The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a...The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.展开更多
Background The invasiveness of Spartina alterniflora Loisel.into the estuarine coastal wetlands has impacted the stability of soil organic carbon,as well as the functional genes of soil microorganisms.However,the mech...Background The invasiveness of Spartina alterniflora Loisel.into the estuarine coastal wetlands has impacted the stability of soil organic carbon,as well as the functional genes of soil microorganisms.However,the mechanisms by which S.alterniflora invasion affects soil organic carbon,especially at the micro-level,is still unclear.Therefore,this study compared the differences in soil carbon cycling(C-cycling)functional genes between invaded and native areas during the cold season,as well as the changes in microbial communities involved in differential functional genes'expression.Results Our results showed that in salt marsh wetlands dominated by Suaeda salsa(L.)Pall.,invasion by S.alterniflora negatively impacts soil microbial biomass carbon(MBC)and reduces the diversity of C-cycling functional genes.The invasion species significantly increased the relative abundance of carbon fixation genes,while decreasing the relative abundance of carbon degradation genes.Additionally,the differential genes-expressing microbial communities exhibited notable differences across groups.At the class level,both generalist taxa(e.g.,Gammaproteobacteria,Deltaproteobacteria)and specialist taxa(e.g.,Nitrospiria,Flavobacteriia)collectively influenced the abundance of C-cycling functional genes.Correlation and hierarchical partitioning analyses revealed that the increased soil carbon fixation capacity was closely associated with increased soil organic carbon(SOC)and decreased MBC,whereas the decline in soil carbon degradation capacity was linked to higher soil electrical conductivity(EC)and a lower C:P ratio.Conclusions Our study filled a gap in research during the cold season and revealed that the invasion of S.alterniflora significantly impacts both soil C-cycling functional genes and their expressing microbial communities,thereby potentially affecting the soil organic carbon of salt marsh wetland ecosystems.展开更多
文摘The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture.
基金supported by the Key R&D Program of Zhejiang Province(2023C02004,2023C02015)the National Natural Science Foundation of China(42277283,42090060)+1 种基金the Fundamental Research Funds for the Central Universities(226-2022-00139)Ningbo Welfare Science and Technology Plan Project(No.2022S118)
文摘Background The invasiveness of Spartina alterniflora Loisel.into the estuarine coastal wetlands has impacted the stability of soil organic carbon,as well as the functional genes of soil microorganisms.However,the mechanisms by which S.alterniflora invasion affects soil organic carbon,especially at the micro-level,is still unclear.Therefore,this study compared the differences in soil carbon cycling(C-cycling)functional genes between invaded and native areas during the cold season,as well as the changes in microbial communities involved in differential functional genes'expression.Results Our results showed that in salt marsh wetlands dominated by Suaeda salsa(L.)Pall.,invasion by S.alterniflora negatively impacts soil microbial biomass carbon(MBC)and reduces the diversity of C-cycling functional genes.The invasion species significantly increased the relative abundance of carbon fixation genes,while decreasing the relative abundance of carbon degradation genes.Additionally,the differential genes-expressing microbial communities exhibited notable differences across groups.At the class level,both generalist taxa(e.g.,Gammaproteobacteria,Deltaproteobacteria)and specialist taxa(e.g.,Nitrospiria,Flavobacteriia)collectively influenced the abundance of C-cycling functional genes.Correlation and hierarchical partitioning analyses revealed that the increased soil carbon fixation capacity was closely associated with increased soil organic carbon(SOC)and decreased MBC,whereas the decline in soil carbon degradation capacity was linked to higher soil electrical conductivity(EC)and a lower C:P ratio.Conclusions Our study filled a gap in research during the cold season and revealed that the invasion of S.alterniflora significantly impacts both soil C-cycling functional genes and their expressing microbial communities,thereby potentially affecting the soil organic carbon of salt marsh wetland ecosystems.
