Development of Sliding Connections for Structural Analysis by a Total Lagrangian FEM Formulation

The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

Section: Positional Finite Element Methodsmentioning

confidence: 99%

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Cavalcante

Maciel

Greco

et al. 2017

“…A is known at all integration points (calculated only once) and 1 A is known as a trial and enables numerical calculations of all necessary values to assemble the iterative solution of geometrically nonlinear problems, see Coda and Carrazedo (2017), Siqueira and Coda (2016) and Pascon and Coda (2013) for instance.…”

Section: Numerical Preliminariesmentioning

confidence: 99%

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

Coda

2021

Self Cite

An alternative elastoplastic model based on the Flory's right Cauchy-Green stretch tensor decomposition is proposed and applied to model soft cores of sandwich panels. It does not follow usual methodologies as the additive decomposition or the Kröner-Lee multiplicative decomposition of strains. It is based on an important hyperelastic relation, Flory's decomposition, from which the total strain is separated in two isochoric and one volumetric parts. Using this decomposition, the volumetric strain energy continues to be elastic during all elastoplastic analysis and the isochoric parts are managed to produce the plastic evolution. As a consequence of Flory's decomposition, the plastic flow direction is known and independent of the yielding surfaces. Moreover, it provides the well known deviatoric nature of plastic strains. For validation purposes, the resulting formulation is implemented using a special 3D prismatic element in a geometrical nonlinear positional FEM computational code. The achieved numerical results are compared with literature experimental data of soft core laminated structural elements.

“…The framework employed to model the dynamical system (Coda and Paccola, 2014;Siqueira and Coda, 2016;2017; is a fully nonlinear finite element approach for large deformations based on a total Lagrangian description of solids. As the formulation uses positions as the main degrees of freedom, instead of displacements, the adopted approach is referred as positional.…”

Section: Introductionmentioning

confidence: 99%

Improved friction model applied to plane sliding connections by a large deformation FEM formulation

Siqueira

Coda

2023

Self Cite

Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.