Slender load-bearing elements in fully connected, joint-free lattices (mechanical metamaterials) develop load-induced rotational imperfections when deformation of adjacent members imposes evolving end rotations on otherwise straight columns. We distinguish these effects from pre-existing geometric imperfections and derive a closed-form nonlinear load–deflection solution for columns with prescribed boundary rotations, complemented by a semi-analytical approach incorporating column shortening. Nonlinear finite-element analyses validate the analytical predictions. Across five representative settings (force-, moment-, and distributed-load systems, architected interfaces, and interaction with pre-existing imperfections), we show that load-induced rotations can significantly reduce load-bearing capability. In a point-loaded two-column system, for instance, the critical force can decrease to 22% of the critical force of the equivalent pinned connected column. The results indicate that joint-free lattices with compliant surroundings may exhibit notable reductions in critical forces due to enforced boundary rotations and deformations of the connecting elements. The framework offers a practical basis for stability assessment of metamaterials and other fully connected structures, where boundary effects depend on the loading rather than being static initial imperfections. • Closed-form solution for columns with load-induced boundary rotations in joint-free lattices. • Semi-analytical extension includes interaction of axial shortening–rotation of the columns. • Differentiates load-induced from pre-existing geometrical imperfections. • Analytical predictions validated against nonlinear finite-element analyses. • Critical force reduction quantified for representative joint-free configurations.
Hedvard et al. (Sun,) studied this question.