Pressure-dependent Yield Criterion Research Articles

3D Finite Element Modelling of FRP Confined Concrete Column

Abstract Modelling concrete columns confined with fiber-reinforced polymer (FRP) using finite element (FEM) analysis is a difficult task due to the need for precise definition of material and interaction parameters. The inclusion of FRP confinement in composites introduces complexities in representing the volumetric behavior of concrete under triaxle stress conditions. The behavior of confined concrete differs from that of non-confined concrete due to the passive nature of FRP confinement, requiring consideration of flow rules, damage parameters, strain hardening/softening constitutive relationships, and a pressure-dependent yield criterion. This project aims to address these challenges by proposing a modified plastic damage model, a concrete dilation model, and a new set of concrete hardening/softening rules using the advanced FE program ABAQUS CAE. The FE model’s strengths and limitations are evaluated by comparing it with experimental results from this project, as well as other findings from literature, including both experimental and analytical studies.

Finite element implementation of hydrostatic pressure-sensitive plasticity and its application to distortional hardening model and sheet metal forming simulations

• The strength-differential (SD) effect of AHSS with ultimate tensile strength exceeding 1 GPa is modeled by a hydrostatic pressure-dependent distortional plasticity theory. • The finite element implementation of the pressure-dependent plasticity theory is proposed in the manuscript. The implemented theory is validated with the comparison study with the associated stand-alone code and experimental measurements. • Both the SD- and strain patch change effects of TIRP1180 are reproduced in finite element simulation by embedding the distortional plasticity model, HAH 20 , in the pressure-dependent yield condition. The effectiveness and applicability of the FE-implemented pressure-dependent distortional plasticity model in sheet metal forming simulations is validated through the springback prediction studies. In this work, the hydrostatic pressure-dependency of the distortional plasticity model HAH 20 was implemented using a finite element (FE) code to account for the strength-differential (SD) effect that has been observed in advanced high-strength steel sheets. To this end, a fully-implicit stress update algorithm formulation was introduced for the pressure-dependent plasticity theory. The implementation was validated by comparing the FE prediction of the material behavior during a number of tests with those of a stand-alone code of the constitutive description as well as with experimental data. In order to investigate the SD effect on the springback simulation results, the U-draw bending test was analyzed within this FE framework. Furthermore, in order to assess the effectiveness and stability of the formulation for a large-scale example, forming simulations of an automotive structural part were conducted. In addition to the SD effect, strain path changes and geometrical aspects were also investigated in this example. It was shown that the distortional plasticity-based pressure-dependent yield criterion well describes the asymmetric SD behavior in sheet metal forming simulations.

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers.

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

Multiphase mesh-free particle modeling of local sediment scouring with μ(I) rheology

Abstract Sediment scouring is a common example of highly dynamic sediment transport. Considering its complexities, the accurate prediction of such a highly dynamic multiphase granular flow system is a challenge for the traditional numerical techniques that rely on a mesh system. The mesh-free particle methods are a newer generation of numerical techniques with an inherent ability to deal with the deformations and fragmentations of a multiphase continuum. This study aims at developing and evaluating a multiphase mesh-free particle model based on the weakly compressible moving particle semi-implicit (WC-MPS) formulation for simulation of sediment scouring. The sediment material is considered as a non-Newtonian viscoplastic fluid, whose behavior is predicted using a regularized μ(I) rheological model in combination with pressure-dependent yield criteria. The model is first validated for a benchmark problem of viscoplastic Poiseuille flow. It is then applied and evaluated for the study of two classical sediment scouring cases. The results show that the high-velocity flow currents and the circulations can create a low-viscosity region on the surface of the sediment continuum. Comparing the numerical results with the experimental measurements shows a good accuracy in prediction of the sediment profile, especially the shape and dimensions of the scour hole.

A multiphase meshfree particle method for continuum-based modeling of dry and submerged granular flows

We develop and fully characterize a meshfree Lagrangian (particle) model for continuum-based numerical modeling of dry and submerged granular flows. The multiphase system of the granular material and the ambient fluid is treated as a multi-density multi-viscosity system in which the viscous behavior of the granular phase is predicted using a regularized viscoplastic rheological model with a pressure-dependent yield criterion. The numerical technique is based on the Weakly–Compressible Moving Particle Semi-implicit (WC–MPS) method. The required algorithms for approximation of the effective viscosity, effective pressure, and shear stress divergence are introduced. The capability of the model in dealing with the viscoplasticity is validated for the viscoplastic Poiseuille flow between parallel plates. The model is then applied and fully characterized (in respect to the various rheological and numerical parameters) for dry and submerged granular collapses with different aspect ratios. The numerical results are evaluated in comparison with the available experimental measurement from the literature as well as some complementary experimental measurements, performed in this study. The results show the capabilities of the presented model and its potential to deal with a broad range of dry and submerged granular flows. They also reveal the impotent role of the regularization, effective pressure, and shear stress divergence calculation methods on the accuracy of the results. For the case of the granular collapse the results characterize the shape, evolution, and flow regimes of granular deposit, as well as the important effect of the ambient fluid.

Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic – perfectly plastic materials obeying a Drucker–Prager or Mohr–Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.

Shock compression of Cu x Zr100−x metallic glasses from molecular dynamics simulations

The shock response of Cu x Zr100−x (x = 30, 50 and 70) metallic glasses (MGs) is characterized using large-scale molecular dynamics simulations. A wide range of piston velocities U p = 0.125–2.5 km/s are simulated corresponding to shock pressures from 3 to 130 GPa. Independent of composition, the metallic glasses exhibit the following shock wave propagation regimes: (1) single elastic shock wave for U p < 0.25 km/s, (2) split elastic and plastic shock waves for 0.25 < U p < 0.75 km/s and (3) overdriven plastic shock wave with a narrow elastic precursor for U p > 0.75 km/s. Within the split wave and overdriven regimes, the amplitude of the elastic precursor increases with increasing shock intensity, thereby indicating a pressure-dependent yield criterion. Hugoniot states are strongly dependent on the Cu content of the MG with Cu70Zr30 exhibiting a much higher resistance to plastic deformation than either Cu50Zr50 or Cu30Zr70.

Planar plastic flow of polymers near very rough walls

The main objective of the present paper is to investigate, by means of a boundary value problem permitting a semi-analytic solution, qualitative behaviour of solutions for two pressure-dependent yield criteria used for plastically incompressible polymers. The study mainly focuses on the regime of friction (sticking and sliding). It is shown that the existence of the solution satisfying the regime of sticking depends on other boundary conditions. In particular, there is such a class of boundary conditions depending on the yield criterion adopted that the regime of sliding is required for the existence of the solution independently of the friction law.

Stress analysis of rotating annular hyperbolic discs obeying a pressure-dependent yield criterion

The Drucker-Prager yield criterion is combined with an equilibrium equation to provide the elastic-plastic stress distribution within rotating annular hyperbolic discs and the residual stress distribution when the angular speed becomes zero. It is verified that unloading is purely elastic for the range of parameters used in the present study. A numerical technique is only necessary to solve an ordinary differential equation. The primary objective of this paper is to examine the effect of the parameter that controls the deviation of the Drucker-Prager yield criterion from the von Mises yield criterion and the geometric parameter that controls the profile of hyperbolic discs on the stress distribution at loading and the residual stress distribution.

Stress and strain fields in rotating elastic/plastic annular discs

The von Mises yield criterion is used in conjunction with its associated flow rule to provide the elastic/plastic stress and strain distributions within the rotating annular discs made of perfectly plastic material under plane stress conditions. The solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one. The strain solution requires a numerical technique to evaluate ordinary integrals. An example is presented to illustrate the general solution. The general method proposed can be readily extended to orthotropic and pressure-dependent yield criteria.

Enlargement of a circular hole in a disc of plastically compressible material

A semi-analytic solution for the elastic/plastic distribution stress and strain in a thin annular disc subject to pressure over its inner radius is presented. It is assumed that a pressure-dependent yield criterion and its associated flow rule are valid in the plastic zone. Thus, the material is plastically compressible, which is a distinguished feature of the solution. Also, in contrast to most studies on elastic/plastic deformation of thin plates and discs under plane stress conditions, the flow theory of plasticity is adopted in conjunction with a smooth yield surface. Numerical methods are only necessary to evaluate ordinary integrals and to solve simple transcendental equations. It is shown that the stress path is not proportional and, therefore, the application of deformation theories of plasticity widely used to calculate the distribution of stresses and strains in thin plates and discs is not justified.

Influence of pressure-dependency of the yield criterion and temperature on residual stresses and strains in a thin disk

Existing plane stress solutions for thin plates and disks have shown several qualitative features which are difficult to handle with the use of commercial numerical codes (non-existence of solutions, singular solutions, rapid growth of the plastic zone with a loading parameter). In order to understand the effect of temperature and pressure-dependency of the yield criterion on some of such features as well as on the distribution of residual stresses and strains, a semi-analytic solution for a thin hollow disk fixed to a rigid container and subject to thermal loading and subsequent unloading is derived. The material model is elastic-perfectly/plastic. The Drucker-Prager pressure-dependent yield criterion and the equation of incompressibity for plastic strains are adopted. The distribution of residual stresses and strains is illustrated for a wide range of the parameter which controls pressure-dependency of the yield criterion.

