Cyclic Loading of Beams Based on Kinematics Hardening Behavior Coupled With Isotropic Damage

2006 ◽  
Author(s):  
Ali Nayebi ◽  
Kourosh H. Shirazi
Keyword(s):  
Cyclic Loading ◽  
Strain Hardening ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Tension And Compression ◽  
Computational Aspects ◽  
Isotropic Damage ◽  
Path Dependent

The kinematic hardening theory of plasticity based on the Prager model and incremental isotropic damage is used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. This allows damage to be path-dependent. The damage and inelastic deformation are incorporated and they are used for the analysis of the beam. The beam material is assumed to follow linear strain hardening property coupled with isotropic damage. The material strain hardening curves in tension and compression are assumed to be both identical for the isotropic material. Computational aspects of rate independent model is discussed and the constitutive equation of the rate independent plasticity coupled with the damage model are decomposed into the elastic, plastic and damage parts. Return Mapping Algorithm method is used for the correction of the elastoplastic state and for the damage model the algorithm is used according to the governed damage constitutive relation. The effect of the damage phenomenon coupled with the elastoplastic kinematic hardening is studied for deformation and load control loadings.

Lifetime Prediction of Rocket Combustion Chamber Wall by Means of Viscoplasticity Coupled With Ductile Isotropic Damage

2012 ◽  
Author(s):  
Vivian Tini ◽  
Ivaylo N. Vladimirov ◽  
Stefanie Reese
Keyword(s):  
Combustion Chamber ◽  
Copper Alloy ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Chamber Wall ◽  
Lifetime Prediction ◽  
Viscoplastic Model ◽  
Material Parameters ◽  
Isotropic Damage ◽  
Wall Materials

This paper presents the application of a viscoplastic damage model for the lifetime prediction of a typical rocket combustion chamber structure. The material modeling is motivated by extension of the classical rheological model for elastoplasticity with Armstrong-Frederick kinematic hardening into a viscoplastic model. The coupling with damage is performed using the concept of effective stress and the principle of strain equivalence. The material parameters are identified based on experimental results for the high temperature copper alloy NARloy-Z, which is one of the typical combustion chamber wall materials. Finally the applicability of the model will be shown by means of sequentially coupled thermomechanical analyses.

A coupled elastoplastic anisotropic damage model for rock materials

2020 ◽  
Vol 29 (8) ◽  
pp. 1222-1245
Author(s):  
Susheng Wang ◽  
Weiya Xu
Keyword(s):  
Coupling Effect ◽  
Damage Model ◽  
Coupled Model ◽  
Yield Function ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Rock Materials ◽  
Return Mapping ◽  
Brittle Ductile Transition ◽  
Proposed Model

In this study, a rigorous constitutive model within the framework of thermodynamics is formulated to describe the coupling process between irreversible deformation and anisotropic damage of rock materials. The coupling effect is reflected based on the “two-surface” formulation. The plastic response is described by a yield function while the anisotropic damage is defined by a novel exponential damage criterion. In the proposed model, another feature lies in introducing parameters β and k in the proposed model to capture strain hardening/softening behaviors and brittle–ductile transition. The computational formulation scheme for the coupled model is deduced in detail by using return mapping algorithm. The validity of the coupled model is compared with the numerical simulation results and the experimental curves of the fine-grained sandstone, Beishan granite, and Jinping marble. The results indicate that the model can take into account the nonlinear mechanical behaviors of rock: coupling anisotropic damage and plasticity as well as brittle-ductile transition behaviors. Without loss of generality, the coupled model is versatile to describe the mechanical characteristics of rock materials.

Effect of Strain Hardening on Monotonic and Cyclic Loading Behavior of Plate-Fin Structures with Two Pore Pressures

2014 ◽  
Vol 626 ◽  
pp. 133-138
Author(s):  
Shuhei Banno ◽  
Dai Okumura ◽  
Nobutada Ohno
Keyword(s):  
Cyclic Loading ◽  
Strain Hardening ◽  
Pore Pressure ◽  
Kinematic Hardening ◽  
Unit Cell ◽  
Viscoplastic Material ◽  
Ratcheting Strain ◽  
Pore Pressures ◽  
Special Cases ◽  
Periodic Unit Cell

We perform finite element homogenization (FEH) analysis to investigate the effect of strain hardening on the monotonic and cyclic loading behavior of plate-fin structures with two pore pressures. As a typical base metal of plate-fin structures, 316 stainless steel is considered and assumed to be the viscoplastic material that obeys the Ohno-Wang kinematic hardening rule. The plate-fin structures are assumed to be periodic and subjected to uniaxial monotonic and cyclic loadings in the stacking direction. A periodic unit cell is used for FEH analysis. Results are compared with those based on three special cases derived from Hill’s macrohomogeneity equation. It is found that the mean pore pressure entirely affect the homogenized viscoplastic behavior. It is further found that the differential pore pressure causes the remarkable accumulation of ratcheting strain in the periodic unit cell, although this internal ratcheting gives no effect on macroscopic relations, resulting in providing a closed hysteresis loop for the plate-fin structures.

