A novel efficient mixed formulation for strain-gradient models

Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work, we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues while being simpler and computationally cheaper. The behavior of the new elements is further demonstrated through two numerical examples.