Related papers: An iterative nonlocal residual constitutive model …
Motivated by the existing complications of finding solutions of Eringen nonlocal model, an alternative model is developed here. The new formulation of the nonlocal elasticity is centered upon expressing the dynamic equilibrium requirements…
The paradoxes of differential nonlocal models have been attributed to the inconsistency in forming the nonlocal boundary conditions. To overcome these paradoxes, nonlocal boundary conditions should be correctly formed. However, still…
In this paper, the bending behaviour of small-scale Bernoulli-Euler beams is investigated by Eringen's two-phase local/nonlocal theory of elasticity. Bending moments are expressed in terms of elastic curvatures by a convex combination of…
The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…
Complications exist when solving the field equation in the nonlocal field. This has been attributed to the complexity of deriving explicit forms of the nonlocal boundary conditions. Thus, the paradoxes in the existing solutions of the…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type,…
We develop a general theory of nonlocal linear elasticity based on nonlocal gradients with general radial kernels. Starting from a nonlocal hyperelastic energy functional, we perform a formal linearization around the identity deformation to…
In this work, we combine the nonlocal theory of Eringen into the E-B beam bending together with nonlinear kinematics [3]. We briefly present the derivation and key equations of this nonlinearnonlocal beam theory and investigate the role of…
Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules…
In materials science, the challenge of rapid prototyping materials with desired properties often involves extensive experimentation to find suitable microstructures. Additionally, finding microstructures for given properties is typically an…
Thick rods are employed in Nanotechnology to build modern electro mechanical systems. Design and optimization of such structures can be carried out by nonlocal continuum mechanics which is computationally convenient when compared to…
We present neural network-based constitutive models for hyperelastic geometrically exact beams. The proposed models are physics-augmented, i.e., formulated to fulfill important mechanical conditions by construction, which improves accuracy…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Eringen's model is one of the most popular theories in nonlocal elasticity. It has been applied to many practical situations with the objective of removing the anomalous stress concentrations around geometric shape singularities, which…
Data-driven models based on deep learning algorithms intend to overcome the limitations of traditional constitutive modelling by directly learning from data. However, the need for extensive data that collate the full state of the material…
While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…
The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…