Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes occurring in the internal heterogeneous structure. These models tend to be intensive from the computational point of view as they adopt an “a priori” discretization anchored to the major material heterogeneities (e.g. grains in particulate materials and aggregate pieces in cementitious composites) and this hampers their use in the numerical simulations of large systems. In this work, this problem is addressed by formulating a general multiple scale computational framework based on classical asymptotic analysis and that (1) is applicable to any discrete model with rotational degrees of freedom; and (2) gives rise to an equivalent Cosserat continuum. The developed theory is applied to the upscaling of the Lattice Discrete Particle Model (LDPM), a recently formulated discrete model for concrete and other quasi-brittle materials, and the properties of the homogenized model are analyzed thoroughly in both the elastic and the inelastic regime. The analysis shows that the homogenized micropolar elastic properties are size-dependent, and they are functions of the RVE size and the size of the material heterogeneity. Furthermore, the analysis of the homogenized inelastic behavior highlights issues associated with the homogenization of fine-scale models featuring strain-softening and the related damage localization. Finally, nonlinear simulations of the RVE behavior subject to curvature components causing bending and torsional effects demonstrate, contrarily to typical Cosserat formulations, a significant coupling between the homogenized stress–strain and couple-curvature constitutive equations.     

Some issues associated with the intermediate space in single-crystal plasticity

In this study we show that some discussions of finite-deformation single-crystal plasticity are conceptually flawed in their focus on a set referred to as the intermediate configuration. Specifically, we prove that what is usually referred to as the intermediate configuration is not a configuration but instead a vector space that we term the intermediate space. We argue that when applied to single crystals this intermediate space represents the lattice.     

Neutron radiation damage in zirconium and its alloys

There has been much research and speculation recently on the nature of radiation induced defects in zirconium and its alloys, and in particular on the absence of voids at high fluences and temperatures in the range 0.3 to 0.5 T _m (T _m is the absolute melting temperature). Wolfenden and Farrell¹ have reviewed the evidence and suggest that α-Zr has so far resisted void formation during neutron irradiation because of: (a) the absence of a dislocation (loop or tangle) structure and/or (b) a low insoluble gas (e.g. helium) content.     

On the lattice structure of the set of stable matchings for a many-to-one model ∗

For the many-to-one matching model with firms having substitutable and q-separable preferences we propose two very natural binary operations that together with the unanimous partial ordering of the workers endow the set of stable matchings with a lattice structure. We also exhibit examples in which, under this restricted domain of firms' preferences, the classical binary operations may not even be matching     

Irreducibility and the distribution of some exponential sums

We relate the distribution of the absolute value of some generalized Gauss sums to the absolute irreducibility of some polynomials in two variables in characteristic 0 and p.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

Weight distributions of a class of cyclic codes with arbitrary number of nonzeros in quadratic case

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three nonzeros. Recently, the authors of [37] constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.     

Steering spatially separated dual sites on nano-TiO2 through SMSI and lattice matching for robust photocatalytic hydrogen evolution

Spatial isolation of different functional sites at the nanoscale in multifunctional catalysts for steering reaction sequence and paths remains a major challenge. Herein, we reported the spatial separation of dual-site Au and RuO₂ on the nanosurface of TiO₂ (Au/TiO₂/RuO₂) through the strong metal-support interaction (SMSI) and the lattice matching (LM) for robust photocatalytic hydrogen evolution. The SMSI between Au and TiO₂ induced the encapsulation of Au nanoparticles by an impermeable TiO_x overlayer, which can function as a physical separation barrier to the permeation of the second precursor. The LM between RuO₂ and rutile-TiO₂ can increase the stability of RuO₂/TiO₂ interface and thus prevent the aggregation of dual-site Au and RuO₂ in the calcination process of removing TiO_x overlayer of Au. The photocatalytic hydrogen production is used as a model reaction to evaluate the performance of spatially separated dual-site Au/TiO₂/RuO₂ catalysts. The rate of hydrogen production of the Au/TiO₂/RuO₂ is as high as 84 μmol h⁻¹ g⁻¹ under solar light irradiation without sacrificial agents, which is 2.5 times higher than the reference Au/TiO₂ and non-separated Au/RuO₂/TiO₂ samples. Systematic characterizations verify that the spatially separated dual-site Au and RuO₂ on the nanosurface of TiO₂ can effectively separate the photo-generated carriers and lower the height of the Schottky barrier, respectively, under UV and visible light irradiation. This study provides new inspiration for the precise construction of different sites in multifunctional catalysts.     

受限于两平行板间的对称星形共聚物Am Bm熔体相行为的格子自洽场理论研究

采用格子自洽场理论计算研究了受限于2个平行板间的对称星形共聚物AmBm(m=1,2,3,4,5)熔体形成的层状相结构.在给定的相互作用下(χNAB不变,χ为Flory-Huggins相互作用参数,NAB=(N?1)/m为单个聚合物分子中一对AB臂的总链节数目),针对平行板间距为体相周期的情况,系统考察了共聚物链长N和单个聚合物分子中A(或B)臂数目m对受限层结构细节及层取向的影响.由计算结果,当N或NAB不变时,受限层的归一化界面宽度随m的增大而减小.受限板为中性时,垂直层结构的单链自由能比平行层结构的低.随着板对共聚物中一种嵌段的选择作用Λ的增大,体系发生垂直层到平行层的转变,该转变为一阶相变.当m不变时,N越小,上述转变出现在越大的Λ值处,体系越容易保持垂直层结构.并且N越小,层状结构周期越小.当N或NAB不变时,m越大体系越容易保持垂直层结构.总之,星形共聚物的链长越短、臂数越多时,垂直层稳定的Λ区间越大、层状结构的界面宽度越小.这些结论可以指导刻蚀应用中对体系参数的选择.