Application of the Virtual Fields Method to the uniaxial behavior of rubbers at medium strain rates

摘要

The Virtual Fields Method (VFM) is used to explore strain-rate dependent mechanical properties of a hyperelastic material. In this method, the principle of virtual work is constructed to inversely obtain the Young's modulus and Poisson's ratio of a given material from optical measurements of displacement obtained during a dynamic loading event. The virtual displacement field is designed so that acceleration fields, and thereby inertial forces, are used to calculate the material properties, and the traction force term in the principle of virtual work can be eliminated. Experimentally, this means that no force measurements are required during dynamic loading. Prior to the experimental investigations, a simple analytical calculation and finite element model were used in order to simulate the method; the output from the VFM showed good agreement with the given material coefficients. For the experimental work, pure silicone rubber was chosen as a model material. This rubber was tested in tension using a drop-weight apparatus at a medium strain rate (c.a. 160 s(-1)), using high speed photography and Digital Image Correlation to provide strain and acceleration data which were subsequently analyzed by use of the VFM. By using static pre-stretching prior to the dynamic load, the hyperelastic behavior can be investigated up to large strains, even though the dynamic loading itself only has a small strain amplitude. By optimizing the differential one-term Ogden model to modulus estimations at each of the pre-stretching locations, the nonlinear stress-strain curves were reconstructed. The initial modulus change between these dynamic experiments and quasi-static tests was compared to the storage modulus increment obtained from DMA tests on the same material. (C) 2015 Elsevier Ltd. All rights reserved.