In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant ...In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant and tangential stiffness matrices of the implicit peridynamic formulations for the nonlinear problems are derived,respectively.The former is con structed from the linearization of the bond strain on the basis of the geometric approximation while the latter is established according to the linearization of the pairwise force by using first-order Taylor’s expansion.Then,a bimodular material model in peridynamics is developed,in which the tensile or compressive behavior of the material at each point is conveniently described by the tensile or compressive states of the bonds in its neighborhood.Moreover,the bimodular material model is extended to deal with the wrinkling and fracture problems of membranes by setting the compressive micro-modulus to be zero.In addition,the incremental-iterative algorithm is adopted to obtain the convergent solutions of the nonlinear problems.Finally,several representative numerical examples are presented and the results demonstrate the accuracy and efficiency of the proposed method for the large deformation,wrinkling and fracture analyses of bimodular structures and membranes.展开更多
Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of contin...Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.展开更多
In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value ...In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.展开更多
基金The work was supported by the National Natural Science Foundation of China(Grants 11672062,11772082,and 11672063)the 111 Project(Grant B08014)the Fundamental Research Funds for the Central Universities.
文摘In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant and tangential stiffness matrices of the implicit peridynamic formulations for the nonlinear problems are derived,respectively.The former is con structed from the linearization of the bond strain on the basis of the geometric approximation while the latter is established according to the linearization of the pairwise force by using first-order Taylor’s expansion.Then,a bimodular material model in peridynamics is developed,in which the tensile or compressive behavior of the material at each point is conveniently described by the tensile or compressive states of the bonds in its neighborhood.Moreover,the bimodular material model is extended to deal with the wrinkling and fracture problems of membranes by setting the compressive micro-modulus to be zero.In addition,the incremental-iterative algorithm is adopted to obtain the convergent solutions of the nonlinear problems.Finally,several representative numerical examples are presented and the results demonstrate the accuracy and efficiency of the proposed method for the large deformation,wrinkling and fracture analyses of bimodular structures and membranes.
文摘Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.
基金The project supported by the Key Project of Chinese Ministry of Education (03145)the Science Fund of Southwest Jiaotong University
文摘In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.