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Автор: Grafiati

Опубліковано: 14 березня 2023

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Wieners, Christian. "Multigrid methods for Prandtl-Reuss plasticity." Numerical Linear Algebra with Applications 6, no. 6 (September 1999): 457–78. http://dx.doi.org/10.1002/(sici)1099-1506(199909)6:6<457::aid-nla173>3.0.co;2-p.

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Demyanov, A. "Regularity of stresses in Prandtl-Reuss perfect plasticity." Calculus of Variations and Partial Differential Equations 34, no. 1 (March 19, 2008): 23–72. http://dx.doi.org/10.1007/s00526-008-0174-5.

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Chełmiński, Krzysztof, and Patrizio Neff. "A note on approximation of Prandtl-Reuss plasticity through Cosserat plasticity." Quarterly of Applied Mathematics 66, no. 2 (February 8, 2008): 351–57. http://dx.doi.org/10.1090/s0033-569x-08-01095-9.

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Kisiel, Konrad, and Krzysztof Chełmiński. "Prandtl–Reuss dynamical elasto-perfect plasticity without safe-load conditions." Nonlinear Analysis 192 (March 2020): 111678. http://dx.doi.org/10.1016/j.na.2019.111678.

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SCHWEIZER, BEN, and MARCO VENERONI. "PERIODIC HOMOGENIZATION OF THE PRANDTL–REUSS MODEL WITH HARDENING." Journal of Multiscale Modelling 02, no. 01n02 (March 2010): 69–106. http://dx.doi.org/10.1142/s1756973710000291.

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We study the n-dimensional wave equation with an elastoplastic nonlinear stress–strain relation. We investigate the case of heterogeneous materials, i.e., x-dependent parameters that are periodic at the scale η>0. We study the limit η→0 and derive the plasticity equations for the homogenized material. We prove the well-posedness for the original and the effective system with a finite-element approximation. The approximate solutions are also used in the homogenization proof which is based on oscillating test functions and an adapted version of the div-curl Lemma.

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Temam, Roger. "A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity." Archive for Rational Mechanics and Analysis 95, no. 2 (June 1986): 137–83. http://dx.doi.org/10.1007/bf00281085.

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Saimoto, Akihide, T. Ino, and Y. Imai. "Delaunay-Tessellation Based Elastic-Plastic Analysis by Body Force Method." Key Engineering Materials 417-418 (October 2009): 245–48. http://dx.doi.org/10.4028/www.scientific.net/kem.417-418.245.

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The occurrence of small scale plasticity can be modeled physically by force doublets embedded in an elastic medium and therefore the plasticity problem can be treated by the superposition of elastic solutions. This idea for the treatment of an inelastic strain is reviewed and generalized to develop a versatile program for two-dimensional elastic-plastic problems based on Body Force Method. In the present study, a treatment of an elastic-perfect plastic body is discussed in detail. The increment of the density of force doublets, which has one to one correspondence to the increment of plastic strain, can be determined from Prandtl-Reuss equation. It was also found the Delaunay triangulation is useful and convenient for the automated elastic-plastic analysis.

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Bartczak, Leszek, and Sebastian Owczarek. "On renormalized solutions for thermomechanical problems in perfect plasticity with damping forces." Mathematics and Mechanics of Solids 24, no. 4 (May 17, 2018): 1030–53. http://dx.doi.org/10.1177/1081286518768673.

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We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl–Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearized in the neighbourhood of a reference temperature. This nonlinear thermal part is imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general, the dissipation term occurring in the heat equation is an integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallouët approach with monotone methods, we prove an existence of renormalized solutions.

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NEFF, PATRIZIO, KRZYSZTOF CHEŁMIŃSKI, WOLFGANG MÜLLER, and CHRISTIAN WIENERS. "A NUMERICAL SOLUTION METHOD FOR AN INFINITESIMAL ELASTO-PLASTIC COSSERAT MODEL." Mathematical Models and Methods in Applied Sciences 17, no. 08 (August 2007): 1211–39. http://dx.doi.org/10.1142/s021820250700225x.

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We present a finite element implementation of a Cosserat elasto-plastic model and provide a rigorous numerical analysis of the introduced time-incremental algorithm. The model allows the use of standard tools from convex analysis as known from classical Prandtl–Reuss plasticity. We derive the dual stress formulation and prove that for vanishing Cosserat couple modulus μc → 0 the classical problem is approximated. Our numerical results show the robustness of the approximation. Notably, for positive couple modulus μc > 0 there is no need for a safe-load assumption. For small μc the response is numerically indistinguishable from the classical response.

