properties and elasto-plastic behaviors under different loading paths, through comparison with analytical models, DIGIMAT-FE method, experimental tests, and literature results.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Chemistry, Physical
Xingshuai Zheng, Tengfei Sun, Jixing Zhou, Rupeng Zhang, Pingmei Ming
Summary: This paper presents a new implementation of Voronoi diagram in Laguerre geometry for generating numerical models of polycrystalline microstructures. The method allows control over grain size and shape, and the modeling of 3D grain boundaries with specified thickness. The distribution of grain sizes in the models is fitted to a lognormal distribution instead of the normal distribution in traditional Voronoi tessellation methods. Statistical analyses and simulations are conducted to verify the effectiveness of the proposed method in modeling polycrystalline ceramic materials.
Article
Engineering, Manufacturing
Quang Thang Do, Cong Hong Phong Nguyen, Young Choi
Summary: A method for cellular structure design based on homogenization and Voronoi tessellation is proposed, improving structural stability and robustness while reducing computation costs.
ADDITIVE MANUFACTURING
(2021)
Article
Mathematics, Applied
Neeraj Yadav, Julian H. Kang, Zofia K. Rybkowski, Matthew T. Yarnold, Weiling He
Summary: This article introduces a method using Voronoi tessellation to optimize the structural form, which reduces the standard deviation of stress, as well as the mean and maximum stress values. The findings suggest that this method has the potential to be applied in structural optimization.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2023)
Article
Chemistry, Multidisciplinary
Siqin Liu, Zhusheng Zhou, Weizu Zeng
Summary: This study combines the Poisson disk node generation algorithm and the centroid Voronoi node adjustment algorithm to achieve an even and random node distribution. The partial derivative of the unknown parameters in the differential equation is represented by the linear combination of the function values of adjacent nodes, solving the problems caused by inconsistent grid divisions. A Cerjan damping boundary condition is proposed to handle boundary reflection and avoid instability introduced by boundary conditions.
APPLIED SCIENCES-BASEL
(2023)
Article
Metallurgy & Metallurgical Engineering
Jian-cong Zhang, Quan Jiang, Guang-liang Feng, Shao-jun Li, Shu-feng Pei, Ben-guo He
Summary: This study investigated the geological characteristics and crack patterns of columnar jointed basalt, and developed a method to simulate irregular polygonal crack patterns. The results revealed that geometric irregularity significantly affects the mechanical properties of columnar jointed rock mass.
JOURNAL OF CENTRAL SOUTH UNIVERSITY
(2022)
Article
Materials Science, Multidisciplinary
Wenlong Tian, Xujiang Chao, M. W. Fu, Lehua Qi, Luyan Ju
Summary: This paper proposes a new algorithm for predicting the coefficients of thermal expansion of different composite systems, which guarantees stress and strain continuities on the representative volume elements for certain composites, while satisfying the micro-macro energy balance and zero macro-stress constraint. The proposed algorithm is validated to accurately predict the CTEs of composites through comparison with experimental tests and other numerical methods.
MECHANICS OF MATERIALS
(2021)
Article
Mathematics
Wayne M. Lawton
Summary: This passage introduces a locally finite multiset and the Radon measure defined by it. It discusses the Bohr almost periodicity of the measure in the sense of Favorov. It presents a proof of existence for the toral type case and computes the density. Additionally, the passage mentions a construction that can be used to study Fourier quasicrystals.
JOURNAL OF GEOMETRIC ANALYSIS
(2022)
Article
Engineering, Multidisciplinary
Helmut Harbrecht, Michael Multerer, Remo von Rickenbach
Summary: This article presents an optimal design approach for the microstructure in scaffolds by combining shape optimization and homogenization. By calculating the effective tensor and using the shape gradient to update the microstructure, the desired effective tensor can be achieved. Extensive numerical studies demonstrate the applicability and feasibility of the approach.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Wenxuan Xia, Erkan Oterkus, Selda Oterkus
Summary: This work presents an ordinary state-based peridynamic homogenization method to obtain effective material properties of periodic micro-structured materials, with the unique advantage of governing equation in integro-differential form. With the rapid advancement in additive manufacturing technology, micro-structured materials with defects have attracted significant attention, and this study provides a new approach to obtain their effective properties.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2021)
Article
Chemistry, Physical
Tuhin Das, Rohan Chakrabarty, Jun Song, Stephen Yue
Summary: This study utilizes a two-fold approach to investigate hydrogen diffusion characteristics in martensitic steels, examining the role of different traps and microstructures on H diffusion. The findings suggest that high angle boundaries have greater influence at low H concentrations, while dislocations have a more pronounced impact at high H concentrations, and the importance of packet boundaries in moderating H diffusion is highlighted.
INTERNATIONAL JOURNAL OF HYDROGEN ENERGY
(2022)
Article
Mathematics, Applied
S. Aiyappan, K. Pettersson
Summary: This paper addresses the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The results show that the homogenization holds in terms of weak L-2 convergence of solutions and flows, assuming natural hypotheses on the regularity of the domain. The strong L-2 convergence of average preserving extensions of solutions and flows is also considered.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Geosciences, Multidisciplinary
Yongyi Wang, Bin Gong, Chunan Tang
Summary: The study investigates the progressive failure process of columnar jointed basalts under different model boundaries and confining pressures using meso-damage mechanics, statistical strength theory, and continuum mechanics. Simulation results show variations in fracture processes and acoustic emission rules under different stress conditions, providing valuable insights into the fracture mechanism and energy evolution of CJBs.
FRONTIERS IN EARTH SCIENCE
(2021)
Article
Mathematics, Applied
Eduard Marusic-Paloka, Igor Pazanin
Summary: The study focuses on viscous flow through a reservoir with a porous boundary using asymptotic analysis and homogenization. By assuming periodicity of the pores, an effective boundary condition is derived and rigorously justified. The velocity on the boundary follows a version of the Darcy law, which can also be interpreted as the Beavers-Joseph law for the tangential component.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)