Determination of material parameters of isotropic and anisotropic hyper-elastic materials using boundary measured data

Abstract

Identification of mechanical properties of isotropic and anisotropic materials that demonstrate non-linear elastic behavior, such as rubbers and soft tissues of human body, is critical for many industrial and medical purposes. In this paper, a method is presented to obtain the mechanical constants of Mooney-Rivlin and Holzapfel hyper-elastic material models which are employed to describe the behavior of isotropic and anisotropic hyper-elastic materials, respectively. By using boundary measured data from a sample with non-standard geometry, and by using an iterative inverse analysis technique, the material constants are obtained. The method uses the results of different experiments simultaneously to obtain the material parameters more accurately. The effectiveness of the proposed method is demonstrated through three examples. In the two first examples, the simulated measured data are used, while in the third example, the experimental data obtained from a polyvinyl alcohol sample are used.

Determination of the Material Parameters in the Holzapfel-Gasser-Ogden Constitutive Model for Simulation of Age-Dependent Material Nonlinear Behavior for Aortic Wall Tissue under Uniaxial Tension

“…Even if these specimens are ready, it is difficult to carry out the biaxial tensile test on these specimens [23,33]. For these reason, the uniaxial test was carried out by many researchers such as Holzapfel [33], Peyraut et al [34], Skacel and Bursa [35], Hajhashemkhani and Hematiyan [36], Karimi et al [37], Shazly et al [38], and Latorre et al [39]. In their research, the material parameters of the HGO model such as C 10 , k 1 , and k 2 were identified using the uniaxial test for each layer or unified layers of soft biological tissue including aorta wall tissue.…”

Efficient Sensitivity Based Reconstruction Technique to Accomplish Breast Hyperelastic Elastography

“…The above-mentioned algorithm could be described in the following steps:The unknown tissue, i.e., tumor, and its surrounding mediums are imaged before/while responding to a ramp excitation (with low rate of increase in the applied load to negate the inertia effect) for a period of time by the employment of a clinical US imaging system.The registered precompression US images, loading specifications, and boundary conditions are delicately regarded to accurately simulate the tumor and its adjacent mediums with the help of the FEM software, Abaqus FEA. Further explanation of the simulation strategies has been provided at the end of the section.In the simulated specimen, the values of 1 Pa and 0.5 are, respectively, assigned to the elastic modulus and Poisson's ratio of the tumor to simulate an equivalent elastic tumor.The displacement fields at some consecutive step times are extractedfor the tumor, from the recorded US RF signals or images, for instance, by the use of the cross-correlation algorithm; i.e., the exact displacement fields in the tumor at some instants are computed;for the simulated elastic tumor, employing the FEM software, Abaqus FEA.The real elastic modulus of the tumor, E real , is computed using ([17, 18, 45])T1Ereal=DTDDTYreal,where Y real and D , respectively, represent the axial displacement values of some points of the tumor and elastic tumor at the specified moments.The tumor strain field could be roughly approximated from the displacement measurements. The estimated elastic modulus for the tumor, E real , is used to calculate a set of stress values, σ , from a set of strain values, ε (which is formed with regard to the strain field in the tissue), through the linear elasticity relation, (24), known as Hook's law,T1σ=Erealε.In view of the obtained results, a set of arbitrary strain values could also be considered, although the selection of strain set based on the available information leads to the significant decrease in the number of iterations.The parameters of the elected hyperelastic models, namely, the Mooney-Rivlin, Yeoh, and polynomial models, are computed using the formed stress and strain sets and the...…”

“…The errors of the elastic parameters estimated for the tumor might not decrease below the defined tolerance value, specifically while the strain set is elected arbitrary. The iterative algorithm based on the sensitivity matrix, as defined by Hajhashemkhani and Hematiyan [17, 18], would be the right choice to converge to accurate estimates of tumor hyperelastic parameters. The attained results indicate that the selection of suitable initial hyperelastic parameters, which could be obtained by the use of the proposed iterative method, is imperative to converge to precise estimates of tumor hyperelastic parameters through the sensitivity-matrix based algorithm; otherwise, the algorithm might approach the local minima.…”

“…The displacement quantities of the selected points of tumor at every specified moment, D i , C (in total, D ), are regarded.false(2false)Based on the hyperelastic model considered for the tumor, the response of the tumor, after slightly altering each of the hyperelastic parameters, C j , for instance, about 0.1% of its value, is simulated; similarly, the displacement quantities of the same points of tumor at every determinate moment, D i,Cj , are extracted. The difference between the calculated displacement vectors at the corresponding step times, ∂ D i , is computed for all the specified moments.false(3false)The sensitivity matrix, S , [17, 18] is constructed as follows:T17S=boldSnormal11boldSnormal12⋯boldSnormal1qboldSnormal21boldSnormal22⋯boldSnormal2q⋮⋮⋱⋮boldSlnormal1boldSlnormal2⋯boldSlq,Sij=∂Di∂Cj,∂Cj=μCj,…”

“…With respect to the geometrically nonlinear response of soft tissues at large deformations, i.e., the nonlinearity of the strain-displacement relation, an integral approach has been proposed by Skovoroda et al [15] to reconstruct the elasticity distribution of soft tissue. Sensitivity based approaches have been applied formerly by Gendy and Saleeb [16] and recently by Hajhashemkhani and Hematiyan [6, 17, 18] to estimate hyperelastic parameters of rubber-like materials and soft tissues. The slope-variation method and Nelder-Mead algorithm have been applied by O'Hagan and Samani [19, 20] and Naini et al [21] to evaluate hyperelastic parameters of abnormal breast and deflated lung tissues.…”