Azimuthal Shear in Compressible Finite Elasticity

In an earlier paper, the broadest classes of compressible isotropic strain energies that support irrotational universal deformations were identified and the problems of cylindrical and spherical inflation or compaction were solved in closed form for all of these strain energies. Similar closed form solutions of the problem of azimuthal shear are presented here.      

Evidence for multiple band terminations in Pd

The level structure of ¹⁰²Pd has been investigated using data collected with the Eurogam 2 array. Several cascades of γ-rays have been established up to high spins. Termination of rotational bands has been observed at I^π = 28⁻ and 32⁺, and tentatively at I^π = 38⁺ and 42⁺. The nucleus ¹⁰²Pd is the first case where rotational bands built on valence space configurations are followed from spin close to zero up to termination and, at higher spins, a smooth rotational band which appears to terminate is built on core excited configurations.     

Noncommutative Deformation Theory

In Gerstenhaber's classical theory of deformations, the deformation parameter commutes with the original algebra. Motivated by some non classical deformations which recently appeared for quantization of Nambu mechanics, we introduce new deformations where the parameter no longer commutes with the original algebra. We find the associated cohomology and Gerstenhaber algebra and give rigidity and integrability criterions. We show that the Weyl algebra (though rigid in classical theory) can be nontrivially deformed, in super-commutative theory, to the supersymmetry enveloping algebra      

On the Equivalence Between Continuous and Differential Deformation Theories

We show that continuous and differential deformation theories of the algebra of smooth functions on are the same, and that the same result holds for the algebra of formal series. We show that preferred quantizations of formal groups are always differential.     

On Compressible Materials Capable of Sustaining Axisymmetric Shear Deformations. Part 4: Helical Shear of Anisotropic Hyperelastic Materials

Conditions on the form of the strain energy function in order that homogeneous, compressible and isotropic hyperelastic materials may sustain controllable static, axisymmetric anti-plane shear, azimuthal shear, and helical shear deformations of a hollow, circular cylinder have been explored in several recent papers. Here we study conditions on the strain energy function for homogeneous and compressible, anisotropic hyperelastic materials necessary and sufficient to sustain controllable, axisymmetric helical shear deformations of the tube. Similar results for separate axisymmetric anti-plane shear deformations and rotational shear deformations are then obtained from the principal theorem for helical shear deformations. The three theorems are illustrated for general compressible transversely isotropic materials for which the isotropy axis coincides with the cylinder axis. Previously known necessary and sufficient conditions on the strain energy for compressible and isotropic hyperelastic materials in order that the three classes of axisymmetric shear deformations may be possible follow by specialization of the anisotropic case. It is shown that the required monotonicity condition for the isotropic case is much simpler and less restrictive. Restrictions necessary and sufficient for anti-plane and rotational shear deformations to be possible in compressible hyperelastic materials having a helical axis of transverse isotropy that winds at a constant angle around the tube axis are derived. Results for the previous case and for a circular axis of transverse isotropy are included as degenerate helices. All of the conditions derived here have essentially algebraic structure and are easy to apply. The general rules are applied in several examples for specific strain energy functions of compressible and homogeneous transversely isotropic materials having straight, circular, and helical axes of material symmetry.     

On the large strain deformation behavior of silicone-based elastomers for biomedical applications

The results of a comprehensive mechanical analysis of five silicone-based elastomers are presented. Large strain monotonic tests were performed under uniaxial, strip biaxial and equi-biaxial stress states. Based on the multiaxial experimental data, hyperelastic constitutive models were determined for each material. The small strain elastic modulus ranges from 49 kPa to 1.5 MPa, and the materials show different degrees of non-linearity of their stress-strain response. Data on the time and history dependence allow determining the deviation from the behavior predicted using a non-dissipative hyperelastic constitutive model. Next to representing a guideline for a comprehensive characterization of highly deformable materials, the present results provide data which can be used for the selection of an appropriate material, depending on the specific application. The corresponding models can be used to simulate the performance of each elastomer in applications involving large strains and multiaxial loading states.     

Analysis of Wet Pressing of Paper: The Three-Phase Model. Part II: Compressible Air Case

In this study we consider a model of wet pressing of paper. We use the techniques and results from the first part of this paper, where a simplified model is studied in details. The model is, using suitable transformation, rewritten in the standard parabolic-hyperbolic form. Numerical solution for typical example is given and the effects of plastic deformations of paper are investigated. Finally, the model is employed to adres the problem of choosing an optimal pressing regime.     

夹持方式对频率转换KDP晶体面形的影响

针对惯性约束聚变（ICF）系统中大口径超薄KDP晶体在不同夹持和不同姿态下的面形变化,采用有限元分析软件ANSYS,建立了大口径超薄KDP晶体在不同夹持和不同姿态下的应变模型及其边界条件的确定方法,计算了四周简支正面点力、四周固支正面压条、四周简支侧面点力、四周固支侧面压条4种夹持方式在30°和垂直姿态下大口径超薄KDP晶体的面形变化,并给出了面形变化的P-V值和RMS值。在此基础上,通过对不同夹持和不同姿态下KDP晶体面形变化的分析和比较,给出了四周固支正面压条是引起晶体面形变化相对较小的夹持方式的结论。