Simulations of Plastic Instabilities in Solid Mechanics

1994 ◽  
Vol 47 (6) ◽  
pp. 171-205 ◽  
Author(s):  
Yoshihiro Tomita
Keyword(s):  
Solid Mechanics ◽  
Shear Banding ◽  
Polymeric Materials ◽  
External Pressure ◽  
Combined Loading ◽  
Thin Plates ◽  
Flow Localization ◽  
Adiabatic Shear Banding ◽  
Wide Range ◽  
Localization Behavior

The purpose of the present article is provide a perspective for computational predictions related to such plastic instabilities as buckling, necking and flow localization including shear–banding under a wide range of deformation rates for a variety of materials, including single– and polycrystals. Computational bifurcation analyses for general cases, axisymmetric to nonaxisymmetric deformation, very thin–walled bodies, and specific materials with nonstandard constitutive equations are given. The postbifurcation analyses and regularization schemes to remedy the problems associated with spurious mesh sensitivity and incorrect convergence in finite element prediction of flow localization behavior are discussed. The instability behavior of thick circular tubes deformed under pressure and combined loading of internal/external pressure and axial force, neck and bulge propagations in polymeric materials, wrinkling of thin plates and shells under sheet metal forming processes, flow localization of thermo–elasto–viscoplastic materials under a wide range of deformation rates including adiabatic shear banding, and flow localization behavior of mono– and polycrystalline solids are reviewed with illustrative examples.

Numerical Study of Impact Penetration Shearing Employing Finite Strain Viscoplasticity Model Incorporating Adiabatic Shear Banding

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Patrice Longère ◽  
André Dragon ◽  
Xavier Deprince
Keyword(s):  
Damage Mechanics ◽  
Numerical Study ◽  
Shear Banding ◽  
Three Dimensional ◽  
Adiabatic Shear ◽  
Deformation Model ◽  
Viscoplastic Material ◽  
Predictive Tool ◽  
Adiabatic Shear Banding ◽  
Wide Range

This work brings forward a twofold contribution relevant to the adiabatic shear banding (ASB) process as a part of dynamic plasticity of high-strength metallic materials. The first contribution is a reassessment of a three-dimensional finite deformation model starting from a specific scale postulate and devoted to cover a wide range of dissipative phenomena, including ASB-related material instabilities (strong softening prefailure stage). The model, particularly destined to deal with impacted structures was first detailed by (Longère et al. 2003, “Modelling Adiabatic Shear Banding Via Damage Mechanics Approach,” Arch. Mech., 55, pp. 3–38; 2005, “Adiabatic Shear Banding Induced Degradation in a Thermo-Elastic/Viscoplastic Material Under Dynamic Loading,” Int. J. Impact Eng., 32, pp. 285–320). The second novel contribution concerns numerical solution of a genuine ballistic penetration problem employing the above model for a target plate material. The ASB trajectories are shown to follow a multistage history and complex distribution pattern leading finally to plugging failure mechanism. The corresponding analysis and related parametric study are intended to put to the test the pertinency of the model as an advanced predictive tool for complex shock related problems.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Recent Advances in Fabrication of Non-Isocyanate Polyurethane-Based Composite Materials

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3497
Author(s):  
Piotr Stachak ◽  
Izabela Łukaszewska ◽  
Edyta Hebda ◽  
Krzysztof Pielichowski
Keyword(s):  
Raw Materials ◽  
Synthesis Method ◽  
Polymeric Materials ◽  
Original Research ◽  
Significant Group ◽  
Oh Groups ◽  
New Class ◽  
Hazardous Chemical ◽  
Wide Range

