Compliance optimization with nonlinear elastic materials: Application to constitutive laws dissymmetric in tension–compression

The compliance as a measure of the global rigidity of a structure is classically used in optimization in the case of linear elasticity. Under the assumption of small strains and small displacements, the aim of the paper is to extend a classical compliance optimization algorithm to nonlinear elastic materials with proportional dual thermodynamics potentials. A systematic method to prove the dual potentials proportionality is developed. It is used for different constitutive laws dissymmetric in tension–compression, and especially in the case of long fiber composite membranes.