Nonlinear Finite Element Analysis with 2D Lattice Models

Linear elastic models are often sufficient in the engineering design of structural and mechanical systems. Given that the yield capacity of the material is not reached or exceeded one finds a reasonable design. However, uncertainties in precise material integrity, construction or manufacturing techniques, processes and service conditions often pose a concern with regards to long term performance of designed systems during their service life. Repetitive utilization of these systems predisposes them to tear and wear and deleterious conditions which may come from the simple effect of cyclic (repetitive) loading. An in-depth study of the nonlinear response of materials to such loading conditions and imperfections in the material are imperatively demanded for a more effective design. A look at the constitutive models depicting these phenomena using rather than a continuum material, a discretized material model (2D lattice models) and employing the finite element method of analysis will unveil characteristic material responses to various load conditions in the mechanics of structures.