Eventos Anais de eventos
MECSOL 2022
8th International Symposium on Solid Mechanics
Presentation and characterization of a new family of strain measures based on the hyperbolic tangent function
Submission Author:
Daniel Peixoto , MG
Co-Authors:
Daniel Peixoto, Marcelo Greco
Presenter: Daniel Peixoto
doi://10.26678/ABCM.MECSOL2022.MSL22-0147
Abstract
The main purpose of this article is to present an objective, symmetrical and versatile family of strain measures based on the hyperbolic tangent function, both in its uniaxial and in its tensor form (3D): the Generalized Hyperbolic Tangent (GHT) strain measure. It is a goal of this work to examine the properties of the strain measure created and to discuss in which practical applications its use could be advantageous. The investigation of the new family of strain measures behavior will be done through the analytical study of pure strain modes and through the analysis of a spatial truss using the Positional Finite Element Method (PFEM). The specific formulae for implementation of the Hyperbolic Tangent strain measure into the PFEM is presented. The mathematical definition of the GHT strain in its tensor form is made by transitioning from the uniaxial definition. To establish its conjugate stress tensor, the spectral decomposition of tensors will be used. With the variation of a single constant (n), versatility is obtained and calibration may be used to adequate the modeling of different materials. The results obtained from the analysis of trusses using the PFEM and analytical investigation of pure deformation modes of solids indicate that the GHT measures are suitable for engineering applications at small and moderate strains. In the present work, only the energy-conservative elastic, isotropic and homogeneous behaviors of materials are considered.
Keywords
Strain Measures, Hyperbolic Tangent, hyperelastic models