Damage and plastic deformation of reservoir rocks: Part 1. Damage fracturing

In this series of studies, we develop a numerical tool for modeling finite deformation of reservoir rocks. We present an attempt to eliminate the main limitations of idealized methods, for example, elastic or kinematic, that cannot account for the complexity of rock deformation. Our approach is to use rock mechanics experimental data and finite element models (Abaqus). To generate realistic simulations, the present numerical rheology incorporates the dominant documented deformation modes of rocks: (1) rock mechanics experimental observations, including finite strength, inelastic strain hardening, strength dependence on confining pressure, strain-induced dilation, pervasive and localized damage, and local tensile or shear failure without macroscopic disintegration; and (2) field observations, including large deformation, distributed damage, complex fracture networks, and multiple zones of failure. Our analysis starts with an elastic–plastic damage rheology that includes pressure-dependent yield criteria, stiffness degradation, and fracturing via a continuum damage approach, using the Abaqus materials library. We then use experimental results for Berea Sandstone in two configurations, four-point beam and dog-bone triaxial, to refine and calibrate the rheology. We find that damage and fracturing patterns generated in the numerical models match the experimental features well, and based on these observations, we define damage fracturing, the fracturing process by damage propagation in a rock with elastic–plastic damage rheology. In part 2, we apply this rheology to investigate fracture propagation at the tip of a hydrofracture.

Numerical modeling of uneven thermoplastic polymers behaviour using experimental stress-strain data and pressure dependent von Mises yield criteria to improve design practices

Classical plasticity theories and yield criteria for ductile materials, such as Tresca and von Mises original formulations predict that yielding is independent on the hydrostatic stress state (pressure), which means that tensile and compressive stress-strain behaviours are considered equal and are equally treated. This approach is reasonable for ductile metallic materials but sometimes inaccurate for polymers, which commonly present larger compressive yield strength, therefore being characterized as uneven. Polymer unevenness can be of great interest for mechanical structural design since components that present regions operating under compression can be optimized taking this phenomenon into account. Compressive stress-strain data for polymers are very scarce in the literature, and as a step in this direction this work presents three key-activities: i) four selected polymers were tested under tension and compression to identify unevenness and assess its levels; ii) pressure dependent yield criteria applicable for polymers were briefly reviewed; iii) experimental results were incorporated in adapted design practices using modified yield criteria implemented in optimization and finite element computations. Results show that taking unevenness into account and implementing modified criteria in the numerical techniques for structural calculation can provide mass reductions up to ∼ 38% even with simple geometric changes, while keeping original safety and stiffness levels.

Finite element modeling of confined concrete-II: Plastic-damage model

This paper presents a modified plastic-damage model within the theoretical framework of the Concrete Damaged Plasticity Model (CDPM) in ABAQUS for the modeling of confined concrete under non-uniform confinement. The modifications proposed for the CDPM include a damage parameter, a strain-hardening/softening rule and a flow rule, all of which are confinement-dependent, and a pressure-dependent yield criterion. The distinct characteristics of non-uniformly confined concrete are also included in this model by defining an effective confining pressure. Finite element models incorporating the proposed CDPM model were developed for concrete in a number of confinement scenarios, including active confinement, biaxial compression, FRP-confined circular and square columns, and hybrid FRP-concrete-steel double-skin tubular columns. The finite element predictions are shown to be in close agreement with the existing test results. The limitations of the proposed model are also discussed towards the end of the paper, pointing to future research needs in this area.

Strength and tension/compression asymmetry in nanostructured and ultrafine-grain metals

The recent literature is reviewed with respect to the strength-limiting deformation mechanisms in nanocrystalline and ultrafine-grain metals. Based on these results, a deformation mechanism map is proposed for FCC metals with ultrafine-grain sizes. In the absence of flaw-controlled brittle fracture, it is concluded that the strength-limiting mechanism in metals with grain sizes between approximately 10 and 500–1000 nm is dislocation emission from grain boundary sources. A simple model for the strength in this regime of grain sizes is developed from classical dislocation theory, based on the bow-out of a dislocation from a grain boundary dislocation source. The model predicts not only the strength as a function of grain size, but also the observed tension/compression asymmetry of the yield strength. The tension/compression asymmetry arises from the pressure dependence of the dislocation self-energy during bow-out. The pressure dependence is a function of material and grain size, consistent with experimental observations. Finally, the model provides a physical basis for a pressure-dependent yield criterion.

