Fragments and blast waves generated by explosions pose a serious threat to protective structures.In this paper,the impact resistance of polyurea-coated steel plate under complex dynamic loading is analyzed and designe...Fragments and blast waves generated by explosions pose a serious threat to protective structures.In this paper,the impact resistance of polyurea-coated steel plate under complex dynamic loading is analyzed and designed for improving comprehensive ballistic and blast resistance using the newly established computational evaluating model.Firstly,according to the thickness and placement effects of the coating on the impact resistance,the steel-core sandwich plates are designed,which are proved to own outstanding comprehensive ballistic and blast resistance.Besides,the distribution diagram of ballistic and blast resistance for different polyurea-coated steel plates is given to guide the design of protective structures applying in different explosion scenarios.Furthermore,the dynamic response of designed plates under two scenarios with combined fragments and blast loading is studied.The results show that the synergistic effect of the combined loading reduces both the ballistic and blast resistance of the polyurea-coated steel plate.Besides,the acting sequence of the fragments and blast affects the structural protective performance heavily.It is found that the first loading inducing structural large deformation or damage is dominant.When fragments impact first,the excellent unit-thickness ballistic performance of the structural front part is strongly needed for improving the comprehensive ballistic and blast resistance.展开更多
Blast-induced traumatic brain injury(b-TBI)is a kind of significant injury to soldiers in the current military conflicts.However,the mechanism of b-TBI has not been well understood,and even there are some contradictor...Blast-induced traumatic brain injury(b-TBI)is a kind of significant injury to soldiers in the current military conflicts.However,the mechanism of b-TBI has not been well understood,and even there are some contradictory conclusions.It is crucial to reveal the dynamic mechanism of brain volume and shear deformations under blast loading for better understanding of b-TBI.In this paper,the numerical simulation method is adopted to carry out comprehensive and in-depth researches on this issue for the first time.Based on the coupled Eulerian-Lagrangian method,the fluid-structure coupling model of the blast wave and human head is developed to simulate two situations,namely the head subjected to the frontal and lateral impacts.The simulation results are analyzed to obtain the underlying dynamic mechanisms of brain deformation.The brain volume deformation is dominated by the local bending vibration of the skull,and the corresponding frequency for the forehead skull under the frontal impact and the lateral skull faced to the lateral impact is as high as 8 kHz and 5 kHz,respectively.This leads to the high-frequency fluctuation of brain pressure and the large pressure gradient along the skull,totally different from the dynamic response of brain under head collisions.While the brain shear deformation mainly depends on the relative tangential displacement between the skull and brain and the anatomical structure of inner skull,being not related to the brain pressure and its gradient.By further comparing the medical statistics,it is inferred that diffuse axonal injury and brain contusion,the two most common types of b-TBI,are mainly attributed to brain shear deformations.And the von Mises stress can be adopted as the indicator for these two brain injuries.This study can provide theoretical guidance for the diagnosis of b-TBI and the development of protective equipment.展开更多
