Explicit and Implicit Integration Algorithms for an Elastoplastic Pipe-Soil Interaction Macroelement Model

2008 ◽  
Author(s):  
Yinghui Tian ◽  
Mark J. Cassidy
Keyword(s):  
Yield Surface ◽  
Nodal Point ◽  
Elastic Behaviour ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Implicit Integration ◽  
Soil System ◽  
Total Displacement ◽  
Integration Algorithms

This paper presents the numerical formulation of an elastoplastic force-resultant model to numerically simulate the interaction of a pipe with the soil. This approach, which accounts for the load-displacement behaviour of the pipe-soil system on a macroelement level, is becoming increasingly popular in offshore engineering. The model consists of a yield surface, a non-associated flow rule, an isotropic hardening law and a description of purely elastic behaviour. It can be used to predict the behavior of one segment of pipe or numerous models can be attached to structural finite elements as nodal point elements. The latter allows the practical analysis of long pipelines. Further, by removing a number of macroelements from the pipeline, the effect of free span can be studied. To numerically incorporate large numbers of macroelements into a structural analysis, efficient and robust integration algorithms are essential. The use of both explicit and implicit integration algorithms are explored in this paper. In the explicit algorithm, the Euler forward integration scheme is adopted to achieve the real force state incrementally for each substep. On the other hand, the Euler backward integration scheme is adopted in the implicit algorithm. In this case the load state is iteratively “returned” back to the yield surface according to the end of the total displacement increment. Illustrative calculation examples are provided in this paper to demonstrate and compare the performance of the suggested algorithms.

scholarly journals Development of a continuum plasticity model for the commercial finite element code ABAQUS

2011 ◽  
Vol 2 (2) ◽  
pp. 275-283
Author(s):  
M. Safaei ◽  
W. De Waele
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Euler Method ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Implicit Integration ◽  
Backward Euler ◽  
User Material Subroutine ◽  
Von Mises ◽  
Future Work

The present work relates to the development of computational material models for sheet metalforming simulations. In this specific study, an implicit scheme with consistent Jacobian is used forintegration of large deformation formulation and plane stress elements. As a privilege to the explicitscheme, the implicit integration scheme is unconditionally stable. The backward Euler method is used toupdate trial stress values lying outside the yield surface by correcting them back to the yield surface atevery time increment. In this study, the implicit integration of isotropic hardening with the von Mises yieldcriterion is discussed in detail. In future work it will be implemented into the commercial finite element codeABAQUS by means of a user material subroutine.

Computational Issues in Rate-Dependent Plasticity Models

2012 ◽  
Vol 566 ◽  
pp. 70-77 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Inviscid Limit ◽  
Integration Scheme ◽  
Computational Results ◽  
Flow Function ◽  
Implicit Integration ◽  
Dependent Plasticity ◽  
Viscosity Parameter ◽  
Fully Implicit ◽  
Rate Dependent ◽  
Integration Algorithms

In the present paper computational issues and numerical integration algorithms are illustrated with reference to the evolutive process in rate-dependent plasticity problems. The adopted methodology conveniently relates the rate-dependent consistency parameter of the plasticity model with the flow function of the constitutive model in use. A fully implicit integration scheme is applied which correctly reduces to the inviscid limit for null viscosity parameter. Numerical examples and computational results are reported which illustrate the effectiveness of the procedure.

A combined hardening model of anisotropically consolidated cohesive soils

1991 ◽  
Vol 28 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Hiroyoshi Hirai ◽  
Takeshi Kamei
Keyword(s):  
Yield Surface ◽  
Kinematic Hardening ◽  
Strain Curve ◽  
Cohesive Soil ◽  
Stress Path ◽  
Yield Function ◽  
Triaxial Tests ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Cohesive Soils

A model introduced in the present paper is capable of describing the mechanical behaviour of anisotropically consolidated cohesive soils reasonably well. The salient features of the proposed model are summarized as follows: (i) generalized forms of the Cambridge models are given to both yield function and plastic potential; (ii) a combination of isotropic and kinematic hardening is used; (iii) a nonassociated-flow rule is proposed; (iv) the isotropic hardening involves plastic work not only related to volumetric change but also to deviatoric deformation; (v) the translation of the yield surface is specified by extending Ziegler's rule of kinematic hardening; (vi) the constitutive model has versatility and flexibility to describe expansion, translation, and rotation of a yield surface in stress space. Several undrained triaxial tests of anisotropically consolidated cohesive soils are simulated, and good agreement is observed between simulation and experimental data. Key words: anisotropy, dilatancy, cohesive soil, consolidated undrained shear, constitutive equation, stress-strain curve, pore pressure - strain curve, effective-stress path.

scholarly journals Implicit integration scheme for porous viscoplastic potential-based constitutive equations

