Three‐dimensional quasi‐static frictional contact by using second‐order cone linear complementarity problem

A new formulation is presented for the three‐dimensional incremental quasi‐static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a second‐order cone linear complementarity problem is formulated, which consists of complementarity conditions defined by bilinear functions and second‐order cone constraints. The equilibrium configurations are obtained by using a combined smoothing and regularization method for the second‐order cone complementarity problem. Copyright © 2005 John Wiley & Sons, Ltd.     

A nonlinear complementarity approach for elastoplastic problems by BEM without internal cells

A nonlinear complementarity approach is presented to solve elastoplastic problems by the boundary element method, in which the equations are formulated by stress equations and complementarity function obtained from the plasticity constitutive law. The domain integrals involved are transformed into boundary integrals by radial integration method, using compactly supported radial basis functions. Two numerical examples demonstrate the algorithm’s applicability and effectiveness.     

无域积分的弹塑性边界元法的非线性互补方法

该文引入非线性互补方法来求解边界元法的弹塑性问题,其中方程组由内部点应力方程和反映塑性本构定律的互补函数形成。涉及的域积分采用径向积分法转化为边界积分。通过受内压的厚壁圆筒的应力、位移和荷载-位移情况表明了该算法的精度。     

Active macro‐zone approach for incremental elastoplastic‐contact analysis

The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact‐detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem. A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem‐elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be introduced, in order to attain the solving equation system governing the elastoplastic‐contact/detachment problem. The elastoplasticity is solved by incremental analysis, called for active macro‐zones, and uses the well‐known concept of self‐equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self‐stress matrix). The solution of the frictionless contact/detachment problem was performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment. Copyright © 2013 John Wiley & Sons, Ltd.     

On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J₂-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms.     

Role of Defects on Domain Wall Propagation in Magnetically Bistable Glass-Covered Microwires

We are trying to reveal the contribution of local defects on DW propagation in amorphous microwires. Consequently, we present a comparative study of single domain wall dynamics and local nucleation fields in Fe- and Co-rich amorphous glass-coated microwires. For this we modified experimental set-up based on the classical Sixtus?CTonks approach introducing additional pick-up coil in order evaluate defects contribution in domain wall propagation. Below some critical magnetic field, H _N , determined by the microwires inhomogeneities, an almost linear DW velocity,?v, dependence on magnetic field, H, is found. Quite fast DW propagation (v?till 3000?m/s at?H about 65?A/m) has been observed. When the applied magnetic field exceeds H _N , new reverse domains can be nucleated and consequently tandem remagnetization mechanism can be realized. The role of defects existing in magnetically bistable microwires is related with nucleation of new reversed domains.     

Second-order cone programming with warm start for elastoplastic analysis with von Mises yield criterion

The incremental problem for quasistatic elastoplastic analysis with the von?Mises yield criterion is discussed within the framework of the second-order cone programming (SOCP). We show that the associated flow rule under the von?Mises yield criterion with the linear isotropic/kinematic hardening is equivalently rewritten as a second-order cone complementarity problem. The minimization problems of the potential energy and the complementary energy for incremental analysis are then formulated as the primal-dual pair of SOCP problems, which can be solved with a primal-dual interior-point method. To enhance numerical performance of tracing an equilibrium path, we propose a warm-start strategy for a primal-dual interior-point method based on the primal-dual penalty method. In this warm-start strategy, we solve a penalized SOCP problem to find the equilibrium solution at the current loading step. An advanced initial point for solving this penalized SOCP problem is defined by using information of the solution at the previous loading step.     

Implicit multilayer J2‐plasticity using Prager's translation rule

In this paper a multilayer J₂‐plasticity model that uses Prager's translation rule for the yield surface and a modified kinematic hardening for the hardening surfaces that avoids their overlapping is developed. An implicit algorithm for the model and the consistent elastoplastic tangent are also formulated in order to obtain second‐order convergence in Newton algorithms. The multiaxial behaviour of the resulting discrete model is compared to that of a virtual bounding surface model and to that of a multilayer implicit one based on Mróz's kinematic rule. The algorithm is also applied to soil dynamics to show its robustness. Copyright © 2001 John Wiley & Sons, Ltd.     

