On asymptotic properties for some parameter-dependent variational inequalities

This paper is concerned with asymptotic and monotonicity properties of some parameter-dependent variational inequalities. The main part of the study deals with inequalities modelling friction problems with normal compliance or Tresca’s conditions in which the parameter stands for the friction coefficient. The corresponding inequalities are (generalizations) of variational inequalities of the second kind. We then study an inequality of the first kind representing the elastoplastic torsion problem where the parameter represents the plasticity yield.     

Thermomechanics of twinning from a parent to a twin with mirror image symmetry

In the paper we develop a modeling with multiple configurations and mirror image of parent crystal in the twinned structure, to describe the behavior of partially twinned structure. In the constitutive framework we take into account that: (1) the untwinned and twinned material have distinct natural configurations by virtue of their miscrostructure being different, (2) the material symmetry groups of the untwinned and twinned structures characterize the peculiar feature that the presence of the mirror image structure is related to the untwinned structure, but it can exist only as a counterpart of the previous one. The partially twinned structure is described by the evolution equations for the growth of twins, characterized by a pair of a deformation like tensorial variable and a scalar field with meaning of the volume fraction for the twins. The capability of the material to twin and untwin at a constant rate of strain in uniaxial compression has been analyzed and the oscillatory behavior predicted by the model reveals qualitative agreement with experimental evidences.      

Thermal effects in orthotropic porous elastic beams

This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then, the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous circular cylinder with a special kind of inhomogeneity.      

Energy decay rate of the thermoelastic Bresse system

In this paper, we study the energy decay rate for the thermoelastic Bresse system which describes the motion of a linear planar, shearable thermoelastic beam. If the longitudinal motion and heat transfer are neglected, this model reduces to the well-known thermoelastic Timoshenko beam equations. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. Actually, the corresponding energy decays exponentially like the classical one-dimensional thermoelastic system. However, the third wave equation about the vertical displacement is only weakly damped. Thus the decay rate of the energy of the overall system is still unknown. We will show that the exponentially decay rate is preserved when the wave speed of the vertical displacement coincides with the wave speed of longitudinal displacement or of the shear angle displacement. Otherwise, only a polynomial type decay rate can be obtained. These results are proved by verifying the frequency domain conditions.      

Γ-convergence for incompressible elastic plates

We derive a two-dimensional model for elastic plates as a Γ-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke et al. (Comm Pure Appl Math 55:1461–1506, 2002). We extend their result to the case of p growth at infinity with p ϵ [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W ^2,2 isometries, which was obtained by Pakzad (J Differ Geom 66:47–69, 2004) for convex domains and by Hornung (Comptes Rendus Mathematique 346:189–192, 2008) for piecewise C ¹ domains.     

Mg-MOF-74对CO2/H2O的吸附性能

以Mg(NO₃)₂·6H₂O和2,5-二羟基对苯二甲酸为原料, 采用溶剂热法制备了金属有机骨架材料Mg-MOF-74. 利用X射线衍射(XRD)、 红外光谱(FTIR)和扫描电子显微镜(SEM)等测试手段对其结构、 形貌和性能进行了分析, 并利用自制穿透实验装置研究了产物吸附CO₂/H₂O的性能. 结果表明: 合成的样品纯度高, 结构完整, 形貌规则有序, 具有较高的CO₂吸附量. 双组分CO₂/H₂O穿透实验结果证实, 在水蒸气存在情况下, 与沸石13X相比, Mg-MOF-74仍具有较高的CO₂吸附能力, 可用于分离高湿烟道气中的CO₂.     

Exact geometric theory of dendronized polymer dynamics

Dendronized polymers consist of an elastic backbone with a set of iterated branch structures (dendrimers) attached at every base point of the backbone. The conformations of such molecules depend on the elastic deformation of the backbone and the branches, as well as on nonlocal (e.g., electrostatic, or Lennard–Jones) interactions between the elementary molecular units comprising the dendrimers and/or backbone. We develop a geometrically exact theory for the dynamics of such polymers, taking into account both local (elastic) and nonlocal interactions. The theory is based on applying symmetry reduction of Hamilton?s principle for a Lagrangian defined on the tangent bundle of iterated semidirect products of the rotation groups that represent the relative orientations of the dendritic branches of the polymer. The resulting symmetry-reduced equations of motion are written in conservative form.     

Existence results for some Kirchhoff-Carrier problems

Analyzing the viscoelastic problem for small vibrations of elastic strings, Kirchhoff and Carrier proposed two different models of nonlinear partial differential equations. By combining these two models, we deal here with some nonlocal hyperbolic problems that cover a large class of Kirchhoff and Carrier type problems. The existence of local solutions of degenerate problems as well as local and nonlocal solutions of nondegenerate problems is established. The proofs are based on the combination of the Schauder fixed point theorem with some asymptotic method.