The least-squares meshfree method for rigid-plasticity with frictional contact

The least-squares meshfree method (LSMFM) for rigid-plasticity based on J₂-flow rule and infinitesimal theory is proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of first-order differential system using the velocity and stress components as nodal unknowns and thus the proposed formulation is a mixed-type method. Also the penalty scheme for the enforcement of the boundary and frictional contact conditions is devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed method does not require any structure of extrinsic cells for the construction of shape functions, the treatment of incompressibility, the integration of variational formulation and the reconstruction of approximation. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed.     

Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation

In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the post-buckling temperature compared with the linear one.     

Beitrag zur Prüfung metallischer Werkstoffe im Torsionsversuch

Zusammenfassung Der Torsionsversuch eignet sich zur Untersuchung des plastischen Verhaltens von Metallen bei erhöhten Temperaturen, wenn die Fließspannung stark von der Umformgeschwindigkeit abhängt. Aus der gemessenen Drehmoment-Drehwinkel-Kurve wird die Fließkurvek _f () berechnet. Hierfür wird ein Fließkriterium benötigt, dessen Unsicherheit im allgemeinen größer ist als alle Meßfehler. Diese Unsicherheit geht aber nicht in die berechnete Dehngeschwindigkeitsempfindlichkeit ein, die somit als Hauptergebnis des Versuches anzusehen ist.Um die Bedingungen technischer Warmumformung zu simulieren, wird die Verwendung extrem kurzer Proben (flacher Scheiben) empfohlen, womit sehr hohe Umformgeschwindigkeiten erreicht werden können. Für die Auswertung derartiger Versuche ist die wirksame Länge der kurzen Proben — experimentell oder semiempirisch — zu bestimmen und die Kerbwirkung zu berücksichtigen. Im Gegensatz zur herkömmlichen Vorgehensweise wird empfohlen, die örtliche Spannung und Verzerrung nicht für die Mantelfläche der Probe zu berechnen, sondern für einen kritischen Radialabstand im Innern der Probe, für den die Schiebung von der Kerbwirkung unabhängig ist, so daß sich die zuverlässigsten Werte ergeben.

---

Summary The torsion test is often used for studying the plastic deformation of metals at elevated temperatures when stress depends strongly on the strain rate. From the measured torque-twisting angle curve, the stress-strain curvek _f () has to be calculated. For this purpose a yield criterion has to be used the uncertaintly of which normally exceeds all experimental errors. This uncertaintly, however, does not propagate into the calculated strain rate sensitivity which therefore may be considered as the main result of the torsion test.For simulating the conditions of technical hot forming processes, the use of extremely short test pieces (flat discs) by which very high strain rates can be obtained is recommended. For evaluating the test data the efficient lenght of short specimens has to be determined. In opposition to the conventional procedure of test evaluation, it is recommended not to calculate stress and strain for the surface of the specimen but for a critical radius for which strain is independent of the notch effect so that the most reliable values are obtained.

Mit 5 Abbildungen     

Numerical analysis of diffuse and localized necking in orthotropic sheet metals

In the present paper the diffuse and localized necking models according to Swift [Swift, H.W., 1952. Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, 11–18], Hill [Hill, R., 1952. On discontinuous plastic states, with special reference to localized necking in thin sheets. Journal of the Mechanics and Physics of Solids 1, 19–30] and Marciniak and Kuczyński [Marciniak, Z., Kuczyński, K., 1967. Limit strains in the process of stretch-forming sheet metal. International Journal of Mechanical Sciences 9, 609–620], respectively, are considered. A theoretical framework for the mentioned models is proposed that covers rigid–plastic as well as elastic–plastic constitutive modelling using various advanced phenomenological yield functions that are able to account very accurately for plastic anisotropy. The mentioned necking models are applied to different orthotropic sheet metals in order to assess their predictive capabilities and to stress out some potential sources for discrepancies between simulations and experiments. In particular, the impact of the applied hardening curve and the equibiaxial r-value, which was recently introduced by Barlat [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Choi, S.-H., Pourboghrat, F., Chu, E., Lege, D.J., 2003. Plane stress yield function for aluminium alloy sheets – part 1: theory. International Journal of Plasticity 19, 297–1319], on formability prediction is investigated. Furthermore, the impact of the Portevin–LeChatelier effect on the formability of aluminum sheet metals is discussed.     

