Article
Mechanics
Giovanni Romano, Marina Diaco
Summary: Nonlocal elasticity models are addressed through a general formulation involving source and target fields in dual Hilbert spaces. The focus is on small movements and a geometrically linearized approximation is assumed feasible. The analysis discusses the linear, symmetric, and positive definite relationship between dual fields in the local elastic law, governed by a strictly convex, quadratic energy functional.
Article
Engineering, Multidisciplinary
Alaa A. Abdelrahman, Ismail Esen, Cevat Ozarpa, Mohamed A. Eltaher
Summary: In this study, a nonclassical dynamic finite element model is developed based on the nonlocal strain gradient theory to analyze the dynamic behavior of perforated nanobeam structures under moving mass/load. The model considers size scale and microstructure effects, and addresses shear locking issues in slender nanobeams. The effects of perforation, mass/load velocities, inertia of mass, microstructure parameter, and nonlocal size scale effects on the dynamic and vibration responses are investigated.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Engineering, Mechanical
Philip Crone, Peter Gudmundson, Jonas Faleskog
Summary: The influence of small, spherical, elastic particles dispersed within a matrix on macroscopic work hardening is studied. A proposed analytical solution based on an initial yield strength model is validated numerically and calibrated against experimental data.
INTERNATIONAL JOURNAL OF PLASTICITY
(2022)
Article
Engineering, Multidisciplinary
Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung, Timon Rabczuk
Summary: A general finite deformation higher-order gradient elasticity theory is proposed in the paper, reducing the material parameters significantly under certain simplifications. A nonlocal operator method is developed and applied to numerical examples, demonstrating the stiffness response of the high gradient solid theory and the capability of the nonlocal operator method in solving higher-order physical problems.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mechanics
Baiwei Zhang, Jun Luo
Summary: In this paper, a novel phase field (PF) model for fracture is developed within the framework of strain gradient elasticity. The model is numerically implemented and validated through analysis of stress fields near static crack tips, with various strain energy decomposition methods compared and discussed for their impact on fracture behavior. The study demonstrates the efficacy of the proposed PF model in predicting complex fracture behaviors under gradient elasticity.
ENGINEERING FRACTURE MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Suchart Limkatanyu, Worathep Sae-Long, Hamid M. Sedighi, Jaroon Rungamornrat, Piti Sukontasukkul, Hexin Zhang, Prinya Chindaprasirt
Summary: In this work, a novel flexibility-based nonlocal frame element for nano-sized frame-like structures is proposed. The element equation is constructed within the framework of flexibility-based finite element formulation, and the material small-scale effect is consistently represented by the stress-driven nonlocal integral model. The proposed nonlocal frame element demonstrates accuracy and characteristics in different numerical examples, showing its applicability in eliminating paradoxical responses and investigating the material small-scale effect.
ENGINEERING WITH COMPUTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: It has been found that the common nonlocal strain gradient theory has inconsistencies, but the local/nonlocal strain gradient (LNSG) theory can solve the transverse vibrations of nanobeams. By introducing a higher order beam element in finite element analysis, numerical and exact solutions for LNSG nanobeams are obtained.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
Tarek Merzouki, Mohammed Sid Ahmed Houari, Mohamed Haboussi, Aicha Bessaim, Manickam Ganapathi
Summary: In this study, a new trigonometric two-variable shear deformation beam nonlocal strain gradient theory is proposed. The combined effects of nonlocal stress and strain gradient on the bending, buckling, and free vibration analysis of nanobeams are investigated. The proposed model shows good predictive capability and accuracy within the nonlocal context, as demonstrated through numerical examples and comparisons with other higher-order shear deformation beam theories.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Omer Civalek, Busra Uzun, Mustafa Ozgur Yayli
Summary: This paper proposes a finite element model to investigate the size-dependent vibrational responses of guide-supported imperfect functionally graded nonlocal beams embedded in an elastic foundation. The nonlocal finite element solution considers nonlocal effect, power-law distribution function, sigmoid distribution function, even and uneven porosity models, elastic foundation parameter, and guide support condition for vibration analysis of imperfect FG nanobeams. Tables and figures are used to show the frequency values of perfect/imperfect FG power-law and sigmoid nanobeams obtained by using a nonlocal FE method.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Chemistry, Multidisciplinary
Ozgur Aslan, Emin Bayraktar
Summary: This work presents analytical solutions for 2D model problems to demonstrate the unique plastic fields generated by the micromorphic approach for gradient plasticity. It also analyzes the constitutive behavior of the material undergoing plastic deformation. Additionally, the matching of analytical solutions with numerical results is demonstrated.
APPLIED SCIENCES-BASEL
(2021)
Article
Mathematics, Applied
Christian Glusa, Marta D'Elia, Giacomo Capodaglio, Max Gunzburger, Pavel B. Bochev
Summary: This study presents a mathematically rigorous formulation for a nonlocal interface problem with jumps, and proposes an asymptotically compatible finite element discretization for the weak form of the interface problem. Numerical tests demonstrate the applicability, numerical convergence to exact nonlocal solutions, convergence to the local limit, and robustness with respect to the patch test of the technique.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Jin Chen, Bipul Hawlader, Kshama Roy, Kenton Pike
Summary: This study implements original and modified nonlocal methods in a Eulerian-based large deformation FE program, using a simplified approach to simulate two biaxial compression tests. The results are compared with nonlocal Lagrangian-based FE analysis and nonlocal Material Point Method (MPM) of simulation. The modified nonlocal methods, especially the over-nonlocal method, show better performance in mesh convergence analysis. Several approaches have been proposed to minimize the computational costs of nonlocal modelling.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Engineering, Mechanical
Mahdi Mojahedi
Summary: This article investigates the mechanical behavior of a nonlinear nanobeam under static and dynamic loading conditions using a nonlinear model that combines analytical and finite-element methods, as well as the non-local strain gradient theory. The equation of motion for the nanobeam is derived using Hamilton's principle and dimensionless parameters are established. The study analyzes the deflection under static loading conditions using the Galerkin method and obtains the time-dependent nonlinear equation under initial conditions using the same method. The natural frequency, nonlinear frequency, and forced vibrations of the nanobeam are determined using the method of multiple scales.
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES
(2023)
Article
Mechanics
Guoqiang Deng, Gary Dargush
Summary: In this paper, a novel mixed convolved action approach is developed for consistent couple stress theory, and it is applied to different problems to study the characteristics of impulsive loading under skew-symmetric couple stress theory.
Article
Materials Science, Multidisciplinary
Nikolaos Aravas, Ioanna Papadioti
Summary: A non-local gradient plasticity model for porous metals accounting for deformation-induced anisotropy is introduced, incorporating the evolution of porosity and anisotropy due to changes in void shape and orientation. The model's mathematical characteristics are analyzed, showing a higher hardening modulus compared to the local model, leading to elliptic behavior and eliminating discontinuous solutions. Numerical integration algorithms, boundary value problem implementation, and analytical methods for eigenvector calculations are discussed, with the non-local model implemented in ABAQUS for various example problems.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
