A variational full-network framework with anisotropic damage and viscoelasticity induced by deformation

Incompressible materials, such as filled rubbers and biological tissues, may exhibit high nonlinear and anisotropic inelastic responses induced by deformations when subject to large strains. The constitutive modeling area has focused on describing the anisotropic behavior of viscosity and damage. However, coupled anisotropic inelastic effects are still a major challenge, with few contributions in the literature. This paper then presents a variational full-network framework capable of representing coupled anisotropic damage and viscoelasticity responses induced by deformation. The proposal extends a variational family to include the advantages of the full-network framework to deal with anisotropic behaviors. Approximations of the potential energies used on the full-network integration scheme associate the inelastic scalar variables at each material point with the quadrature points directions, resulting naturally in a set of scalar minimization problems. Numerical tests are presented to show the ability of the framework to represent anisotropic damage and viscoelasticity. Two variational models, specialized for filled rubber and soft biological tissues, are also implemented on finite element software to assess the model into practical applications. The results show the proposed model's versatility to simulate anisotropic viscoelasticity, anisotropic mechanical damage, and viscous and damage coupled phenomena, maintaining accuracy for large strain and time increments.