A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.展开更多
A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding ...A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.展开更多
基金Project supported by the National Council of Humanities,Sciences,and Technologies of Mexico(Nos.CF-2023-G-792 and CF-2023-G-1458)the National Council for Scientific and Technological Development of Brazil(No.09/2023)the Research on Productivity of Brazil(No.307188/2023-0)。
文摘A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
基金Project supported by the Desenvolvimento e Aplicaoes de Mtodos Matemticos de Homogeneizaao(CAPES)(No.88881.030424/2013-01)the Homogeneizao Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases(CNPq)(Nos.450892/2016-6and 303208/2014-7)the Caracterizacin de Propiedades Efectivas de Tejidos Biolgicos Sanos y Cancerosos(CONACYT)(No.2016–01–3212)
文摘A family of one-dimensional(1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method(RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.
