Development And Application Of Hybrid Formulation For Chemo-mechanical Coupling Problems

The multi-field coupling problem considering chemical effects widely exists in frontier fields such as aerospace,new energy,new materials and biomedicine,etc.There have been a lot of researches on the constitutive theory of chemo-mechanical coupling problems,but new numerical algorithms need to be developed.Based on the explicit rate-type generalized variational principles,this study established the chemo-mechanical hybrid finite element formulations and compared them with the traditional irreducible finite element formulation.The main research work of this paper is as follows:In order to develop the numerical algorithm directly,an explicit expression of rate-type functional is proposed.Through the variation of the functional,an equivalent mathematical form describing the chemo-mechanical coupling problem studied can be obtained.Based on the explicit rate-type functional,the irreducible finite element formulation of chemo-mechanical coupling problem is constructed.Based on the above chemo-mechanical rate-type functional,an explicit rate-type Hellinger-Ressinar functional that can be equivalent to all the governing equations and boundary value conditions is proposed.Through the generalized variational principle and the Legendre transformation of rate-type chemical Gibbs free energy,the three-variable and four-variable chemo-mechanical coupling hybrid finite element formulations have been established.Taking the plane quadrilateral four-node and eight-node elements as the research objects,based on the user-defined element(UEL)subroutine of ABAQUS,the algorithm of irreducible chemo-mechanical coupling elements(CMQ4,CMQ8)based on assumed displacement and concentration and hybrid stress elements(CMQ4H1,CMQ8H1)based on assumed displacement,concentration and stress are constructed.Taking the convergent solution under the dense mesh of the irreducible element as the reference solution,the established elements are tested for their convergence and anti-distortion performances.The results show that the hybrid element has faster convergence than the irreducible element,and is not sensitive to distortion mesh.In addition,the performance of the proposed CMQ8H1 element is best.This research starts with the basic theory,and develops,implements and tests the numerical algorithm.The method discussed in this paper has important reference significance for the numerical solution of multi-field coupling problems,especially,chemo-mechanical coupling problems,and the application of advanced numerical algorithms such as hybrid finite element method in multi-field coupling problems.