A Finite Element Model For Inverse Design Problems In Large Deformations Anisotropic Hyperelasticity

Abstract

This paper introduces a finite element model for the inverse design of pieces with large displacements
in the elastic range. The problem consists in determining the initial shape of the piece, such
that it attains the designed shape under the effect of service loads. The model is particularly focused on
the design of pieces with a markedly anisotropic behavior, like laminated turbine blades. The formulation
expresses equilibrium on the distorted configuration. However, it uses the standard constitutive equation
library, which is usually expressed for measures attached to the undistorted configuration. Modifications
in standard finite elements codes are then restricted to the routines for the computation of the finite element
internal forces and tangent matrix. Two application examples are given, the first one for validation
purposes, while the second application has industrial interest for the design of turbine blades.