Fast Plastic Integration Algorithm for Damage Prediction in Forming Process Simulations

2015 ◽  
Vol 784 ◽  
pp. 342-349
Author(s):  
Ali Halouani ◽  
Yu Ming Li ◽  
Boussad Abbès ◽  
Ying Qiao Guo
Keyword(s):  
Large Strain ◽  
Damage Model ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Forming Process ◽  
Integration Algorithm ◽  
Damage Prediction ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Process Simulations

The iterative Return Mapping Algorithm (RMA) is widely used for the plastic integration owing to its accuracy and efficiency, but it is CPU time consuming and may cause divergence problems in case of large strain increments. This paper presents a fast plastic integration method called Direct Scalar Algorithm (DSA) for the damage prediction in forming process simulations. A simplified three-dimensional (3D) strain-based damage model is coupled with the plasticity and implemented into the DSA which does not need iterative solution to make the plastic integration very fast and robust even for very large strain increments. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier ∆λ can be directly calculated. The DSA is as accurate as RMA but much faster for the plastic integration.

scholarly journals On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

2021 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Small Strain ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Hardening Rule ◽  
Return Mapping ◽  
Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Necessity of Kinematic Strain Hardening in Simulating Impact Events

2017 ◽  
Author(s):  
Sharang Kirloskar ◽  
Gurmeet Singh ◽  
Avinash Kumar
Keyword(s):  
Strain Hardening ◽  
Impact Loading ◽  
High Speed ◽  
Kinematic Hardening ◽  
Material Behavior ◽  
Isotropic Hardening ◽  
Measurement Systems ◽  
Tension And Compression ◽  
Hardening Rules ◽  
Impact Events

Impact events are very high speed and short duration events. Experimental analysis of such events tends to be extremely expensive and challenging to study because of the apparatus and measurement systems required to capture the event. Due to this, impact events are studied extensively through simulations. The ability to simulate these events is a dictating factor for developing better and more efficient designs. Traditionally, loads occurring due to impact events are assumed to monotonically increase and hence pure isotropic strain hardening is sufficient to model the material behavior. However, this assumption doesn’t hold true for all impact events. When the loads caused by an impact do not monotonically increase but instead oscillate causing tension and compression cycles, pure isotropic hardening could lead to unrealistic results. In this work, different strain hardening rules are studied and analyzed for a plate under impact loading. The process to obtain a parameter which sets a realistic combination of isotropic and kinematic strain hardening rules is demonstrated and discussed. Limitations of the existing practice of using isotropic hardening in impact loading cases are studied. An alternative approach to accommodate the kinematic hardening rule into material models using LS-DYNA, a finite element solver, is discussed.

Three-dimensional elastoplastic damage concrete model by dissipation-based arc-length method

2016 ◽  
Vol 19 (12) ◽  
pp. 1949-1962
Author(s):  
Cheng Ma ◽  
Wei-zhen Chen
Keyword(s):  
Damage Model ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Yield Function ◽  
Flow Rule ◽  
Arc Length ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Operator Split ◽  
Elastoplastic Damage

This article presents a three-dimensional isotropic elastoplastic damage model for concrete structures. The plasticity of concrete is described by a nonassociated flow rule, using a three-parameter yield function as well as a modified Drucker–Prager-type potential. The damage of concrete is seen as a contribution work of tensile and compressive damage, with the evolution histories driven by the internal tensile and compressive variables, respectively. The iterative solution of plasticity and damage is carried out according to the concept of operator split, where a return-mapping algorithm as well as a substepping strategy is used. The consistent tangent stiffness considering the recursive relationship among substeps is derived. For the solution of global iteration, a dissipation-based arc-length method is employed. Good agreements are found in comparisons between numerical results and experimental data on both elementary and structural levels. Furthermore, the sensitivities of parameters that control strain softening are investigated.

Application of an efficient anisotropic damage model to the prediction of the failure of metal forming processes

2019 ◽  
Vol 28 (10) ◽  
pp. 1556-1579 ◽  
Author(s):  
Ali Salehi Nasab ◽  
Mohammad Mashayekhi
Keyword(s):  
Constitutive Equations ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Ductile Damage ◽  
Irreversible Processes ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Integration Schemes ◽  
Return Mapping Algorithm

The main objective of this study is the numerical implementation of an advanced elastic–plastic model fully coupled with anisotropic ductile damage. The implemented formulation has been defined in the framework of thermodynamics of irreversible processes and a symmetric second-order tensor is adopted to describe the anisotropic damage state variable. After a summary of the main constitutive equations is given, the numerical integration of constitutive equations is performed using implicit and asymptotic integration schemes. Finite element simulation is performed using ABAQUS/Explicit software and the developed VUMAT subroutine. Next, the application of the developed model to T-shaped hydroforming of tubes and square-cup deep drawing metal forming processes is thoroughly discussed and failure onset zones due to anisotropic ductile damage growth are predicted and the results were consistent with the literature. Finally, by making an assumption that kinematic hardening can be ignored, an elastic predictor/plastic corrector algorithm requiring the solution of one equation is introduced. The assessment of the developed one-equation return-mapping algorithm is carried out by applying it to the simulation of the tensile test of a pre-notched bar. The Central Prossessing Unit time decreases noticeably using one-equation return mapping algorithm compared to the conventional return mapping algorithm and the numerical results are in good agreement with previous numerical simulations and experiments.

scholarly journals Deep learning predicts path-dependent plasticity

2019 ◽  
Vol 116 (52) ◽  
pp. 26414-26420 ◽  
Author(s):  
M. Mozaffar ◽  
R. Bostanabad ◽  
W. Chen ◽  
K. Ehmann ◽  
J. Cao ◽  
...  
Keyword(s):  
Deep Learning ◽  
Constitutive Models ◽  
Strain History ◽  
Surface Evolution ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
History Of ◽  
Yield Loci ◽  
Path Dependent

Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress–strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.

Sign in / Sign up

Export Citation Format

Share Document