Theoretical Modeling And Numerical Calculation For The Analysis Of General Imperfect Interface In Porous Composites

Composite materials are extensive applied in aerospace engineering,national defence,civil engineering,medical bionics and other fields because of the the excellent physical performances and the properties designability.The composite material is a multiphase material composed of matrix phase,inclusion phase and transition layer.In the process of manufacture,owing to to the complicated technics,a transition layer with different microstructure and physical properties is formed between the matrix and the inclusion phase.The transition layer,which significantly affects the mechanical properties of the composite,has the capacity of load transfer.Therefore,the exploration about the properties of transition layer can make a profound understanding for the influencing factors of the composite performance.Then,the relationships that the properties and microstructure of the constituting materials determine the macroscopic properties of composite materials are established,and the response rules of composite materials under certain operating conditions are revealed.These provide necessary theoretical basis and means for optimization design and performance evaluation of composite materials.However,the complexity of the microstructure and the small thickness make it is difficulty to measure the transition layer accurately.If the transition layer is considered as the interphase with nonzero thickness,it need more workload and may be difficult to implement the theoretical analysis and numerical calculation.To avoid this,a general imperfect interface model with zero thickness is established to replace the transition layer in this thesis.In the first part,we choose the poroelasticity composite as the study object and recall the constitutive equations of it.Then the Hadamard’s relation and the interface operators are introduced.Based on this,the method appeared in the Gu and He is employed to derive the jumps of the physical fields across the imperfect interface in a compact and coordinate-free manner.The extreme cases of the imperfect interface are discussed in detail.The main purpose of the second part is to propose an effective numerical method to analyze porous composites with a general imperfect interface.According the discontinuous relationships derived previously,we establish the governing equations of a composite which contains the general imperfect interface in a complicated coupled boundary conditions.Then,employing the pore pressure and displacement as the control variables,the weak forms of this system are deduced by the the principle of the virtual work.In the frame of XFEM and LSM,we employ the appropriate enrichment function to characterize the strong and weak discon-tinuity and discretize the the weak forms which provide theoretical base for the numerical implemented.A cubic composite material with a single spherical inclusion is considered as the analysis model.Applying the discontinuous relationships of the general imperfect interface,the analytical expression for the physical fields of this model in the coupled boundary condition is figured out.The analytical solution of the extreme cases for this model have been discussed.Meanwhile,we use the Matlab to compile the computing program to work out the numerical solution of this model in the same condition.Then the results of the numerical and analytical methods are compared to illustrate the applicability and generality of the numerical method.Both the capacity of the numerical procedure that can capture the strong and weak discontinuity and the influence of the interphase thickness are discussed in detail.