Constitutive approach to rate-independent properties of filled elastomers

Filled rubber material is used in many technical applications. These structures are often subjected to dynamic loading. Apart from the materialʹs stiffness characteristics dissipative properties are of great importance. At high frequencies rubber material behaves mainly viscoelastically. But at low strain-rate the response is nearly rate-independent. This observation can be interpreted as "internal material friction" and is dealt with in the following article. A constitutive approach is presented, which can be motivated by investigations on the molecular level. This phenomenological description is composed of an elastic model--idealized as an elastic spring--and elasto-plastic Prandtl-elements in parallel. The formulation is derived for small and finite strains. The large strain case is based on a multiplicative decomposition of the deformation gradient. Experimental results and numerical simulations are presented utilizing a mixed finite element formulation to give a robust algorithm and reliable results. © 1998 Elsevier Science Ltd