In situ forming PLGA implant for 90 days controlled release of leuprolide acetate for treatment of prostate cancer

In prostate cancer, hormone therapy via leuprolide acetate drug (LUP) is used to lower the level of testosterone down to castration level to effectively control the development of prostate cancer. The objective of this study was to evaluate the effective parameters in degradation and controlled release of an injectable in situ formed polymeric implant, loaded with leuprolide acetate, in order to achieve an optimum formulation for sustained drug release for 90 days with minimum burst release. The main problem associating with such implants is their high burst release. Designing an injectable implant with sustained and minimum burst release has thus become an attractive challenge in drug delivery field. Effects of type of poly(lactic‐co‐glycolic acid) 75:25 copolymers (RG752, RG756) and addition of nano‐hydroxyapatite (HA) particles on degradation rates of the implants and release profiles were examined in vitro and in vivo in a rabbit animal model. Results showed that implants containing polymers with higher molecular weights had significantly lower weight loss and molecular weight reduction. Adding nanoparticles of hydroxyapatite into poly(lactic‐co‐glycolic acid) implants caused further reduction in degradation rates, leading to a more sustained drug release in vivo, with reduced burst release. Different conventional kinetic models were applied to drug release and degradation data. The degradation data fit well to the first‐order degradation model. Higuchi model was the best kinetic release model fitted to the experimental in vitro release data. This study led to an optimum formulation (RG756:RG752 3:1 + 5% HA) with sustained leuprolide release and testosterone suppression over a 90‐day period with significant decrease of burst release phase (50%, p < 0.001) compared with the conventional Eligard formulation. The histopathology test showed that the formulated implant had no effects of toxicity or tissue necrosis in organs of the animal model. Copyright © 2017 John Wiley & Sons, Ltd.     

Plastic surface strain mapping of bent sheets by image correlation

A technique using a single CCD camera, a precision rotation/translation stage, a telecentric zoom lens, and digital image correlation software is described for measuring surface profiles and surface plastic strain distributions of a bent thin sheet. The measurement principles, based on both parallel and pinhole perspective projections, are outlined and the relevant mathematical equations for computing the profiles and displacement fields on a curved surface are presented. The typical optical setup as well as the experimental measurement and digital image correlation analysis procedure are described. The maximum errors in the in-plane and out-of-plane coordinates or displacements are about ±5 and ±25 μm, respectively, and the maximum errors in surface strain mapping are about 0.1% or less based on a series of evaluation tests on flat and curved sample surfaces over a physical field of view of 15.2 × 11.4 mm². As an application example, the shape and surface plastic strain distribution example, the shape and surface plastic strain distributions around a bent apex of a flat 2 mm thick automotive aluminum AA5182-O sheet, which underwent a 90° bend with three bend ratios of 2t, 1t, and 0.6t, are determined using the proposed technique.     

爆炸成型弹丸贯穿混凝土的实验研究

介绍几种聚能装药对混凝土层的破坏效果，并对聚能装药的结构设计与破坏效果的相互关系进行了分析与讨论。文中重点对截卵形药型罩、亚半球变壁厚药型罩、双功能药型罩的装药结构、破甲能力及目标结构特性进行了研究。     

板材冲压成形有限元数值模拟界面摩擦约束处理方法

基于弹塑性大变形板材冲压成形增量有限元法,采用线性弹簧单元提出一种空间三维板材冲压成形等效界面摩擦力的处理方法.这种方法的优点是可以反映界面摩擦力的同步、被动产生效果,同时它还可以保证约束后刚度矩阵的对称性.将提出的摩擦约束处理算法引入自主开发的板材成形模拟软件FASTAMP,计算了汽车油底壳的成形过程,计算结果的厚度分布与实际冲压件吻合比较好,验证了等效界面摩擦力约束处理方法的有效性.     

Reliable solutions to the problem of periodic oscillations of an elastoplastic beam

We consider time-periodic oscillations of a beam with a spatially inhomogeneous Prandtl–Ishlinskii constitutive law describing the elastoplastic hysteresis. The data (mass density, Prandtl–Ishlinskii distribution, external load) are assumed to be uncertain. It is shown that a unique solution exists and is stable with respect to the data variation. Considering the total dissipated energy as a measure for the accumulated material fatigue, we identify and estimate from above the ‘worst scenario’ case, where the dissipation over one period is maximal within an admissible set of data obtained from inaccurate measurements.     

On the dynamic behaviour of a flexible beam carrying a moving mass

The behaviour of a system containing a mass traveling on a cantilever beam is considered. The mass is induced to move by an applied force as opposed to the case which has been considered in most literature where the position of the moving mass is assumed to be known and independent of the motion of the beam. Furthermore, the system to be discussed has the unique characteristic that the motions of the mass and the beam are coupled. The mathematical model of the system includes two coupled nonlinear integral/partial differential equations which are impossible to solve analytically and are difficult to solve numerically in their original form. As a remedy, the solution is discretized into space and time functions and the equations of motion are reduced to a set of ordinary differential equations. The shape function is chosen so that it satisfies the boundary conditions of the beam as well as the transient conditions imposed by the traveling mass. This choice of the shape function, which considers the mass-beam interaction, provides an improvement over the conventional method of using a simple cantilever beam mode shapes.The ordinary differential equations of motion using the improved shaped functions, are solved numerically to obtain the dynamic behaviour of the system. The results illustrate the validity of the model, and demonstrate the advantages of the improved model to the un-improved equations.