Shape sensitivity analysis of an elastic contact problem: Convergence of the Nitsche based finite element approximation

In a recent work, we introduced a finite element approximation for the shape optimization of an elastic structure in sliding contact with a rigid foundation where the contact condition (Signorini’s condition) is approximated by Nitsche’s method and the shape gradient is obtained via the adjoint state method. The motivation of this work is to propose an a priori convergence analysis of the numerical approximation of the variables of the shape gradient (displacement and adjoint state) and to show some numerical results in agreement with the theoretical ones. The main difficulty comes from the non-differentiability of the contact condition in the classical sense which requires the notion of conical differentiability.     

Large deviations and phase transition for random walks in random nonnegative potentials

We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on Z^d${\mathbb{Z}}^d$. We complement the analysis of M.P.W. Zerner [Directional decay of the Green’s function for a random nonnegative potential on Z^d${\mathbb{Z}}^d$, Ann. Appl. Probab. 8 (1996) 246–280], where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting.     

Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains

The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate , describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.

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优化设计中梁截面参数间函数关系的形状乘子法

提出了处理优化设计中梁截面参数间函数关系的形状乘子法。这种方法可以适用于各种复杂的梁截面，并且灵活地运用在含有梁截面的优化设计中。利用这种方法可以使含梁结构的优化更广泛地运用到工程实际问题中。     

The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis

The construction of effective models for materials that undergo martensitic phase transformations requires usable and accurate functional representations for the free energy density. The general representation of this energy is known to be highly non-convex; it even lacks the property of quasi-convexity. A quasi-convex relaxation, however, does permit one to make certain estimates and powerful conclusions regarding phase transformation. The general expression for the relaxed free energy is however not known in the n-variant case. Analytic solutions are known only for up to 3 variants, whereas cases of practical interests involve 7-13 variants. In this study we examine the n-variant case utilizing relaxation theory and produce a seemingly obvious but very powerful observation regarding a lower bound to the quasi-convex relaxation that makes practical evolutionary computations possible. We also examine in detail the 4-variant case where we explicitly show the relation between three different forms of the free energy of mixing: upper bound by lamination, the Reuß lower bound, and a lower estimate of the -measure bound. A discussion of the bounds and their utility is provided; sample computations are presented for illustrative purposes.     

The influence of surface energy on stress-free microstructures in shape memory alloys

Certain alloys such as In-Tl, Ni-Ti, Ag-Cd or Cu-Al-Ni display remarkable mechanical properties such as the shape memory effect or pseudo-elasticity. This behaviour is related to a solid-solid phase transformation which leads to a complicated microscopic arrangement of different phases. In recent studies such microstructures have been analyzed by the minimization of elastic energy. We discuss the influence of additional surface energy terms on the existence of stress-free microstructures both in the nonlinear and a geometrically linear setting.

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Sommario Certe leghe come quelle di In-Tl, Ni-Ti, Ag-Cd o Cu-Al-Ni mostrano proprietà meccaniche notevoli quali la memoria di forma o la pseudoelasticità. Questo comportamento è determinato da una trasformazione di fase solido-solido che conduce a complicati arrangiamenti a livelo microscopico. In studi recenti tali microstrutture sono state analizzate attraverso la minimizzazione dell'energia elastica. Noi discutiamo l'influenza di termini addizionali di energia superficiale sull'esistenza di microstrutture in uno stato naturale sia in un contesto lineare che non lineare.

     

Electrochemical characterization of poly 3-thiopheneacetonitrile: Technique,solvent and relaxation effects

Characterization and electosynthesis of 3-thiopheneacetonitrile (TA) on a platinum electrode have been studied. Different solvents such as Nitrobenzene (NB), 1,2-Dichloroethane (DCE), Dichloromethane (DCM) and Acetonitrile (AN) were used. Many techniques were used for the electrodeposition of films such as potentiodynamic, chronoamperometric and galvanostatic techniques. Poly 3-thiopheneacetonitrile PTA has been subjected to relaxation effect. When the polymer is left at a potential value in its insulating state for some time, the reverse peak in the voltammetric profile during the first positive run differs from the steady state wave. The effect of solvent on the relaxation of the polymer has been studied. A weak or no relaxation was found by using different solvents such as NB, DCE, and DCM.     

New understanding on the memory effect of crystallized iPP

In this study, recovery processes of isotactic polypropylene(iPP) melted spherulites at 135 °C after melting at higher temperatures(170 °C–176 °C) were investigated with polarized optical microscopy and Fourier transform infrared spectroscopy. The recovery temperature was fixed to exclude the interference from heterogeneous nuclei. After melting at temperatures between 170 °C and 174 °C, the melted spherulite could recover back to the origin spherulite at low temperatures. Interestingly, a distinct infrared spectrum from iPP melt and crystal was observed in the early stage of recovery process after melting at low temperatures, where only IR bands resulting from short helices with 12 monomers or less can be seen, which indicates that the presence of crystal residues is not the necessary condition for the polymer memory effect. Avrami analysis further indicated that crystallization mainly took place in melted lamellae. After melting at higher temperatures, melted spherulite cannot recover. Based on above findings, it is proposed that the memory effect can be mainly ascribed to melted lamellae, during which crystalline order is lost but conformational order still exists. These conformational ordered segments formed aggregates, which can play as nucleation precursors at low temperatures.     

Observation of metastable phase separation and amorphous phase in Fe67Co33 alloy thin films synthesized by pulsed laser depositions

Pulsed laser deposition technique has been used to manipulate the structural order of Fe₆₇Co₃₃ films grown at various substrate temperatures. Films deposited at room temperature exhibited two phases including the stable crystalline phase embedded in the amorphous phase. The crystalline phase separated into two distinct bcc phases as evident from the splitting of (110) reflections, as compared to the bulk counterpart which crystalize into the single phase bcc structure. Both crystalline phases and the amorphous phase were metastable. Films prepared at higher substrate temperatures (∼500 °C), crystallized into the single stable equilibrium bcc structure. Orientation dependent magnetic properties are also presented for the films prepared at both room temperature and higher substrate temperatures. As expected, the easy axes lie parallel to the plane of the substrate due to shape anisotropy. Out of plane magnetization for the films which exhibited short range ordering is found to saturate at smaller field compared to films where single phase bcc structure is stabilized.