Strain-Gradient Bar-Elastic Substrate Model with Surface-Energy Effect: Virtual-Force Approach
Suchart Limkatanyu,
Worathep Sae-Long,
Hamid Mohammad-Sedighi,
Jaroon Rungamornrat,
Piti Sukontasukkul,
Woraphot Prachasaree,
Thanongsak Imjai
Affiliations
Suchart Limkatanyu
Department of Civil and Environmental Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand
Worathep Sae-Long
Civil Engineering Program, School of Engineering, University of Phayao, Phayao 56000, Thailand
Hamid Mohammad-Sedighi
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 6135783151, Iran
Jaroon Rungamornrat
Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand
Piti Sukontasukkul
Construction and Building Materials Research Center, Department of Civil Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Woraphot Prachasaree
Department of Civil and Environmental Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand
Thanongsak Imjai
School of Engineering and Technology, Center of Excellence in Sustainable Disaster Management, Walailak University, Nakhon Si Thammarat 80161, Thailand
This paper presents an alternative approach to formulating a rational bar-elastic substrate model with inclusion of small-scale and surface-energy effects. The thermodynamics-based strain gradient model is utilized to account for the small-scale effect (nonlocality) of the bar-bulk material while the Gurtin–Murdoch surface theory is adopted to capture the surface-energy effect. To consider the bar-surrounding substrate interactive mechanism, the Winkler foundation model is called for. The governing differential compatibility equation as well as the consistent end-boundary compatibility conditions are revealed using the virtual force principle and form the core of the model formulation. Within the framework of the virtual force principle, the axial force field serves as the fundamental solution to the governing differential compatibility equation. The problem of a nanowire embedded in an elastic substrate medium is employed as a numerical example to show the accuracy of the proposed bar-elastic substrate model and advantage over its counterpart displacement model. The influences of material nonlocality on both global and local responses are thoroughly discussed in this example.
