2017/01/05 by Amit Patra, Patra, Amit K., S. Gopalakrishnan +3
Engineering · Materials Science · #Composite Structure Analysis and Optimization #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Nonlocal and gradient elasticity in micro/nano structures #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1701.01457
openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a unified nonlocal rational continuum enrichment technique is\npresented for improving the dispersive characteristics of some well known\nclassical continuum equations on the basis of atomistic dispersion relations.\nThis type of enrichment can be useful in a wide range of mechanical problems\nsuch as localization of strain and damage in many quasibrittle structures, size\neffects in microscale elastoplasticity, and multiscale modeling of materials. A\nnovel technique of transforming a discrete differential expression into an\nexact equivalent rational continuum derivative form is developed considering\nthe Taylor's series transformation of the continuous field variables and\ntraveling wave type of solutions for both the discrete and continuum field\nvariables. An exact equivalent continuum rod representation of the 1D harmonic\nlattice with the non-nearest neighbor interactions is developed considering the\nlattice details. Using similar enrichment technique in the variational\nframework, other useful higher-order equations, namely nonlocal rational\nMindlin-Herrmann rod and nonlocal rational Timoshenko beam equations, are\ndeveloped to explore their nonlocal properties in general. Some analytical and\nnumerical studies on the high frequency dynamic behavior of these novel\nnonlocal rational continuum models are presented with their comparison with the\natomistic solutions for the respective physical systems. These enriched\nrational continuum equations have crucial use in studying high-frequency\ndynamics of many nano-electro-mechanical sensors and devices, dynamics of\nphononic metamaterials, and wave propagation in composite structures.\n