Identification Of Fractional Derivative Viscoelasticity Model Parameters Together With Its Finite Element Implementation

Soft/hard biological tissues,highly filled composites,polymers and so forth commonly show viscoelasticity to a certain extent.This property significantly affects not only the extreme elastic response of the material itself and the structures made of such material,but also their damage evolution,failure mechanism and usage life in actual applications.Therefore,establishing an effective method to accurately identify the parameters of material viscoelasticity models and developing the relevant simulation codes are of vital importance for practical applications.So far,material viscoelasticity is commonly characterized by the Prony model.However,there are some limitations on the strategy of this kind:(1)the relaxation modulus Y(t)and the creep compliance J(t)cannot be obtained simultaneously with one indentation test;(2)it is pretty hard to find a data-fitting formula when nanoindentations with a spherical indenter are conducted for samples of quite small dimensions.To this end,this thesis aims to extend the fractional viscoelasticity model to fitting the viscoelasticity data tested by nanoindentations,and also to establish a simulation method framed within the finite element method.Experimental tests by nanoindentations are first categorized in this study based on the objective parameter combined with the indenter shape into four distinct cases.Then,the Fractional Derivative Zener model(FDZM)is employed to deduce the explicit data-fitting formulas,and a detailed fitting scheme is also established.As for each of the four experiment cases,the data-fitting formula and least square method are applied to fit the data tested and the validity of our strategy is verified by comparing the results in the open literature.The results indicate that our data-fitting formulas can accurately describe the experimental data tested with different objective parameters and differently shaped indenters.In comparison with the Prony model,two merits present with the model adopted:(1)fewer model coefficients necessitate being determined with the aid of the experimental data;(2)the relaxation modulus Y(t)and the creep compliance modulus J(t)can be obtained through one indentation test,and their exact interconversion is guaranteed as well.Besides,this thesis developed a computational approach with the aid of the finite element method and the FDZM to simulate the viscoelasticity response under the static and quasi-static loadings,and numerically implemented with the C++ language.The correctness and validity of the computational approach and the finite element program are verified by solving two typical simplified examples and comparing the predictions with both the results evaluated by ANSYS and the analytical solutions.Finally,the verified FEA program is applied to analyze the viscoelasticity response of a composite laminate,influences imposed by viscoelasticity of adhesive are researched through deformation and stress distribution in interlamination.