In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers...In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers)coated with interphase layers,based on linear elasticity theory.The interphase between heterogeneity and a matrix are regarded as in the third phase(elastic layers),in contrast to the perfect interface of the spring-like Voronoi cell finite element model(VCFEM)in the literature.In this model,both stress and the displacement field are assumed to be independent in an element.Formulations of stress are derived for each of the three phases in an element,as is the type of functional.Numerical examples were used to study the microscopic and macroscopic properties,such as the effective modulus,of the composites.The results of the proposed VCFEM were compared with analytical solution and numerical results obtained from a standard finite element analysis to confirm its effectiveness.展开更多
In the process of shale gas exploitation,there exits two difficult problems:one is the real numerical simulation of a tremendous number of holes in actual shale;the other is the fluid–solid coupling problem involved ...In the process of shale gas exploitation,there exits two difficult problems:one is the real numerical simulation of a tremendous number of holes in actual shale;the other is the fluid–solid coupling problem involved in holes,where the difficulty of transition at the interface between the Eulerian grid and the Lagrangian grid becomes the most important.In response to these two problems,this paper establishes an element model with both fluid and solid.At the fluid–solid interface,the equilibrium condition of the surface force is introduced to obtain the modified complementary energy functional,and a new hybrid stress element with fluid is derived.The comparison of the simulation results with those of the ordinary commercial finite element software verifies the effectiveness and efficiency of this element,and proves its applicability in the problem of shale with numerous holes.Furthermore,this element can be extended to general problems of solid with fluid in.展开更多
基金supported by the National Natural Science Foundation of China(Grants 11402103 and 11572142).
文摘In this paper,a Voronoi cell finite element model is developed to study the microscopic and macroscopic mechanical behaviors of heterogenous materials,including arbitrary distributed heterogeneity(inclusions or fibers)coated with interphase layers,based on linear elasticity theory.The interphase between heterogeneity and a matrix are regarded as in the third phase(elastic layers),in contrast to the perfect interface of the spring-like Voronoi cell finite element model(VCFEM)in the literature.In this model,both stress and the displacement field are assumed to be independent in an element.Formulations of stress are derived for each of the three phases in an element,as is the type of functional.Numerical examples were used to study the microscopic and macroscopic properties,such as the effective modulus,of the composites.The results of the proposed VCFEM were compared with analytical solution and numerical results obtained from a standard finite element analysis to confirm its effectiveness.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11572142 and 12072135).
文摘In the process of shale gas exploitation,there exits two difficult problems:one is the real numerical simulation of a tremendous number of holes in actual shale;the other is the fluid–solid coupling problem involved in holes,where the difficulty of transition at the interface between the Eulerian grid and the Lagrangian grid becomes the most important.In response to these two problems,this paper establishes an element model with both fluid and solid.At the fluid–solid interface,the equilibrium condition of the surface force is introduced to obtain the modified complementary energy functional,and a new hybrid stress element with fluid is derived.The comparison of the simulation results with those of the ordinary commercial finite element software verifies the effectiveness and efficiency of this element,and proves its applicability in the problem of shale with numerous holes.Furthermore,this element can be extended to general problems of solid with fluid in.