Development of experimental method to characterize pressure-dependent yield criteria for polymeric foams

In addition to lightweight and moldable characteristics, polymeric foams possess an excellent energy-absorbing capability that can be used for a wide range of commercial applications, especially for crash protection in automobiles. The purpose of the present study is to develop an experimental methodology to characterize the pressure dependent yield behavior of energy-absorbing polymeric foams. A device was designed to perform a compression test in a triaxial stress state. For the test material, polyurethane foams of two different densities were used. The displacement of the specimen, the load applied to the specimen, and hydrostatic pressure applied to the specimen were measured and controlled. Stress–strain curves and yield stresses for different hydrostatic pressures were obtained. The experiments conducted in this study revealed that the polyurethane foams exhibited significant increase in yield stress with applied hydrostatic pressure or mean normal stress. Based on this observation, a yield criterion which included the effect of the stress invariant was established for the foams. The experimental constants obtained which constituted the pressure-dependent yield criterion were verified.

Influence of hydrostatic pressure on the mechanical behavior and properties of unidirectional, laminated, graphite-fiber/epoxy-matrix thick composites

Abstract This paper reviews and gives new insight into earlier work by the author and his co-workers on the experimental investigation of the influence of superimposed hydrostatic pressure on the mechanical behavior and properties of the epoxy used for the matrix and unidirectionally laminated, graphite-fiber/ epoxy-matrix thick composites. The direction of the fibers was, respectively, 0°, 45° and 90° for the compressive test samples and 0°, 45° -45° and 90° for the shear samples. Hydrostatic pressure induces very significant, often dramatic changes in the compressive and shear stress/ strain behavior of composites, and consequently in the elastic, yielding, deformation and fracture properties. The range of pressures covered for the compressive experiments was 1 bar to 4 kbar, and for the shear tests 1 bar to 6 kbar. The shear modulus (G) of the epoxy increased bilinearly with pressure, with the break, or the discontinuity point, occurring at ∼2 kbar. The compressive elastic modulus (E) and the shear modulus (G) of the composites increase in the same manner as for the epoxy. The break, which is located at ∼2 kbar, represents a pressure at which physical changes in the molecular motion of the matrix epoxy occur. That is, segmental motion of molecules between the cross-links is frozen in by 2 kbar pressure. This pressure is known as the secondary glass transition pressure of the epoxy at room temperature. Alternatively, the sub-zero secondary glass transition temperature of the epoxy is shifted to ambient temperature by 2 kbar pressure. The increase in the moduli may also be given a mechanical interpretation. The elastic or shear modulus of an isotropic, elastic material due to small compressive or shear deformations, respectively, superimposed on a finite volume deformation, which is caused by hydrostatic pressure, increases with pressure. Such an increase in E or G has been predicted using finite deformation theory of elasticity. The normally brittle epoxy develops yielding when the superimposed hydrostatic pressure exceeds 2 kbar. The shear yield stress (1% off-set) of the epoxy increases linearly with pressure above 2 kbar. This kind of yielding behavior can be predicted by a pressure-dependent yield criterion. The compressive yield strength of the 45° and 90° composites increases bilinearly with pressure, and the shear yield strength of the 0°, 45° and 90° composites also increases bilinearly with pressure. This bilinear behavior is also due to the secondary glass transition pressure of the matrix epoxy, being located at 2 kbar. The fracture strength of the composites also increases with pressure linearly and the greatest increase occurs in the 45° composite in compression and in the −45° composite in shear. The fracture modes of the composites undergo changes with increasing hydrostatic pressure. For instance, the 0° composite undergoes a brittle-ductile transition under shear stress, while no such transition appears to set in under compressive stress. The fracture mode of the 45° composite changes from matrix failure at lower pressures to fiber failure at high pressures under shear stress.

Dynamic fracture under impact and high-strain-rate loading

A constitutive model based on a pressure-dependent yield criterion is used to predict damage evolution and ductile fracture under dynamic loading conditions. The model predicts the influence of porosity on plastic flow in metals and the nucleation, growth, and coalescence of internal microvoids to cause ductile fracture. The constitutive equations have been implemented in the DYNA2D finite-element code and have been used to simulate three high-strain-rate experiments: (i) the symmetric Taylor cylinder impact, (ii) the plate impact, and (iii) the tensile split Hopkinson bar experiments. In each case, the model is shown to capture qualitatively the damage and fracture within the experiments modelled. Comparison with recent symmetric Taylor impact experiments on leaded brass suggests that the model over-predicts the rate of damage evolution under the high-strain rate, high-triaxiality conditions associated with impact.

Accounting for the Hugoniot elastic limits of polymers by using pressure-dependent yield criterion

A factor of over 20 is measured between the Hugoniot elastic limits (HEL) of some polymers and their static shear strengths as measured under 1D stress conditions. This factor is too large to be accounted for by strain rate effects. In the present work we derive a new relation between the HEL and the shear strength which is based on a pressure-dependent yield criterion (like the Mohr–Coulomb criterion). The agreement between the experimental value for HEL of Plexiglas and its compressive yield strength is very good, strongly supporting our approach.