Background: Civilian explosion blast injury is more frequent in developing countries, including China. However, the incidence, casualties, and characteristics of such incidents in China are unknown.Methods: This is a ...Background: Civilian explosion blast injury is more frequent in developing countries, including China. However, the incidence, casualties, and characteristics of such incidents in China are unknown.Methods: This is a retrospective analysis of the State Administration of Work Safety database. Incidents during a period from January 1, 2000 to April 30, 2017 were included in the analysis. The explosions were classified based on the number of deaths into extraordinarily major, major, serious and ordinary type. Descriptive statistics was used to analyze the incidence and characteristics of the explosions. Correlation analysis was performed to examine the potential correlations among various variables.Results: Data base search identified a total of 2098 explosions from 2000 to 2017, with 29,579 casualties: 15,788 deaths(53.4%), 12,637 injured(42.7%) and 1154 missing(3.9%). Majority of the explosions were serious type(65.4%). The number of deaths(39.5%) was also highest with the serious type(P=0.006). The highest incidence was observed in the fourth quarter of the year(October to December), and at 9:00–11:00 am and 4:00–6:00 pm of the day. The explosions were most frequent in coal-producing provinces(Guizhou and Shanxi Province). Coal mine gas explosions resulted majority of the deaths(9620, 60.9%). The number of explosion accidents closely correlated with economic output(regional economy and national GDP growth rate)(r=–0.372, P=0.040;r=0.629, P=0.028).Conclusions: The incidence and civilian casualties due to explosions remain unacceptable in developing China. Measures that mitigate the risk factors are of urgently required.展开更多
In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin (SUPG/PSPG) extended finite element method (XFEM) is presented to model incompressible immiscible two-phase flows...In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin (SUPG/PSPG) extended finite element method (XFEM) is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.展开更多
现实防护工程中,硬1软复合结构在人员装甲(如头盔的外壳/衬里系统)中的应用可以有效减轻爆炸伤害.由于缺乏有效可靠的实验方法评估防护结构的防爆性能,直接接触型防护结构的发展受到限制,本文针对硬/软复合材料结构的防爆性能测试提出...现实防护工程中,硬1软复合结构在人员装甲(如头盔的外壳/衬里系统)中的应用可以有效减轻爆炸伤害.由于缺乏有效可靠的实验方法评估防护结构的防爆性能,直接接触型防护结构的发展受到限制,本文针对硬/软复合材料结构的防爆性能测试提出一种新的实验及数值评估方法,并对其防爆机理进行了分析.受测的硬/软结构由超高分子量聚乙烯(UHMWPE)复合材料和膨胀聚乙烯(EPE)泡沫组成.现场爆炸试验通过7.0 kg TNT球形炸药在3.8 m处产生的爆炸波来完成.设计了一种压力测试装置用于支撑被测结构并测量穿透防护结构的爆炸压力脉冲.实验结果表明,通过使脉冲波形更平坦、减小压力幅度和延迟脉冲到达时间,硬/软结构可以将爆炸压力脉冲减弱为三角形压力脉冲.7mmUHMWPE复合材料和20mmEPE泡沫的组合防护结构可将爆炸压力振幅降低40%.通过有限元模拟分析爆炸缓解机制.数值结果表明,爆炸压力脉冲的衰减主要发生在硬/软界面上,通过界面反射压力波和软材料层变形吸收动能来完成.在此基础上提出的理论模型可以很好地解释实验和数值结果,对评价和设计高性能的防爆结构具有重要意义.展开更多
The success of hydraulic fracturing for shale gas recovery has motivated much research interest in understanding the underlying mechanisms (1-3)When hydraulic fractures (HFs) expand, multiple cracks and crack branches...The success of hydraulic fracturing for shale gas recovery has motivated much research interest in understanding the underlying mechanisms (1-3)When hydraulic fractures (HFs) expand, multiple cracks and crack branches can result in complex damage zones and are generally considered to be a stimulated reservoir volume (SRV).展开更多
Microfibers formed by Bacillus subtilis(B. subtilis) have attracted interest because of their potential for use as biodegradable fibers. In this work, an efficient method based on the micro-liquid bridge method(LBM) i...Microfibers formed by Bacillus subtilis(B. subtilis) have attracted interest because of their potential for use as biodegradable fibers. In this work, an efficient method based on the micro-liquid bridge method(LBM) is proposed to investigate the mechanical properties and the deformation evolution in individual fibers. For the first time, tensile testing of fibers of this type containing several cells is conducted in a scanning electron microscope(SEM) chamber and the in situ deformation evolution of the fibers and the septa is observed. Experimental results show that these fibers are almost broken at the positions of the septa at low humidity, but also show that their fracture morphologies are different. At high humidity, local necking deformation occurs at the septum position. To explore the deformation mechanism of an individual bacterial fiber with a diameter of several hundred nanometers under different humidity conditions, we use the finite element method(FEM) to analyze the tensile deformation behavior of these fibers when their septa are at various separation levels. The numerical results indicate that weak interactions among the septa lead to the dispersion of both the fibrous tensile strength and the modulus. These results may be helpful in understanding the deformation mechanism, thus leading to further improvements in the mechanical performance of these fibers.展开更多
