Eringen’s Nonlocal Integral Elasticity and Applications for Structural Models

A review of size-dependent continuum mechanics models for micro- and nano-structures

“…-Having more reasonable results peculiar to the integral form for the sake of the energy consistent quadratic relations [31][32][33] -Nonself-adjointness of energy performance [194][195][196][197].…”

“…-Paradox outcomes pertinent to the obtained eigenfrequency values against the classical model (Softening response against hardening behavior of the model) [53,70] -Having contrary results for some special cases of boundary conditions and loading such as a concentrated load at free end, or a clamped-pinned as well as a clamped-clamped structure [53,70] -Having non-conservative problems for the differential form [53,70,[196][197][198] -Dislocations and disclinations (the elastic strain energy of defects) [53,[196][197][198] -Wave dispersion especially for higher values and surface waves [31,32] -Stress field at the Griffith crack [31,32] -M/NEMS cantilever actuators [195] -Fracture and plastic yielding [31,32] Cosserat theory -Considered as a particular model of complex medium [200].…”

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

“…Therefore, using the nonlocal strain-gradient model size-dependent model gives a more realistic model at micro/nano-scale. In this regard, there are many advantages, drawbacks, and key applications pertinent to using the nonlocalstress gradient size-dependent methods [55][56][57][58][59][60]. For example, this hybrid model contains both nonlocal and material length scale parameters and predict the stiffness-hardening influences using the length scale parameter [61][62].…”