Formulation methods of geometric and material nonlinearity problems

Abstract

A concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.