The fluid-saturated transversely isotropic poroelastic medium could be widely found in nature, e.g., the sedimentary rocks underground. To determine the eight independent material constants for the transversely isotro...The fluid-saturated transversely isotropic poroelastic medium could be widely found in nature, e.g., the sedimentary rocks underground. To determine the eight independent material constants for the transversely isotropic poroelastic medium, a series of tests are discussed. Two undrained tests and one drained test are suggested as a set of tests of the least amount. For the verification purpose, two additional drained tests are also introduced as an option. The atmospheric dried test is discussed as a replacement of the traditional infiltrated drained test to save the time waiting for an equilibrium state. Some microscopic material constants, i.e.,the unjacketed bulk coefficients, the porosity, and the compressibility of porous fluid, are measurable but unnecessary to determine the independent material constants of a poroelastic medium.展开更多
Hydraulic fracture(HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method(XFEM) coupling with Biot...Hydraulic fracture(HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method(XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures(NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk(KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.展开更多
Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It lea...Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM), which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.展开更多
Repeated Unit Cell(RUC)is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element(DFE)method,and merely applying Periodic Displacement Boundary Conditions(PDBCs)to RUC is ...Repeated Unit Cell(RUC)is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element(DFE)method,and merely applying Periodic Displacement Boundary Conditions(PDBCs)to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions(PTBCs,also known as traction continuity conditions)are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element(FE)analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional(UD)fiber-reinforced composites.展开更多
基金supported by the Science Challenge Project, No. TZ2018002National Natural Science Foundation of China, under Grant No. 11972205, 11972210 and 11921002the National Key Research Development Program of China (No. 2017YFB0702003)
文摘Fragments and blast waves generated by explosions pose a serious threat to protective structures.In this paper,the impact resistance of polyurea-coated steel plate under complex dynamic loading is analyzed and designed for improving comprehensive ballistic and blast resistance using the newly established computational evaluating model.Firstly,according to the thickness and placement effects of the coating on the impact resistance,the steel-core sandwich plates are designed,which are proved to own outstanding comprehensive ballistic and blast resistance.Besides,the distribution diagram of ballistic and blast resistance for different polyurea-coated steel plates is given to guide the design of protective structures applying in different explosion scenarios.Furthermore,the dynamic response of designed plates under two scenarios with combined fragments and blast loading is studied.The results show that the synergistic effect of the combined loading reduces both the ballistic and blast resistance of the polyurea-coated steel plate.Besides,the acting sequence of the fragments and blast affects the structural protective performance heavily.It is found that the first loading inducing structural large deformation or damage is dominant.When fragments impact first,the excellent unit-thickness ballistic performance of the structural front part is strongly needed for improving the comprehensive ballistic and blast resistance.