2011 ◽  
Vol 10 ◽  
pp. 1544-1549 ◽  
Author(s):  
S. Msolli ◽  
O. Dalverny ◽  
J. Alexis ◽  
M. Karama
Keyword(s):  
Constitutive Equations ◽  
Integration Scheme ◽  
Implicit Integration

Crystal Visco-Plastic Model for Ni-Base Superalloys Under Thermomechanical Fatigue

2020 ◽  
Author(s):  
Navindra Wijeyeratne ◽  
Firat Irmak ◽  
Ali P. Gordon ◽  
Jun-Young Jeon
Keyword(s):  
Kinematic Hardening ◽  
Thermomechanical Fatigue ◽  
Temperature Cycling ◽  
Material Behavior ◽  
Integration Scheme ◽  
Flow Rule ◽  
Anisotropic Behavior ◽  
Modeling Framework ◽  
Crystallographic Slip ◽  
Slip Planes

Abstract Gas turbine blades are subjected to complex mechanical loading coupled with extreme thermal loading conditions which range from room temperature to over 1000°C. Nickel-base superalloys exhibit high strength, good resistance to corrosion and oxidation, long fatigue life and is capable of withstanding high temperatures for extended periods of time. Consequently, Ni-base superalloys (NBSAs) are highly suitable as blading materials. The cyclic strains due to mechanical as well as thermal cycling leads to Thermomechanical fatigue (TMF). Damage from TMF takes the form of microstructural material cracking which consequently lead to the failure of the component. In order to increase the service life and reliability and reduce operating costs, development of simulations that accurately predict the material behavior for TMF is highly desirable. To support the mechanical design process, a framework consisting of theoretical mechanics, experimental analysis and numerical simulations must be used. Capturing the effects of thermomechanical fatigue is extremely important in the prediction of the material behavior and life expectation. Single crystal (SX) Ni-base superalloys exhibit anisotropic behavior. A modeling framework which is capable of simulating the physical attributes of the material microstructure is essential. Crystallographic slip along the slip planes controls the microstructural evolution of the material Crystal Visco-Plasticity (CVP) theory captures anisotropic behavior as well as the slip along the slip planes. CVP constitutive models can capture rate-, temperature, and history-dependence of these materials under a variety of conditions. Typical CVP formulations consist of a flow rule, internal state variables, and parameters. The model presented in the current study includes the inelastic mechanism of kinematic hardening and isotropic hardening which are captured by the back stress and drag stress, respectively. Crystallographic slip is accounted for by the incorporation of twelve octahedral six cubic slip systems. An implicit integration scheme which uses Newton-Raphson iteration method is used to solve the required solutions. The CVP model is implemented through a general-purpose finite element analysis software (i.e., ANSYS) as a User-Defined Material (USERMAT). A small batch of uniaxial experiments were conducted in key orientations (i.e., [001], [011], and [111] to assess the level of elastic and inelastic anisotropy. Modeling parameters are expressed as temperature-dependent to allow for simulation under non-isothermal conditions. An optimization scheme based in MATLAB utilizes this experimental data to calibrate the CVP modeling constants. The CVP model has the capability to simulate material behavior for monotonic and cyclic loading coupled with in phase and out phase temperature cycling for a variety of material orientations, strain rates, strain and temperature ranges. A CVP model that predicts SX behavior across various rates, orientations, temperatures and load levels have not been presented before now.

Transient Small-Scale Yield Behavior of Textured Copper Tubing Under Biaxial Loading

1986 ◽  
Vol 108 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Hamid Garmestani ◽  
Brent L. Adams
Keyword(s):  
Yield Surface ◽  
Bauschinger Effect ◽  
Biaxial Loading ◽  
Small Scale ◽  
Isotropic Hardening ◽  
Initial Surface ◽  
Transient Time ◽  
Dependent Behavior ◽  
Copper Tubing ◽  
Final Yield

Biaxial microplastic yielding (8 microstrain) of 101 copper tubing was studied at room temperature to assess the transient time-dependent behavior of subsequent yielding following small prestrains (2000 microstrain). The specimens investigated were thin-walled tubes loaded in variable combinations of uniaxial tension/compression and internal pressurization. Prestraining in three different directions introduced a Bauschinger effect as manifested by a translation of the yield surface in the direction of stressing. The yield surface also showed an expansion in size. Subsequent yield surfaces, measured at other time intervals, showed that the Bauschinger effect recovered up to 90 percent after 120 hours, and the final yield locus retained the same shape anisotropy as the initial surface. This implies a shift from kinematic to isotropic hardening. Hart’s phenomenological model was used to predict the experimental data. In this model, the Bauschinger effect and other shape changes of the yield surface are attributed to anelastic phenomena.

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