The Asymptotic Expansion Load Decomposition elastoplastic beam model

A new higher‐order elastoplastic beam model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher‐order elastic beam model using the asymptotic expansion method. This model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the beam. In order to capture the effect of plasticity on the structure, the present elastoplastic model considers the plastic strain as an eigenstrain imposed on the structure, and new degrees of freedom are added on the fly into the kinematics during the incremental‐iterative process. The radial return algorithm of J₂ plastic flow is used. Because of the constant evolution of beam kinematics, the Newton‐Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever beam loaded at its free extremity is presented and compared to a three‐dimensional reference solution. The beam model shows satisfying results even at a local scale and for a significantly reduced computation time.     

Nonlinear elastoplastic analysis of pressure sensitive materials

When structures undergo extreme loading conditions, the materials pass the elastic limits. Therefore, to preserve economy as well as safety, it is essential to perform a realistic elastoplastic analysis using the constitutive equations in plasticity. On the other hand, computing the stress alongside its associated variables on Gauss points is a delicate process and virtually the most important part of these analyses. In this study, an efficient stress-updating technique is presented for the constitutive rate equations of the pressure sensitive materials such as concrete, rock, soil and some kind of metals. Accordingly, the Drucker–Prager plasticity is utilized to consider the hydrostatic pressure in addition to the J ₂-invariant of the deviatoric stress. Moreover, the isotropic and kinematic hardenings are used to take into account more realistic behavior of the materials. Finally, a wide range of numerical tests is carried out to show the performance of the presented method together with the application of the suggested formulations in elastoplastic analysis of a gravity dam.     

Lower bound limit analysis by bem: Convex optimization problem and incremental approach

The lower bound limit approach of the classical plasticity theory is rephrased using the Multidomain Symmetric Galerkin Boundary Element Method, under conditions of plane and initial strains, ideal plasticity and associated flow rule. The new formulation couples a multidomain procedure with nonlinear programming techniques and defines the self-equilibrium stress field by an equation involving all the substructures (bem-elements) of the discretized system. The analysis is performed in a canonical form as a convex optimization problem with quadratic constraints, in terms of discrete variables, and implemented using the Karnak.sGbem code coupled with the optimization toolbox by MatLab. The numerical tests, compared with the iterative elastoplastic analysis via the Multidomain Symmetric Galerkin Boundary Element Method, developed by some of the present authors, and with the available literature, prove the computational advantages of the proposed algorithm.     

Needleless electrospray of magnetic film from magnetization-induced cone array

Electrospray is a simple and versatile approach to deposit thin-films. Traditionally, electrospray is achieved through capillary nozzle electrode to create fluid jet. Here, we report a novel needleless electrospray approach to continuously deposit the magnetic film from the magnetization-induced self-assembling cone array of poly(vinyl pyrrolidone) (PVP)/Fe₃O₄ ferrofluid without any nozzle and feed unit. A spiral tower is used to pump the PVP/Fe₃O₄ ferrofluid and a 3D peak-cluster is self-assembled on the tip surface under an external magnetic field. The multiple and parallel jets can be continuously emitted from the cone array of 3D peak-cluster, and get deposited on the aluminum foil as a smooth magnetic film when a high-voltage electric field is further applied. This needleless electrospray approach is simple, and cost-effective with a high productivity. The prepared magnetic film mainly composed of Fe₃O₄ nanoparticles and PVP polymer exhibits superparamagnetic property and good magnetic field responsive property.     

Implicit J2‐bounding surface plasticity using Prager's translation rule

A bounding surface J₂‐plasticity model that uses Prager's translation rule is presented. The model preserves Masing's rules and is developed from the same ideas as classical infinitesimal J₂‐plasticity, resulting in the same formulation with the exception of the algorithm for the computation of the hardening function. Instead of utilizing a loading surface as in a previous formulation, hardening surfaces are introduced; the formulation is similar to that of multilayer plasticity using Prager's rule, presented in previous work. An implicit algorithm based on the radial return concept is used, and the consistent elastoplastic tangent is also developed in closed form. Examples illustrating anisotropic behaviour are presented and compared to that predicted by a multilayer J₂‐plasticity model. The model is also applied to a soil dynamics problem to show the robustness of the algorithm and its applicability to complex loading. Copyright © 2002 John Wiley & Sons, Ltd.     

Implicit plane stress algorithm for multilayer J2‐plasticity using the Prager–Ziegler translation rule

A totally implicit algorithm for plane stress multilayer plasticity is presented. The algorithm presents the plane stress version of the 3D/plane strain model for multilayer plasticity presented in a previous work. As in the 3D/plane strain case, the model is consistent with the principle of maximum dissipation and it may be considered as an extension of classical J₂‐plasticity for anisotropic non‐linear kinematic behaviour preserving Masing's rules. In order to obtain the asymptotic second‐order convergence of the Newton algorithm, the consistent tangent moduli are also given. Copyright © 2003 John Wiley & Sons, Ltd.     

