Thermally and mechanically induced strain gradient fields in architected 2D materials and beam structures

Abstract

The current contribution investigates the strain-gradient thermomechanical performance of architected materials and structures with uniform and graded inner designs. To that scope, an integral representation of strain-gradients in thermoelasticity, along with its Galerkin Boundary Element Method (GBEM) implementation are elaborated. The formulation accounts for both mechanical and thermal strain-gradients for the first time. Thereupon, the complete strain-gradient response upon uniaxial tensile (UT) and thermal loading (Th) is analyzed, performing direct comparisons among the strain-gradient fields induced in each case and providing summarizing statistics that associate higher-order thermal and mechanical effects. The numerical framework is used as a basis for the quantification of the impact of the underlying structural patterns on the equivalent internal length parameters of architected beam-type structures under thermomechanical loads in the context of simple gradient theory. It is found that thermal loads relate to comparable, yet lower, internal length parameters with respect to the ones obtained for uniaxially tensioned structures with uniform inner cellular designs. Both internal length and temperature variation contributions determine the strain-gradient thermomechanical response of beam-type architected structures, for which, exact, higher-order equivalent 1D displacement field solutions are first derived. Thermally-induced, higher-gradient displacements are found to be comparable with the ones obtained in UT-loaded structures with uniform inner cellular topologies. Moreover, inner material gradings are found to be able to considerably mitigate higher-order effects, a sensitivity that is not reproduced in the UT loading case. The results provided, along with the numerical and analytical methodologies elaborated, set the basis for the thermomechanical strain-gradient analysis of advanced architected media well-beyond the designs here investigated.