# Chaotic behavior analysis of two-bar trusses under inelastic effects through Lyapunov exponents

## Palavras-chave:

Mixed-hardening model, Lyapunov exponents, Positional Finite Element Method, Nonlinear analysis## Resumo

The advancement of engineering structures is increasingly leading to slender and light elements that

require more complex analysis. Instability problems are frequently observed in such situations, and their study is

of fundamental importance. Numerical methods are commonly used in those analyses. It is proposed in this work

to use a variation of the Finite Element Method, called for a Positional Formulation (PFEM), with the advantage

that the geometric nonlinearity is naturally incorporated into the method. In terms of physical nonlinearity, a

mixed-hardening model is used in the Formulation. The dynamic analysis is carried out by Newmark‘s method

of integration in the time domain, and the Newton-Raphson Method is used to solve the equations of equilibrium.

Also, Lyapunov exponents are employed to determine the regions where the chaotic behavior occurs. One example

of a two-truss bar is used to verify the effectiveness of the implemented formulation and the influence of inelasticity

in the chaotic behavior. The analysis is done by different values of the initial conditions, since chaos is sensitive to

such variations.