Further MN rule for thermally activated high field conduction in bulk samples of glassy Se100−xSbx alloys

In the present paper, we report the observation of the Meyer-Neldel rule (MNR) in thermally activated high field conduction in bulk samples of glassy Se_100−xSb_x alloys. We have investigated Meyer-Neldel rule by two different approaches.In first approach, the temperature dependence of d.c. conductivity is studied at different electric fields without changing the composition of the glassy system. In the second approach, the composition itself varies at a particular electric field.We found that the conductivity obeys the Meyer-Neldel rule as the pre-exponential factor depends on activation energy. We also found a strong correlation between pre-factor σ₀₀ and Meyer-Neldel energy in both cases. The observation of the correlation between pre-factor σ₀₀ and Meyer-Neldel energy can be described by multiple excitations stimulated by phonon energy as described by Yelon and Movaghar.     

Evaluation of critical strain for crack nucleation of magnesium di-boride superconductor using indentation method

To fulfill the promises of MgB₂ and MgB_2−xC_x in superconducting electrical transportation, the components made by these materials need to undergo plastic work process, for which the knowledge of their mechanical behavior (i.e. elastoplastic and strength properties) is critical. This study proposes the use of a convenient method based on indentation to evaluate both the elastoplastic and strength properties of MgB₂ and MgB_2−xC_x. Through the reverse analysis using dual sharp indenters, we first extract the yield stress and work hardening exponent quantitatively. Next, the critical stress for crack nucleation (fracture strength) is estimated from a combination of experiment and numerical simulation of indentation stress field using the deduced elastoplastic properties. The critical fracture strain of MgB₂ is evaluated to be reasonably close to that from conventional tensile test. We further show that in MgB_2−xC_x, the material stiffness, yield stress and fracture strength are degraded due to carbon additive, while the work hardening exponent is slightly higher. Therefore, the addition of C does not improve the mechanical properties of MgB₂. The findings shed some useful light on the workability of MgB₂, and may become a basis for understanding the feasibility of fabrication and usage of superconductor (where the mechanical and electrical properties are coupled).     

Magnetometer Design for Measuring Ultralow DC Magnetic Fields Using YBa2Cu3O7−x Superconductors

In the present work we examined a special sensor design using a YBa₂Cu₃O_7?x superconductor as a sensing element for the detection of ultralow DC magnetic fields. The experimental results have shown that the sensor signal, which is the second harmonic signal generated by co-application of AC and DC fields to high-T _c superconductors, varies linearly with the applied DC field even in the ?0.5 Oe to 0.5 Oe range. The critical factors affecting the strength of the second harmonic signal, such as the frequency and amplitude of the AC field, the intergrain critical field H _c1J , and the minimum field required for penetration through the entire specimen H ^?, were optimized. In this way we could detect DC magnetic fields as low as 1 nT.     

Standardization of strength evaluation methods using critical distance stress

The stress and displacement fields near the bonding edge, sharp notch, and contact edge show singularity behaviors, so methods of evaluating the strength of these points using maximum stresses calculated by a numerical stress analysis, such as the finite element method, are generally not valid. We have previously presented a new method of evaluating the strength of these singular points using two stress singularity parameters H and λ. The difficulty with this method was in obtaining the critical value of the intensity of the stress singularity parameter H_c for each order of stress singularity λ. Then we have developed a method of formularizing critical value of stress singularity parameter H_c for each order of stress singularity λ by utilizing critical distance stress theory. Firstly we apply this method to the delamination strength evaluation. The estimated delamination criteria H_c(λ) agrees well with the experimental results. Then we apply this method to general sharp notch corner and contact edge fatigue problems. In these cases the fatigue-crack initiation criteria can be derived from two typical strength parameters, namely, fatigue limit σ_w0 and threshold stress intensity factor range ΔK_th. These estimated critical H_th(λ) value agrees well with the experimentally measured value. Using this simple critical distance stress approach we estimated the fretting fatigue-crack initiation criteria for any contact edge angle and optimized the contact edge geometry. Moreover, we can apply this new strength criterion to stress singularity fields for general stress-concentration structures.