This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend...This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.展开更多
A physically-based continuum theory that captures the microstructure-dependent and temporal effects of both permanent and transient polymer networks is still lacking,despite the fact that it is greatly needed for the ...A physically-based continuum theory that captures the microstructure-dependent and temporal effects of both permanent and transient polymer networks is still lacking,despite the fact that it is greatly needed for the analysis of polymeric microstructures.To fill in this gap,this work proposes a physically-based spatiotemporally nonlocal continuum field theory.A general frame-work is established that quantitatively connects microscopic descriptions of polymer networks(chain energetics,chain-length distribution,assembly structure of the interpenetrating network,and rate of bond exchange reactions)to key components in the spatiotemporally nonlocal constitutive relations(explicit form of the nonlocal kernel function,magnitude of nonlocal characteris-tic length,two-phase weighting factors,and explicit form of the relaxation function),based on three hypotheses on the continuum viewpoint of the underlying discrete network structure:the existence of a finite bottom bound of volume to define intensive quan-tities,uniformity of energy density field inside the representative volume of a polymer network,and the condition for initiation of chain stretch.Applying the general framework to a permanent 8-chain concentric network yields a concrete two-phase nonlocal elasticity constitutive relation,where the explicit form of the kernel function can be derived by simply assuming an implicit form.Application to a transient network with bond exchange reactions yields a spatiotemporally nonlocal constitutive relation.The spatiotemporally nonlocal continuum theory can be helpful for exploring transformative and subversive high-performance materials involving the specific spatial stacking and arrangement of functional units through artificial design.展开更多
基金supported by a grant from the National Science and Technology Council of the Republic of China(Grant Number:MOST 112-2221-E-006-048-MY2).
文摘This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.
基金supported by the National Natural Science Foundation of China(Grant Nos.52175095,51775201,and 51605172)Young Top-notch Talent Cultivation Program of Hubei Province of China.
文摘A physically-based continuum theory that captures the microstructure-dependent and temporal effects of both permanent and transient polymer networks is still lacking,despite the fact that it is greatly needed for the analysis of polymeric microstructures.To fill in this gap,this work proposes a physically-based spatiotemporally nonlocal continuum field theory.A general frame-work is established that quantitatively connects microscopic descriptions of polymer networks(chain energetics,chain-length distribution,assembly structure of the interpenetrating network,and rate of bond exchange reactions)to key components in the spatiotemporally nonlocal constitutive relations(explicit form of the nonlocal kernel function,magnitude of nonlocal characteris-tic length,two-phase weighting factors,and explicit form of the relaxation function),based on three hypotheses on the continuum viewpoint of the underlying discrete network structure:the existence of a finite bottom bound of volume to define intensive quan-tities,uniformity of energy density field inside the representative volume of a polymer network,and the condition for initiation of chain stretch.Applying the general framework to a permanent 8-chain concentric network yields a concrete two-phase nonlocal elasticity constitutive relation,where the explicit form of the kernel function can be derived by simply assuming an implicit form.Application to a transient network with bond exchange reactions yields a spatiotemporally nonlocal constitutive relation.The spatiotemporally nonlocal continuum theory can be helpful for exploring transformative and subversive high-performance materials involving the specific spatial stacking and arrangement of functional units through artificial design.
