Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

• DOI: 10.1007/s00466-015-1184-8
• Publication Date: 2015-08-01T09:19:25Z
• Authors: Marcos Latorre; Francisco Javier ...
• Keywords: Orthotropic material; Finite strain theory; Transverse isotropy

[EN] In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials.<br/>Partial financial support for this work has been given by grant DPI2011-26635 from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of Spain<br/>