Strain gradient viscoelastic solution and cross-scale hardening-softening behavior for a pressurized thick spherical shell cell

The thick spherical shell cell is a common structural element employed routinely in constructing the new advanced materials. The strain gradient viscoelastic solution of a pressurized thick spherical shell cell is presented based on a strain gradient viscoelasticity theory. This solution captures the hardening and softening effects of materials by means of a gradient parameter, in which the higher-order viscosity is included by introducing a higher-order viscoelastic model. The hardening-softening behavior at the micro-/nano-scale is displayed, and the positive/inverse Hall-Petch character can be explained using the strain gradient viscoelastic model. During the derivation, the variational principle is used to obtain the governing equation and boundary conditions. The solution of the strain gradient viscoelastic problem with specific boundary conditions is then derived in detail by employing the Laplace transformation. Moreover, the strain gradient viscoelastic solution is obtained directly from the strain gradient elastic solution using the correspondence principle between the strain gradient viscoelasticity and the strain gradient elasticity. The stiffness of the pressurized spherical shell is discussed and compared with the result of the traditional simplified strain gradient elasticity. The strain gradient viscoelastic solution of stiffness is related to the material parameters with both time and scales.

Automated summary

The paper presents a strain gradient viscoelastic solution for a pressurized thick spherical shell cell, capturing the hardening and softening effects of materials through a gradient parameter and higher-order viscoelastic model. The behavior at micro-/nano-scale and the Hall-Petch character can be explained using this model. The stiffness of the pressurized spherical shell is discussed in relation to material parameters with both time and scales.