Determination of the Viscoelastic Properties of Apple Flesh under Quasi-Static Compression Based on Finite Element Method Optimization

Abstract

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.

Analysis of Mechanical Properties of Whole Apple Using Finite Element Method Based on Three-Dimensional Real Geometry

“…1 and 3). The average modulus of elasticity (7.732 MPa) determined in this research by FEM simulation on whole apples was much greater than that determined by viscoelastic FEM optimization on cylindrical specimens of 'Fuji' apple flesh (2.366 MPa, Kim et al, 2008). These results could be explained by that a whole apple, in general, has an anisotropic structure with many complex and small curvatures, has flesh texture bonded biologically, and is covered with more elastic membrane shell (modulus of elasticity of 12.89 MPa for apple skin and 3.41 MPa for apple flesh, Williams et al, 2005) which contributes to prevent dehydration during compression.…”

“…These results could be explained by that a whole apple, in general, has an anisotropic structure with many complex and small curvatures, has flesh texture bonded biologically, and is covered with more elastic membrane shell (modulus of elasticity of 12.89 MPa for apple skin and 3.41 MPa for apple flesh, Williams et al, 2005) which contributes to prevent dehydration during compression. Also, the whole apple specimen has intact texture which breaks while preparing specimen of an apple flesh (Kim et al, 2008).…”

“…To determine the modulus of elasticity of each model apple by FEM simulation, its value was continuously adjusted until the difference between the reaction forces obtained by the actual compression test and FEM simulation fell below 1% at a loading condition of 0.5 BP. A fixed value of 0.333 was utilized for the Poisson's ratio of model apple (Kim et al, 2008). Also, stress distribution within each model apple was analyzed at the same loading condition of 0.5 BP by using Von Mises stress of Eq.…”

“…Mechanical properties of apple fruit, such as apparent modulus of elasticity and contact stress, can be determined by uniaxial compression test using either a cored specimen of uniform cross section or the whole fruit. In case of the tests using cored specimens, the simple geometry makes the analysis straight forward, while the problems related to the mass imbalance due to the loss of fruit juice and the deterioration of fl esh integrity often prevent researchers from collecting reliable data (Kim et al, 2008). Test with whole, intact fruit is an alternative to eliminate these problems (Kim et al, 1992;Park, 1993).…”

“…Among these, FEM shows increasing usage in analyzing food materials because it decomposes continuous medium into elements of simple and finite geometry, and then applies some approximate mathematical methods to describe the physical behavior of whole body (Kim et al, 2008). The FEM has been utilized to assess the firmness of apples (Chen and De Baerdemaeker, 1993;Jung, 2003) and melons (Chen et al, 1996) by analyzing vibration modes, and to analyze the stress distribution within the internal texture of grape via compression simulation (Rong et al, 2004).…”