Do Van Thom^1,*, Pham Van Hoan², Nguyen Huu Phan²

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 1711-1734, 2025, DOI:10.32604/cmes.2025.071187 - 26 November 2025

Abstract This research utilizes analytical solutions to investigate the issue of nonlinear static bending in nanobeams affected by the flexomagnetic effect. The nanobeams are exposed to mechanical loads and put in a temperature environment. The equilibrium equation of the beam is formulated based on the newly developed higher-order shear deformation theory. The flexomagnetic effect is explained by the presence of the strain gradient component, which also takes into consideration the impact of small-size effects. This study has used a flexible transformation to derive the equilibrium equation for a single variable, which significantly simplifies the process of More >

Shubham Desai, Sai Sidhardh^*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 1271-1334, 2025, DOI:10.32604/cmes.2025.068141 - 31 August 2025

Abstract The increasing integration of small-scale structures in engineering, particularly in Micro-Electro-Mechanical Systems (MEMS), necessitates advanced modeling approaches to accurately capture their complex mechanical behavior. Classical continuum theories are inadequate at micro- and nanoscales, particularly concerning size effects, singularities, and phenomena like strain softening or phase transitions. This limitation follows from their lack of intrinsic length scale parameters, crucial for representing microstructural features. Theoretical and experimental findings emphasize the critical role of these parameters on small scales. This review thoroughly examines various strain gradient elasticity (SGE) theories commonly employed in literature to capture these size-dependent effects… More >

Hsin-Yi Kuo^*, Li-Huan Yang

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.1, pp. 841-872, 2025, DOI:10.32604/cmes.2025.065452 - 31 July 2025

Abstract This study aims to investigate the propagation of harmonic waves in nonlocal magneto-electro-elastic (MEE) laminated composites with interface stress imperfections using an analytical approach. The pseudo-Stroh formulation and nonlocal theory proposed by Eringen were adopted to derive the propagator matrix for each layer. Both the propagator and interface matrices were formulated to determine the recursive fields. Subsequently, the dispersion equation was obtained by imposing traction-free and magneto-electric circuit open boundary conditions on the top and bottom surfaces of the plate. Dispersion curves, mode shapes, and natural frequencies were calculated for sandwich plates composed of BaTiO₃ and More >

Oswaldo González-Gaxiola¹, Anjan Biswas^2,3,4,*, Ahmed H. Arnous⁵, Yakup Yildirim^6,7

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.3, pp. 2513-2525, 2025, DOI:10.32604/cmes.2025.062177 - 03 March 2025

Abstract Computational modeling plays a vital role in advancing our understanding and application of soliton theory. It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions. In the present study, we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity. This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures. The numerical simulation is accomplished through the application of an algorithm that integrates the classical… More >

Youngjin Hwang, Seungyoon Kang, Junseok Kim^*

CMC-Computers, Materials & Continua, Vol.82, No.2, pp. 1811-1838, 2025, DOI:10.32604/cmc.2025.061071 - 17 February 2025

Abstract This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts. Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications. The phase-field model, in particular, is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time. In this paper, we discuss the principles and implementations of various numerical methodologies More >

Ömer Ekim Genel^*, Hilal Koç, Ekrem Tüfekci

CMC-Computers, Materials & Continua, Vol.82, No.2, pp. 2043-2059, 2025, DOI:10.32604/cmc.2025.060111 - 17 February 2025

Abstract Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that… More >

Jianfeng Zhao^1,*, Xu Zhang², Guozheng Kang², Michael Ziaser³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.4, pp. 1-1, 2024, DOI:10.32604/icces.2024.012582

Abstract A continuum model of dislocation transport incorporating grain boundary transmission was developed within a dislocation-based crystal plasticity framework, which was then adopted to study the deformation mechanisms of gradient-structured material and bimodal-grained material. The nonlocal nature of the model on the slip system level enables the direct investigation of strain gradient effects caused by internal deformation heterogeneities. Furthermore, the interaction between dislocations and grain boundaries leads to the formation of pileups near grain boundaries, which is key to studying the grain size effects in polycrystals. Finite element implementation of the model for polycrystals with different… More >

Shaoqi Zheng¹, Zihao Yang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012200

Abstract This study proposes a novel method for predicting the microcrack propagation in composites based on coupling the local and non-local micromechanics. The special feature of this method is that it can take full advantages of both the continuum micromechanics as a local model and peridynamic micromechanics as a non-local model to achieve composite fracture simulation with a higher level of accuracy and efficiency. Based on the energy equivalence, we first establish the equivalent continuum micromechanics model with equivalent stiffness operators through peridynamic micromechanics model. These two models are then coupled into a closed equation system, More >

Haolun Zhang¹, Mengna Yang¹, Jie Wei², Yufeng Nie^2,*

Digital Engineering and Digital Twin, Vol.2, pp. 49-77, 2024, DOI:10.32604/dedt.2023.044180 - 31 January 2024

Abstract This paper mainly considers the formulation and theoretical analysis of the reduced-order numerical method constructed by proper orthogonal decomposition (POD) for nonlocal diffusion problems with a finite range of nonlocal interactions. We first set up the classical finite element discretization for nonlocal diffusion equations and briefly explain the difference between nonlocal and partial differential equations (PDEs). Nonlocal models have to handle double integrals when using finite element methods (FEMs), which causes the generation of algebraic systems to be more challenging and time-consuming, and discrete systems have less sparsity than those for PDEs. So we establish… More >

Linjuan Wang^1,*, Jianxiang Wang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09355

Abstract The prediction of overall dynamics of composite materials has been an intriguing research topic more than a century, and numerous approaches have been developed for this topic. One of the most successful representatives is the classical micromechanical models which assume that the behavior of a composite is the same as its constituents except for the difference in mechanical properties, e.g., effective moduli. With the development of advanced composite materials in recent years, especially metamaterials, it is found that the classical micromechanical models cannot describe complex dynamic responses of composites such as the dispersion and bandgaps… More >