文摘Blast-induced traumatic brain injury(b-TBI)is a kind of significant injury to soldiers in the current military conflicts.However,the mechanism of b-TBI has not been well understood,and even there are some contradictory conclusions.It is crucial to reveal the dynamic mechanism of brain volume and shear deformations under blast loading for better understanding of b-TBI.In this paper,the numerical simulation method is adopted to carry out comprehensive and in-depth researches on this issue for the first time.Based on the coupled Eulerian-Lagrangian method,the fluid-structure coupling model of the blast wave and human head is developed to simulate two situations,namely the head subjected to the frontal and lateral impacts.The simulation results are analyzed to obtain the underlying dynamic mechanisms of brain deformation.The brain volume deformation is dominated by the local bending vibration of the skull,and the corresponding frequency for the forehead skull under the frontal impact and the lateral skull faced to the lateral impact is as high as 8 kHz and 5 kHz,respectively.This leads to the high-frequency fluctuation of brain pressure and the large pressure gradient along the skull,totally different from the dynamic response of brain under head collisions.While the brain shear deformation mainly depends on the relative tangential displacement between the skull and brain and the anatomical structure of inner skull,being not related to the brain pressure and its gradient.By further comparing the medical statistics,it is inferred that diffuse axonal injury and brain contusion,the two most common types of b-TBI,are mainly attributed to brain shear deformations.And the von Mises stress can be adopted as the indicator for these two brain injuries.This study can provide theoretical guidance for the diagnosis of b-TBI and the development of protective equipment.
基金supported by Major State Research Projects (613307)Army Medical Center Talent Innovation Ability Training Program (2019CXJSB007)+1 种基金Thirteenth Five-Year"Double"Construction Research and Innovation Project of PLA (2019)Medical Research Funding of PLA (ASW14C003)。
文摘Background: Civilian explosion blast injury is more frequent in developing countries, including China. However, the incidence, casualties, and characteristics of such incidents in China are unknown.Methods: This is a retrospective analysis of the State Administration of Work Safety database. Incidents during a period from January 1, 2000 to April 30, 2017 were included in the analysis. The explosions were classified based on the number of deaths into extraordinarily major, major, serious and ordinary type. Descriptive statistics was used to analyze the incidence and characteristics of the explosions. Correlation analysis was performed to examine the potential correlations among various variables.Results: Data base search identified a total of 2098 explosions from 2000 to 2017, with 29,579 casualties: 15,788 deaths(53.4%), 12,637 injured(42.7%) and 1154 missing(3.9%). Majority of the explosions were serious type(65.4%). The number of deaths(39.5%) was also highest with the serious type(P=0.006). The highest incidence was observed in the fourth quarter of the year(October to December), and at 9:00–11:00 am and 4:00–6:00 pm of the day. The explosions were most frequent in coal-producing provinces(Guizhou and Shanxi Province). Coal mine gas explosions resulted majority of the deaths(9620, 60.9%). The number of explosion accidents closely correlated with economic output(regional economy and national GDP growth rate)(r=–0.372, P=0.040;r=0.629, P=0.028).Conclusions: The incidence and civilian casualties due to explosions remain unacceptable in developing China. Measures that mitigate the risk factors are of urgently required.
文摘In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin (SUPG/PSPG) extended finite element method (XFEM) is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.
基金the Science Challenge Project(Grant No.TZ2018002)the National Natural Science Foundation of China(Grant Nos.11972205 and 11722218)+1 种基金the National Key Research Development Program of China(Grant No.2017YFB0702003)Opening Project of Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province.
文摘现实防护工程中,硬1软复合结构在人员装甲(如头盔的外壳/衬里系统)中的应用可以有效减轻爆炸伤害.由于缺乏有效可靠的实验方法评估防护结构的防爆性能,直接接触型防护结构的发展受到限制,本文针对硬/软复合材料结构的防爆性能测试提出一种新的实验及数值评估方法,并对其防爆机理进行了分析.受测的硬/软结构由超高分子量聚乙烯(UHMWPE)复合材料和膨胀聚乙烯(EPE)泡沫组成.现场爆炸试验通过7.0 kg TNT球形炸药在3.8 m处产生的爆炸波来完成.设计了一种压力测试装置用于支撑被测结构并测量穿透防护结构的爆炸压力脉冲.实验结果表明,通过使脉冲波形更平坦、减小压力幅度和延迟脉冲到达时间,硬/软结构可以将爆炸压力脉冲减弱为三角形压力脉冲.7mmUHMWPE复合材料和20mmEPE泡沫的组合防护结构可将爆炸压力振幅降低40%.通过有限元模拟分析爆炸缓解机制.数值结果表明,爆炸压力脉冲的衰减主要发生在硬/软界面上,通过界面反射压力波和软材料层变形吸收动能来完成.在此基础上提出的理论模型可以很好地解释实验和数值结果,对评价和设计高性能的防爆结构具有重要意义.
