Determination of the coefficients of the green-type material model by non-linear programming

Material planning is an important and developing part of applied mechanics. The problem is usually solved by FEM, which leads to highly non-linear equations causing several numerical problems. This paper presents a method for the determination of the coefficients of a Green-type material model using mathematical programming based on the theorem of virtual force. The material model is included in the compatibility equations. The material parameters appear as unknowns in the non-linear objective function, while the conditions remain linear. The uniqueness and stability of the material model (e.g. Drucker postulates) are assured by inequality conditions. The boundary conditions are considered. Sample problems were run by a program for non-linear mathematical programming problems written in Fortran 77