H Yperelastic Constitutive Modeling And Finite Element Implementation Of Fiber-reinforced Heterogeneous Materials

Fiber-reinforced heterogeneous hyperelastic materials(e.g.blood vessels,liver,macromolecular materials and so forth)have been widely applied in biomedicine,material bionics,flexible electronics and many other fields because of their unique mechanical properties along the fiber direction.Establishing the constitutive model,which may accurately describe the elastic response of such materials,together with the relevant simulation method can not only guide the product/structure design,fatigue life estimation and reliability analysis,but also lay a foundation for the failure/damage mechanism analysis of heterogeneous materials,new composite synthesis and performance-optimization.Commonly,these materials are constituted by very complex microstructures,and their elastic properties are significantly size-dependent and affected by random factors as well.Though lots of studies have been conducted concerning the materials of this kind,by far,there is no unified constitutive formula that can simultaneously describe all behaviors of such materials and the structures made of them.According to the literatures published,a certain part of the strain energy functions proposed are not convex,thus,the existence and uniqueness of the solution can not be guaranteed.Further,only a small portion of these hyperelastic models can be applied for finite element implementations due to the restriction of the strain measurement,while they may not satisfy all physical requirements during finite strain deformations.Therefore,it is of vital importance to establish a hyperelastic constitutive formula,which satisfies all physical requirements during the finite strain deformation,has a simple expression and can be easily implemented in the finite element framework,for fiber-reinforced heterogeneous materialsIn this thesis,our focus is mainly on developing a hyperelastic model for heterogeneous materials reinforced by one family of fibers,identifying the relevant model coefficients with the experimental data in the open literature and implementing the proposed model in the finite element framework.The main content of this thesis is summarized as follows:(1)Based on the invariants of the right Cauchy-Green strain and tensor analysis,a novel strain energy function which can properly describe the incompressibility and hyperelasticity of fiber-reinforced heterogeneous materials is established,and the relation between the second PK stress and the right Cauchy-Green strain together with the expression of the tangential stiffness matrix is derived.Besides,the analytical solutions to the boundary value problems of fiber reinforced materials under two specific loading conditions are also obtained,and an iterative method is proposed for identifying the model coefficients with the aid of the least square approach.Hereafter,the experimental data of a heterogeneous material reinforced by one family of fibers in the open literature is employed to fit the coefficients of the proposed hyperelastic model,whose validity is thus examined by comparing the theoretical predictions and the experimental results.(2)The governing equations for hyperelastic responses of fiber reinforced materials and the corresponding discrete equations for finite element implementation are derived,and the simulation codes are then programmed with MATLAB.The validity of the computational method and the correctness of the developed program are illustrated by comparing the numerical predictions with the experimental data together with the analytical solutions,which laid a foundation for further simulating hyperelastic responses of practical heterogeneous biological tissues.(3)The finite element model of a porcine liver microstructure is constructed based on its true constitution.Then,the influences of the material composition,fiber orientation and model coefficients on the deformation and stress distribution of soft tissues individually under the tension and compression loadings are analyzed by taking account of the material properties of different phases and using the self-developed finite element program.