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Guarracino, Federico, and Maria Grazia Simonelli. "Numerical Evaluation of Plastic Buckling of Short Cylinders Under Combined Loading." International Journal of Structural Stability and Dynamics 18, no. 06 (June 2018): 1850081. http://dx.doi.org/10.1142/s0219455418500815.

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The so-called “plastic buckling paradox” originates from the fact that the Prandtl–Reuss’ flow theory of plasticity overestimates the plastic buckling load of plates and shells, whereas Hencky’s deformation theory of plasticity provides results that are more accurate. However, it has been shown that this problem can be overcome by introducing certain initial imperfection in accurate finite element (FE) simulations based on the flow theory of plasticity. 1 – 4 The present study goes deeper into the problem and reveals that in the case of short cylinders under combined loading, which have long been the object of extensive research in the elastic range, 5 a different modeling of the material behavior can also trigger a mode jumping from the initial imperfection, which may even reverse the reported predictions by the flow and deformation theories of plasticity. This fact must be taken in maximum consideration when performing nonlinear FE analyses for estimating the plastic buckling of thin and moderately thin short cylindrical shells.

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Kargarnovin, Mohammad H., and Hassan Shokrollahi. "Nonlinear elasto-plastic analysis of a sandwich cylindrical shell with core plasticity included." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 2 (May 7, 2014): 205–15. http://dx.doi.org/10.1177/0954406214533527.

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In this paper, static response of a sandwich cylindrical shell under elasto-plastic deformation is investigated. The faces are made of some isotropic materials and the core is made of an orthotropic material both with linear work hardening behavior. The faces are modeled as thin cylindrical shells obeying the Kirchhoff-Love assumptions. The core material is modeled as a special orthotropic solid in which its in-plane stresses are assumed to be negligible. The Prandtl-Reuss plastic flow theory and von Mises yield criterion are used in the analysis. The governing equations are derived using the principle of virtual displacements. Using Ritz method, the equations are solved for deformation components. After verification of the results, the analysis is extended by changing the values of different parameters.

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AUNG, TUN MYINT, C. M. WANG, and J. CHAKRABARTY. "PLASTIC BUCKLING OF MODERATELY THICK ANNULAR PLATES." International Journal of Structural Stability and Dynamics 05, no. 03 (September 2005): 337–57. http://dx.doi.org/10.1142/s0219455405001611.

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This paper is concerned with the plastic buckling of moderately thick annular plates under a uniform compressive stress state. The analysis is based on the incremental theory of plasticity which employs the Prandtl–Reuss equations and the plate material is assumed to obey the Ramberg–Osgood stress–strain relation. The effect of transverse shear deformation is taken into consideration by adopting the Mindlin plate theory. The governing differential equations for the plastic buckling problem are solved analytically and the plastic buckling stress factors for annular plates with the allowance of transverse shear deformation are presented for the first time. The influences of the boundary conditions, thickness to outer radius ratios, and inner to outer radius ratios on the buckling stress factors are also examined.

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Cheng, J. H., and N. Kikuchi. "An Incremental Constitutive Relation of Unilateral Contact Friction for Large Deformation Analysis." Journal of Applied Mechanics 52, no. 3 (September 1, 1985): 639–48. http://dx.doi.org/10.1115/1.3169114.

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An incremental constitutive relation of friction contact is presented for large deformation analysis. After a brief review of published explanations of friction, a model is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and nonlocal effects are discussed. Formulations of a quasistatic boundary value problem based on the updated Lagrangian approach are summarized. The elastoplastic material is assumed to behave according to the generalized Prandtl-Reuss constitutive equation. Finite element methods are employed to solve the problem. Two examples are selected to demonstrate the capability and adequacy of the proposed model.

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Rees, D. W. A. "An examination of the neutral loading condition in plasticity theory." Journal of Strain Analysis for Engineering Design 23, no. 2 (April 1, 1988): 47–60. http://dx.doi.org/10.1243/03093247v232047.

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An examination is made of a number of neutral loading experiments according to classical plasticity theory. For work hardening materials the question as to whether plastic deformation occurs during neutral loading depends strongly upon the deformation produced from initial loading. Initial elastic loading with a subsequent stress path that follows the boundary of the initial vield surface is truly neutral with a wholly elastic response. However, when plastic strain is produced from initial loading then plastic flow is produced from a subsequent stress path that follows the boundary of a surface that is an isotropic expansion of the initial yield surface. Since this violates the assumption of isotropic hardening the usefulness and limitations of the rule of kinematic hardening are examined. It is further shown that the results from recent experiments are particularly relevant to the appraisal of modern developments to plasticity theory. Neutral loading without work hardening will produce plastic flow. It is shown that the corresponding Prandtl—Reuss theoretical solutions are representative of observed behaviour for both severely pre-strained materials and for others that do not harden appreciably. The concept is introduced of lower and upper bounds on the deformation that can be expected from neutral loading. These correspond to the extreme purely elastic and non-work-hardening solutions, respectively.

