Continuum Mechanics Description of Plastic Flow Produced by Micro-Shear Bands

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Some applications of Burzynski yield condition in metal plasticity

The classical J2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure sen sitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyn´ ski yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto plastic constitutive equations for the paraboloid case of Burzyn´ ski’s yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plastic ity theory with the paraboloid case of Burzyn´ ski’s yield condition describes adequately the strength dif ferential effect, which is present in many kinds of materials significant for recent applications.The authors gratefully acknowledge the financial support given by the Spanish Ministerio de Educación y Ciencia, Project Reference DPI/2008 06408.Publicad

Macroscopic Properties of Open-Cell Foams Based on Micromechanical Modelling

This paper presents a micromechanical analysis for the assessment of macroscopic behaviour of threedimensional open-cell solid foams. The analysis is based on material properties of a solid phase and topological arrangement of cell structure. A foam structure consists of idealized tetrahedral unit cells, which are built of four identical half-struts forming a diamond-like structure and identified as Plateau borders. Such a unit cell represents the essential microstructural features of foam. An analytical formulation of force-displacement relations for struts can be found by considering the affinity of node displacements in tensile, bending, and shear deformation. The elements of the stiffness matrix for a single cell are expressed as functions of the compliance coefficients for stretching and bending of struts. The effective elastic constants for metallic foam considered as isotropic material are determined as functions of foam relative density and compared with available results. In this paper we define an energy-based limit condition of linear elasticity for open-cell foams and calculate the critical energy density pertinent to a particular orthogonal energy state accounting for elementary interactions in a microstructure. The study based on the assumption of linear elasticity leads to simple analytical formulas. Nevertheless, it should be stressed that the proposed theoretical basis of micromechanical modelling could be also applied for the analysis of nonlinear elastic behaviour, plasticity, and failure of foams. Such problems require, however, a more complex numerical approach

Modelling of thermo-viscoplastic behaviour of DH-36 and Weldox 460-E structural steels at wide ranges of strain rates and temperatures, comparison of constitutive relations for impact problems

In this paper, the thermo-viscoplastic behaviour of DH-36 and Weldox-460-E steels is analyzed at wide ranges of strain rates and temperatures. These materials are commonly used for naval applications. Thus, they may be subjected to a wide range of exploitation temperatures and at the same time to high strain rates due to accidental impact or explosion. The thermo-viscoplastic behaviour of these materials has been modeled by application of RK (Rusinek-Klepaczko) constitutive relation. The predictions obtained using RK constitutive relation have been compared with JC (Johnson-Cook) and PB (Physical Base) constitutive relations with use of the experimental results reported in the works of Nemat-Nasser and Guo [Nemat-Nasser, S., Guo, W.G., 2003. Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures. Mech. Mat. 35, 1023-1047] and Borvik et al. [Borvik, T., Hopperstad, O.S., Berstad, T., Langseth, M., 2001. A computational model of viscoplasticity and ductile damage for impact and penetration. Eur. J. Solid. Mech. A. 20, 685-712]. For both metals, a satisfactory agreement is reported between the experimental results and the analytical predictions using RK model at wide ranges of strain rates and temperatures (10-3 s-1 to 104 s-1, and 77 K to about 1000 K). Especially for high strain rate level, the predictions of RK model are notably more precise than those predictions obtained using PB and JC models. This proof converts RK model in suitable for modeling impact problems. Finally, numerical simulations of perforation process of DH-36 and Weldox 460-E steel plates impacted by conical non-deformable projectiles have been carried out using RK and JC models. Numerical results using FE simulations have revealed substantial influence of the constitutive relation concerning the ballistic limit, residual velocity and failure time predictions for the same initial and boundary conditions.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (Project UC3M/DPI 3395) and to the Ministerio de Educatión y Ciencia de España (Project DPI/2005 06769)Publicad

Chaotic temperature dependence at zero temperature

We present a class of examples of nearest-neighbour, boubded-spin models, in which the low-temperature Gibbs measures do not converge as the temperature is lowered to zero, in any dimension

Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries

We consider various sufficiently nonlinear sigma models for nematic liquid crystal ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show that they exhibit a first-order transition in the temperature. The result holds in dimension 2 or more for the RP^{N-1} models and in dimension 3 or more for the lattice gauge models. In the two-dimensional case our results clarify and solve a recent controversy about the possibility of such transitions. For lattice gauge models our methods provide the first proof of a first-order transition in a model with a continuous gauge symmetry

Realistic spin glasses below eight dimensions: a highly disordered view

By connecting realistic spin glass models at low temperature to the highly disordered model at zero temperature, we argue that ordinary Edwards-Anderson spin glasses below eight dimensions have at most a single pair of physically relevant pure states at nonzero low temperature. Less likely scenarios that evade this conclusion are also discussed.Comment: 18 pages (RevTeX; 1 figure; to appear in Physical Review E

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Physical nature of shear bands formation and constitutive modelling for plastic instability

No abstract availabl

Relaxation methods for fixed route demand responsive transit

This article examines a partially responsive ride-sharing transit service with predetermined cyclic routes and deterministic travel times. The main operational challenge is setting the time schedule, which varies from day to day in response to upfront passenger requests. The need of passengers to adjust their departure times from their desired value causes inconvenience, which we wish to minimize. A previous study of the fixed route dial a ride problem (FRDARP) considered strict fleet constraints. We solve two relaxed formulations, related to the one-dimensional p-median location problem, by efficient dynamic programming embedding the SMAWK algorithm. Numerical results show the potential benefit of the FRDARP compared to fixed schedule (traditional) service and illustrate the impact of demand level and fleet constraints. In addition, based on these results, we characterize the wide range of scenarios where an easier to solve relaxed formulation can be nearly as useful as the constrained formulation