Polyurethanes (PUs) are a significant group of polymeric materials that, due to their outstanding mechanical, chemical, and physical properties, are used in a wide range of applications. Conventionally, PUs are obtained in polyaddition reactions between diisocyanates and polyols. Due to the toxicity of isocyanate raw materials and their synthesis method utilizing phosgene, new cleaner synthetic routes for polyurethanes without using isocyanates have attracted increasing attention in recent years. Among different attempts to replace the conventional process, polyaddition of cyclic carbonates (CCs) and polyfunctional amines seems to be the most promising way to obtain non-isocyanate polyurethanes (NIPUs) or, more precisely, polyhydroxyurethanes (PHUs), while primary and secondary –OH groups are being formed alongside urethane linkages. Such an approach eliminates hazardous chemical compounds from the synthesis and leads to the fabrication of polymeric materials with unique and tunable properties. The main advantages include better chemical, mechanical, and thermal resistance, and the process itself is invulnerable to moisture, which is an essential technological feature. NIPUs can be modified via copolymerization or used as matrices to fabricate polymer composites with different additives, similar to their conventional counterparts. Hence, non-isocyanate polyurethanes are a new class of environmentally friendly polymeric materials. Many papers on the matter above have been published, including both original research and extensive reviews. However, they do not provide collected information on NIPU composites fabrication and processing. Hence, this review describes the latest progress in non-isocyanate polyurethane synthesis, modification, and finally processing. While focusing primarily on the carbonate/amine route, methods of obtaining NIPU are described, and their properties are presented. Ways of incorporating various compounds into NIPU matrices are characterized by the role of PHU materials in copolymeric materials or as an additive. Finally, diverse processing methods of non-isocyanate polyurethanes are presented, including electrospinning or 3D printing.

Materials Selection for Sandwich Pipes Under the Combined Effect of Pressure, Bending and Temperature

2007 ◽  
Author(s):  
Allan R. de Souza ◽  
Theodoro A. Netto ◽  
Ilson P. Pasqualino
Keyword(s):  
Structural Strength ◽  
Material Selection ◽  
Low Cost ◽  
Polymeric Materials ◽  
External Pressure ◽  
Core Material ◽  
Annular Layer ◽  
Oil And Natural Gas ◽  
Longitudinal Bending ◽  
Logic Approach

Recent researches point to the great potential of the sandwich pipe conception for ultra deepwater exploitation and production of oil and natural gas. Its configuration is very simple and comprises two concentric metallic pipes with a core material, polymeric or ceramic, in the annulus. The main functions of the annular layer are: to provide satisfactory thermal insulation so as to avoid the formation of wax and hydrates along the pipeline during production shutdown; to improve the overall structural strength of the system. Polypropylene and cement have been recently proposed for these applications. The reason for the choice of these materials was the low cost and the extensive availability in industry. Here a systematic material selection approach is employed in order to assess the applicability of other polymeric materials. The attributes of materials needed to meet the design specification are thoroughly studied. The list of possible materials was enlarged and the modified digital logic approach is used with the purpose to define a top group of materials for further numerical comparative study. Finite element analyses are carried out to assess the structural strength of the sandwich pipe under pure external pressure or longitudinal bending and combined external pressure and bending. Additionally, the effect of thermal gradient is included to the numerical analyses to evaluate each pre-selected material of the top group. Results indicate that other potential materials such as PEEK and polycarbonate can improve the structural performance of the sandwich pipe conception and yet meet other several design criteria.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

scholarly journals Rational Modeling of Ultimate Pipe Strength Under Bending and External Pressure

2000 ◽  
Author(s):  
André C. Nogueira ◽  
Glenn A. Lanan
Keyword(s):  
Deep Water ◽  
Limit State ◽  
Local Buckling ◽  
External Pressure ◽  
Pressure Effects ◽  
Combined Loading ◽  
Empirical Prediction ◽  
Limit State Design ◽  
Controlled Conditions ◽  
Offshore Pipeline

