A procedure for determining the viscoelastic properties of apple flesh has been proposed based on compression tests and FEM optimization. Short-term simple compression tests and long-term relaxation tests were performed with cylindrical specimens of apple flesh to measure mechanical properties, and the viscoelastic behavior was predicted using FEM optimization models. Through short-term optimization, the elastic modulus and Poisson's ratio were determined by comparing two kernel functions based on 1) shear only and 2) shear and bulk terms. Long-term stress-relaxation behavior of the specimen was reasonably predicted by two FEM optimization steps within 3.8 % error. The FEM optimization algorithms developed in this research might be applied to determine the viscoelastic properties of bio-materials and also to predict mechanical behavior of these materials under various loading conditions.

This study was intended to build 3D FEM geometry models of actual 'Fuji' apples by digitizing their surfaces, and to determine elastic modulus by FEM simulation based on the F-D curves of radial compression test from a point on apple equator. Also, the general protocol of ASAE S368.4 for predicting the apparent modulus of elasticity and the maximum contact stress for convex-shape food materials was evaluated for its appropriateness. The model apple for FEM analysis was composed of approximately 35,000 geometry elements that closely resemble the surface of an actual apple. Through FEM simulation, the average elastic modulus of 7.732 MPa was obtained at the loading condition of 0.5 BP, which was 8.3% smaller than the average apparent modulus of elasticity predicted by the ASAE standard. The maximum Von Mises stress at the points of initial contact with the compression target plates evaluated by FEM simulation was about 37% smaller than the maximum contact stress determined by the ASAE standard, and a poor correlation was found between the results of the two methods. These results could be explained by that a whole apple, in general, has an anisotropic structure with many complex and small curvatures, has fl esh texture bonded biologically, and is covered with more elastic membrane shell which contributes to prevent dehydration during compression.

An FEM algorithm was developed to determine the viscoelastic properties of soft tissues of agar/agargelatin gels based on the curve-averaged data from stress relaxation experiment of parallel plate compression and FEM optimization technique. This approach enabled more realistic and pertinent expression of the mechanical behavior of the gels than conventional methods, and allowed simultaneous and logical characterization of all viscoelastic parameters, based on geometry, relating to both Prony series and Maxwell model such as elastic modulus, Poisson's ratio, relative modulus, relaxation time, and dynamic viscosity, etc. Several assumptions were made in the FEM model such that the soft tissue materials were homogeneous in phase and isotropic, gravity effect was negligible, and the response was transient and controlled by displacement. To demonstrate the validity of the FEM model, the results of FEM optimization were compared with those of conventional method of nonlinear regression for agar/agar-gelatin gels, and also the predicted mechanical behavior of FEM on compressive creep as an interrelation with stress relaxation by the FEM model was compared with the experimental creep of 1% agar gel. The reliability of the FEM optimization method was confirmed by small stress deviation within 4.7% between experimental data and the FEM simulation using optimized parameters for stress-relaxation evaluation for agar/agargelatin gels and by strain deviation within 3.4% for creep prediction of 1% agar gel.