基金supported by the National Natural Science Foundation of China(Grant No.11532008)the Special Research Grant for Doctor Discipline by Ministry of Education,China(Grant No.20120002110075)
文摘The success of hydraulic fracturing for shale gas recovery has motivated much research interest in understanding the underlying mechanisms (1-3)When hydraulic fractures (HFs) expand, multiple cracks and crack branches can result in complex damage zones and are generally considered to be a stimulated reservoir volume (SRV).
基金supported by the National Natural Science Foundation of China(Grant Nos.11872035,11472151,11632010,and 11227202)
文摘Microfibers formed by Bacillus subtilis(B. subtilis) have attracted interest because of their potential for use as biodegradable fibers. In this work, an efficient method based on the micro-liquid bridge method(LBM) is proposed to investigate the mechanical properties and the deformation evolution in individual fibers. For the first time, tensile testing of fibers of this type containing several cells is conducted in a scanning electron microscope(SEM) chamber and the in situ deformation evolution of the fibers and the septa is observed. Experimental results show that these fibers are almost broken at the positions of the septa at low humidity, but also show that their fracture morphologies are different. At high humidity, local necking deformation occurs at the septum position. To explore the deformation mechanism of an individual bacterial fiber with a diameter of several hundred nanometers under different humidity conditions, we use the finite element method(FEM) to analyze the tensile deformation behavior of these fibers when their septa are at various separation levels. The numerical results indicate that weak interactions among the septa lead to the dispersion of both the fibrous tensile strength and the modulus. These results may be helpful in understanding the deformation mechanism, thus leading to further improvements in the mechanical performance of these fibers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11532008,and 11722218)the Tsinghua University Initiative Scientific Research Programthe Drilling Research Institute of China National Petroleum Corporation
文摘The fluid-saturated transversely isotropic poroelastic medium could be widely found in nature, e.g., the sedimentary rocks underground. To determine the eight independent material constants for the transversely isotropic poroelastic medium, a series of tests are discussed. Two undrained tests and one drained test are suggested as a set of tests of the least amount. For the verification purpose, two additional drained tests are also introduced as an option. The atmospheric dried test is discussed as a replacement of the traditional infiltrated drained test to save the time waiting for an equilibrium state. Some microscopic material constants, i.e.,the unjacketed bulk coefficients, the porosity, and the compressibility of porous fluid, are measurable but unnecessary to determine the independent material constants of a poroelastic medium.
基金supported by the National Natural Science Foundation of China(Grant Nos.11532008,and 11372157)
文摘Hydraulic fracture(HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method(XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures(NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk(KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.
基金Project supported by the National Natural Science Foundation of China(No.10876100)
文摘Based on the concept of constitutive relation error along with the residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed in this paper. It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM), which involves enrichment to solve a stress singularity in the crack. Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation, the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work. By comparing the reliability of the stress intensity factor calculation, the accuracy of two programs in different cases is evaluated and the source of error is discussed. A 2-dimensional XFEM example is given to illustrate the computational procedure.
文摘Repeated Unit Cell(RUC)is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element(DFE)method,and merely applying Periodic Displacement Boundary Conditions(PDBCs)to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions(PTBCs,also known as traction continuity conditions)are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element(FE)analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional(UD)fiber-reinforced composites.
基金supported by the National Natural Science Foundation of China(Grant Nos.51731009,12102216,and 11972205)the Fundamental Research Funds for the Central Universities(Grant No.2020XZZX005-02)the China Postdoctoral Science Foundation(Grant Nos.2021M691796,and 2021T140379).