# A simple formulation applied to finite strain viscoelastic solids and compressive flows

## Palavras-chave:

Large strain hyperelasticity, Kelvin-like viscoelasticity, Compressive isothermal fluid flow, Total Lagrangian formulation## Resumo

When writing movement equations in stresses for continuous media, it makes no difference if the

media is solid or fluid. The fundamental difference in the solution of these two problems relies on the respective

constitutive laws. For solids shear stresses are related to shear strains and the Navier-Cauchy equation takes

place, while for fluids, shear stresses are related to the time rate of shear strains, resulting in the Navier-Stokes

equation. For solid and fluid isothermal problems, the pressure is related to the volumetric change. Based on

hyperelastic relations, we present an original total Lagrangian numerical approach capable of modeling simple

large strain viscoelastic solids (Kelvin-like) and free-surface compressive viscous isothermal fluid flows. The

proposed model is implemented in an in house positional prismatic finite element formulation and is explored in

numerical examples.