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Hasrati, E., R. Ansari, and H. Rouhi. "A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 19-20 (August 9, 2019): 7041–61. http://dx.doi.org/10.1177/0954406219867726.

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Presented herein is the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation under radial loading based on a variational numerical method named as variational differential quadrature. To accomplish this aim, a first-order shear deformable plate model is developed in the context of incremental theory of plasticity (IT) (with the Prandtl-Reuss constitutive equations) and the deformation theory of plasticity (DT) (with the Hencky constitutive equations). It is considered that the material of plates exhibits strain hardening characterized by the Ramberg-Osgood relation. Also, the Winkler and Pasternak models are employed in order to formulate the elastic foundation. To implement the variational differential quadrature method, the matrix formulations of strain rates and constitutive relations are first derived. Then, based upon Hamilton's principle and using the variational differential quadrature derivative and integral operators, the discretized energy functional of the problem is directly obtained. Selected numerical results are presented to study the effects of various parameters including thickness-to-radius ratio, elastic modulus-to-nominal yield stress ratio, power of the Ramberg-Osgood relation and parameters of elastic foundation on the elastic/plastic buckling of circular and annular plates subject to different boundary conditions. Moreover, several comparisons are provided between the results of two plasticity theories, i.e. IT and DT. The effect of transverse shear deformation is also highlighted.

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Lei, Xin, and Cliff J. Lissenden. "Pressure Sensitive Nonassociative Plasticity Model for DRA Composites." Journal of Engineering Materials and Technology 129, no. 2 (September 13, 2006): 255–64. http://dx.doi.org/10.1115/1.2400273.

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Discontinuously reinforced aluminum (DRA) is currently used where design considerations include specific stiffness, tailorable coefficient of thermal expansion, or wear resistance. Plastic deformation plays a role in failures due to low cycle fatigue or simple ductile overload. DRA is known to exhibit pressure dependent yielding. Plastic deformation in metals is widely regarded to be incompressible, or very nearly so. A continuum plasticity model is developed that includes a Drucker–Prager pressure dependent yield function, plastic incompressibility via a nonassociative Prandtl–Reuss flow rule, and a generalized Armstrong–Frederick kinematic hardening law. The model is implemented using a return mapping algorithm with backward Euler integration for stability and the Newton method to determine the plastic multiplier. Material parameters are characterized from uniaxial tension and uniaxial compression experimental results. Model predictions are compared to experimental results for a nonproportional compression–shear load path. The tangent stiffness tensor is nonsymmetric because the flow rule is not associated with the yield function, which means that the commonly used algorithms that require symmetric matrices cannot be used with this material model. Model correlations with tension and compression loadings are excellent. Model predictions of shear and nonproportional compression–shear loadings are reasonably good. The nonassociative flow rule could not be validated by comparison of the plastic strain rate direction with the yield function and the flow potential due to scatter in the experimental results. The model is capable of predicting the material response obtained in the experiments, but additional validation is necessary for the condition of high hydrostatic pressure.

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Kumar, Dileep, and Dineshkumar Harursampath. "Application of Variational Asymptotic Micromechanical Method to Strength Analysis of Composite Materials." Key Engineering Materials 801 (May 2019): 95–100. http://dx.doi.org/10.4028/www.scientific.net/kem.801.95.

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One of the most important features of a material to know before using it is the maximum limit of the load at which it fails. This paper presents a micromechanical strength theory to estimate the tensile strength of the unidirectional fiber reinforced composite. The fibers used can be considered transversely isotropic and elastic till failure, but the matrix material is considered to be Elastic-plastic. The mathematical formulation used is the Variational-Asymptotic Method (VAM), which is used to construct the asymptotically-correct a reduced-dimensional model that is free of a priori assumption regarding the kinematics. The 3-D strain generated in each constituent material is explicitly expressed in 1-D strains and initial curvatures. The advantage of using VAM is that the stress state correlation of constituent materials is taken care of while applying warping constraints. Prandtl-Reuss plasticity theory has been implemented for the plastic region constitutive relationship. The other advantage of this work is that the load-bearing capacity of the composite beyond the elastic region has been considered. Good agreement has been found between experimental data and VAM analysis.