The capacity of pipelines to resist collapse or local buckling under a combination of external pressure and bending moment is a major aspect of offshore pipeline design. The importance of this loading combination increases as oil and gas projects in ultra deep-water, beyond 2,000-m water depths, are becoming reality. The industry is now accepting, and codes are explicitly incorporating, limit state design concepts such as the distinction between load controlled and displacement controlled conditions. Thus, deep-water pipeline installation and limit state design procedures are increasing the need to understand fundamental principles of offshore pipeline performance. Design codes, such as API 1111 (1999) or DNV (1996, 2000), present equations that quantify pipeline capacities under combined loading in offshore pipelines. However, these equations are based on empirical data fitting, with or without reliability considerations. Palmer (1994) pointed out that “it is surprising to discover that theoretical prediction [of tubular members under combined loading] has lagged behind empirical prediction, and that many of the formula have no real theoretical backup beyond dimensional analysis.” This paper addresses the ultimate strength of pipelines under combined bending and external pressure, especially for diameter-to-thickness ratios, D/t, less than 40, which are typically used for deep water applications. The model is original and has a rational basis. It includes considerations of ovalization, anisotropy (such as those caused by the UOE pipe fabrication process), load controlled, and displaced controlled conditions. First, plastic analysis is reviewed, then pipe local buckling under pure bending is analyzed and used to develop the strength model. Load controlled and displacement controlled conditions are a natural consequence of the formulation, as well as cross section ovalization. Secondly, external pressure effects are addressed. Model predictions compare very favorably to experimental collapse test results.

scholarly journals Originals of operating images for generalized problems of unsteady heat conductivity

2019 ◽  
Vol 14 (4) ◽  
pp. 77-86 ◽  
Author(s):  
E. M. Kartashov
Keyword(s):  
Mathematical Models ◽  
Bessel Functions ◽  
Applied Mathematics ◽  
Operational Calculus ◽  
Polymeric Materials ◽  
Thermal Reaction ◽  
Heaviside Step Function ◽  
External Influences ◽  
Wide Range ◽  
Variable Function

A series of operating (Laplace) non-standard images, the originals of which are absent in well-known reference books on operational calculus, are considered. By reducing one of the basic images to the Riemann-Mellin contour integral for the modified Bessel functions and analyzing the corresponding inversion formula using the approaches of the complex variable function theory, an analytical form of the original original is found, which is abrupt in nature with a break point. It is shown that analytical solutions of the corresponding mathematical models using the found originals have a wave character, which is expressed by the presence of the Heaviside step function in the solutions. The latter means that at any time there is a region of physical disturbance to the point of discontinuity and an unperturbed area after the point of discontinuity. The images studied are included in the operational solutions of mathematical models in many areas of applied mathematics. physics, thermomechanics, thermal physics, in particular in the theory of thermal shock of viscoelastic bodies, in the study of the thermal reaction of solids based on the classical Maxwell-Cattaneo-Lykov-Vernott phenomenology, taking into account the final rate of heat propagation. These models are needed to study the thermal reaction of relatively new consolidated structurally sensitive polymeric materials in structures exposed to high-intensity external influences. The analytical relations obtained for the originals and the original improper integrals resulting from them, containing combinations of Bessel functions, can be used in the general methodology of constructing and applying various mathematical models in a wide range of external influences on materials in many fields of science and technology.

The Role of Rate Effects and of Thermomechanical Coupling in Shear Localization

1997 ◽  
Vol 119 (4) ◽  
pp. 322-331 ◽  
Author(s):  
Y. Estrin ◽  
A. Molinari ◽  
S. Mercier
Keyword(s):  
Numerical Simulations ◽  
Strain Localization ◽  
Mechanical Energy ◽  
Shear Banding ◽  
Rate Sensitivity ◽  
Thermomechanical Coupling ◽  
Face Centered Cubic ◽  
Adiabatic Shear Banding ◽  
Thin Walled Tube ◽  
Face Centered

A dislocation density related constitutive model that accounts for the strain-rate sensitivity of the flow stress and, notable, of the strain-hardening coefficient was applied to describe adiabatic shear banding in face centered cubic metals. The parameter values of a prototype material, for which numerical simulations were carried out, are close to those of copper. The effect of the material parameters, especially of those reflecting the two rate sensitivities, on the occurrence of strain localization in a thin-walled tube under torsion containing a geometrical defect was investigated systematically. The results obtained provide some guidance with respect to design of materials with high resistance to strain localization and high mechanical energy absorption. Another outcome of this study is the recognition that for the problem in question linear stability analysis cannot provide a reliable criterion even for the onset of strain localization, and that numerical simulations have to be invoked.

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