Isogeometric analysis of first and second strain gradient elasticity

The elastic energy in the conventional Cauchy continuum model depends on the gradient of the displacement field, which is not adequate to show the behavior of a system under point and line forces. Applying these kinds of boundary conditions to the continuum will lead to singularities. To overcome this problem, a generalization of the Cauchy continuum concept is a choice. In this paper, isogeometric analysis is used to simulate the behavior of second- and third-gradient materials. As expected, a significant improvement in the efficiency and accuracy of the attained results compared to the conventional finite element method is noticed.