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Dbouk, Talib, Pierre Montmitonnet, and Nicolas Legrand. "Two-Dimensional Roll Bite Model with Lubrication for Cold Strip Rolling." Advanced Materials Research 966-967 (June 2014): 48–62. http://dx.doi.org/10.4028/www.scientific.net/amr.966-967.48.

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To help optimize cold rolling operations, mixed lubrication models have been developed and embedded in roll bite models. The resulting models combine micro-fluidics in a porous medium (the lubricant flow between the contacting rough surfaces), microplasticity (roughness flattening / scratching), macro-plasticity (strip reduction) and roll thermo-elasticity. They are therefore really complex and need a lot of physical data. Based on previous developments, a new, simpler version of our lubrication model has been coupled with a new roll bite model recently presented: slab method for the strip elastic-plastic deformation (Prandtl-Reuss equations), a complete influence functions set for the roll deformation with circumferential displacements, and an efficient, adaptive relaxation technique when iterating between roll and strip models. The lubrication model is elaborated on Wilson and Sheu’s mixed lubrication model. The paper describes the implementation and compares its results with our previous, more complex version; a reasonable agreement is found. Several test cases of increasing difficulty show the robustness of the model and of its implementation. As a conclusion, a brief perspective is provided on how this new type of roll bite model could be used in industry.

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Malomo, B. O., S. A. Ibitoye, and L. O. Adekoya. "The Study of Elastic-Plastic Fatigue Behavior of Nigerian-Rolled NST 37-2 Steel." International Journal of Engineering Research in Africa 3 (November 2010): 28–41. http://dx.doi.org/10.4028/www.scientific.net/jera.3.28.

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The NST 37-2 steel represents about 75% volume of Nigerian-produced steel which is yet to be fully characterized for its fatigue behavior. Thus, its suitability for many applications is questionable. This paper presents a framework based on the theory of elasto-plasticity in order to make appropriate recommendations in this regard. Experimentally, tensile tests were carried out on test specimens to establish the baseline material properties of the steel in annealed, as-rolled, normalized and hardened/tempered conditions. Fatigue tests were then conducted at 60% Su; 70% Su and 80% Su of the test material and fractographic examinations on the test specimens were subsequently carried out. The frequency harmonic fatigue analysis was implemented in the ANSYS software environment for the numerical study. The elastic-plastic material property was described by the von Mises yield criterion, the flow rule of Prandtl-Reuss, and the kinematic hardening rule of Prager. The numerical results indicate with respect to rate-dependence fatigue behavior that the annealed test specimen is most resilient under cyclic deformation as compared with the normalized, hardened/tempered and as-rolled specimens respectively. The experimental and numerical results were found to be in close agreement and based on the general performance, the steel material is recommended for use in low cycle, quasi-static fatigue applications.

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Ullah, Zahur, Will Coombs, and C. Augarde. "Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods." Engineering Computations 33, no. 4 (June 13, 2016): 1161–91. http://dx.doi.org/10.1108/ec-06-2015-0166.

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Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

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Hintermueller, Michael, and Simon Roesel. "DUALITY RESULTS AND REGULARIZATION SCHEMES FOR PRANDTL-REUSS PERFECT PLASTICITY." ESAIM: Control, Optimisation and Calculus of Variations, January 12, 2018. http://dx.doi.org/10.1051/cocv/2018004.

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"Applications of classical plasticity theory to non-radial loading paths." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 410, no. 1839 (April 8, 1987): 443–75. http://dx.doi.org/10.1098/rspa.1987.0048.

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The experimental results from published plasticity studies conducted under a wide range of non-radial loading paths are employed to examine critically the validity of the classical Prandtl-Reuss incremental flow theory of plasticity and the Levy-Mises flow rule upon which this theory is based. Comparisons are made between theory and experiment both for materials that do not work-harden and for those that do in a linear and parabolic manner. In general, it is shown that the theory is consistent with experimental observations, although discrepancies are found to arise in the presence of initial anisotropy, creep and the Bauschinger effect. Initial anisotropy is commonly the most troublesome of these, although its effect is small for heat-treated materials. It is shown that by quantifying the particular test conditions in which other discrepancies arise, the extent to which the theory may be employed reliably in engineering applications has been established. That is, in the absence of initial anisotropy, isotropic hardening may be satisfactorily assumed to describe the room-temperature deformation in a wide range of engineering alloys except when a strong Bauschinger effect is induced.

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