Numerical approach for a continuum theory with higher stress gradients

Abstract

We use an extended balance of linear momentum derived from stress field analysis of higher order terms in power series expansion. Thus, the balance equation accounts for higher gradients of stress in the contiguity of continuum points. Interestingly, it does not coincide with the balance of linear momentum from strain gradient elasticity. As shown in [1], it exhibits an inverse sign for the extended term compared to strain gradient elasticity. We are interested in the mechanical interpretation of this inversed sign since it seems to inverse the stiffening effect of strain gradient elasticity. Therefore, we set up the weak form of our extended balance equation by means of Galerkin's approach. Then, we use the Finite Element Method to approximate the weak form with help of different shape functions. In this context we also use Isogeometric Analysis since it is very promising for a numerical model with higher gradients.