Scale-dependent nonlocal strain gradient isogeometric analysis of metal foam nanoscale plates with various porosity distributions

A scale-dependent nonlocal strain gradient isogeometric model of metal foam nanoscale plates with various porosity distributions is proposed. Three porosity distributions through the plate thickness including uniform, symmetric and asymmetric distributions are considered. The present model is efficient to capture both nonlocal and strain gradient effects in nanoplates. The strain–displacement relations are assumed to be derived from the higher-order shear deformation plate theory. Achieved relations will be then incorporated with the nonlocal strain gradient theory (NSGT) to reach deflections of metal foam nanoplates by using isogeometric analysis (IGA). Thanks to higher-order derivatives and continuity of NURBS basic functions, the IGA fulfills the weak form of nanoplates which requires at least the third-order derivatives in approximate formulations. The effects of different parameters including porosity distribution, porosity coefficient, length-to-thickness ratios, boundary condition, nonlocal parameter and length scale parameter on static and dynamic deflections of metal foam nanoplate are investigated. The reported results indicate that the mechanisms of stiffness-softening and stiffness-hardening mechanisms are pointed out in the present model. Also, a rise of porosity coefficient leads to a decrease of the plate stiffness, and a symmetrically porous metal foam is generally used to manufacture the nanoplate.