Strain gradient theory based on a new framework of non-local model

Abstract

A new framework of non-local model for the strain energy density is proposed in this paper. The global strain energy density of the representative volume element is treated as a non-local variable and can be obtained through a special integral of the local strain energy density. The local strain energy density is assumed to be dependent on both the strain and the rotation-gradient. As a result of the non-local model, a new strain gradient theory is derived directly, in which the first and second strain gradients, as well as the triadic and tetradic stress, are introduced in the context of work conjugate. For power law hardening materials, size effects in thin metallic wire torsion and ultra-thin cantilever beam bend are investigated. It is found that the result predicted by the theoretical model is well consistent with the experimental data for the thin wire torsion. On the other hand, the calculation result for the micro-cantilever beam bend clearly shows the size effect.

A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory

“…Since the classical continuum mechanics has failed to predict or interpret the experimentally observed size-dependent behaviors in small-scale structures [8][9][10][11], some nonclassical continuum theories such as the nonlocal, strain gradient and couple stress theories have been introduced, developed and utilized for analyzing this type of structures [12][13][14][15][16][17]. In the two latter nonclassical theories, there are some higher-order stress components beside the classical stresses.…”

A nonlocal treatment technique based on the background cell concept for micro-mechanical damage modeling

“…A common difficulty in this approach is in implementation into a commercial FE code, moreover, searching adjoining points is a time-consuming task and a challenge for the storage capacity, especially for 3D modeling. (2) The gradientdependent model is developed by taking into account the gradients of porosity or plastic strains for regulating strain distributions [3][4][5][6][7][8][9]. This approach was very popular in 1990s, and various models were suggested.…”

Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

“…According to the failure of classical continuum theory (CCT) to anticipate the size effect, various nonclassical theories have been developed with higher-order stress [11][12][13][14][15][16]. It is easier to examine the rotation of material elements with higher-order stress (the couple stress).…”