Technical Report Characterisation of nonlinear material parameters of foams based on indentation tests B. Li, Y.D. Gu, R. English, G. Rothwell, X.J. Ren * School of Engineering, Liverpool John Moores University, Liverpool L3 3AF, UK article info Article history: Received 19 May 2008 Accepted 24 September 2008 Available online 10 October 2008 abstract Closed cell polymeric foams, for example EVA foams, are widely used in engineering, sport and biomed- ical fields. The mechanical behaviours of foam is highly nonlinear, and the foams are often under complex loading conditions in service over different spectrums of strain. Foam testing and determination of the nonlinear foam constitutive parameters are important to predict their performance in service and to aid materials development and product design. Current testing approaches normally involve the use of conventional compression or shear tests, which require well defined sample shapes and sizes. In this work, the use of continuous indentation test and inverse FE modelling method to determine the nonlinear material parameters was systematically investigated. This potentially could provide a much more simple testing approach with the capacity for in situ situation where standard testing specimens are not attain- able. The results were directly compared to conventional compression test and combined compression– shear tests of EVA foams. The accuracy and validity of each method were comparatively studied and dis- cussed. Results showed that the indentation approach produced comparable results to the combined compression–shear tests, while uniaxial compression test could not provide accurate material data to simulate complex loading conditions. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Closed cell foams, such as EVA foam, are widely used in engi- neering, sport and biomedical fields. The properties of EVA foams are highly nonlinear and viscoelastic [1,2], which are best de- scribed by nonlinear material models. For example, the mechanical behaviour of EVA foams is normally described using the Ogden model [3,4], which constitutes several material parameters. Deter- mination of these parameters through foam testing is important to provide data for the simulation of their service performances, product design and quality control. However, many of these mod- els involve materials constants without physical meaning and it is a challenging task to determine these parameters. Conventionally, the determination of material parameters is based on the use of test samples with a standardised geometry un- der a simplified strain state, such that particular conditions on the stress and strain field are satisfied in the sample/or part of the sam- ple. Then the unknown model parameters are obtained using curve fittings from experimental data. For foam materials, a wide range of tests have been used (e.g. compression test, shear test, and vol- umetric test) in order to predict these parameters [3–5]. These methods normally require large numbers of tests and samples with well-defined geometries. In some cases, such as shear test, the assembly has to use adhesives to bond the sample to the loading platen which limits the strain level that can be reached by the maximum strength of the adhesive bond [4]. In addition the meth- od is inconvenient or even impossible where standard specimens are not readily available, or for in situ monitoring the mechanical strength of the materials. Indentation tests represent a much more simple form of testing, which simulates conditions of variable pressures and deformation. However, conventional hardness tests, such as the Shore method, requires special samples (at least 6 mm thick) and the method only provides information about the hardness of a sample, which could not be directly used to model the detailed material behaviour in service. Recent development of continuous indentation methods has greatly improved the information that can be determined from indentation tests for different types of materials [6,7]. It has been used to predict the plastic properties of metal materials and elastic properties of biomaterials such human heel skin [8,9]. These could have the potential to extract the parameters of the nonlinear foam models. In this work, EVA foams were tested using continuous indenta- tion, compression and shear tests. A numerical-experimental ap- proach based on the Kalman filter method has been developed to analyse the indentation data. The nonlinear foam parameters determined from indentation testing, uniaxial compression testing, and combination of compression–shear testing data were quantita- tively compared. The advantages and disadvantages of each meth- od were discussed. 0261-3069/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2008.09.040 * Corresponding author. Tel.: +44 (0)151 231 2525; fax: +44 151 231 22529. E-mail address: x.j.Ren@ljmu.ac.uk (X.J. Ren). Materials and Design 30 (2009) 2708–2714 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes