scholarly journals Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil

2021 ◽  
Author(s):  
Kateryna Oliynyk ◽  
◽  
Matteo Ciantia ◽  
Keyword(s):  
Water Pressure ◽  
Deformation Gradient ◽  
Elastic Behaviour ◽  
Internal Variables ◽  
Isotropic Hardening ◽  
Free Energy Function ◽  
Plastic Deformations ◽  
Structure Degradation ◽  
Average Grain Size ◽  
Non Local

In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.

Comparison of Crystal Plasticity and Isotropic Hardening Predictions for Metal-Matrix Composites

1993 ◽  
Vol 60 (1) ◽  
pp. 70-76 ◽  
Author(s):  
A. Needleman ◽  
V. Tvergaard
Keyword(s):  
Volume Fraction ◽  
Matrix Material ◽  
Isotropic Hardening ◽  
Slip Systems ◽  
Matrix Composites ◽  
Plastic Deformations ◽  
Crystalline Plasticity ◽  
Planar Crystal ◽  
Crystal Model ◽  
Flow Theory Of Plasticity

In a numerical micromechanical study of the tensile properties of a metal reinforced by short whiskers, the elastic-plastic deformations of the metal are described in terms of crystalline plasticity, using a planar crystal model that allows for either two or three slip systems. Plane strain analyses are carried out for a periodic array of aligned whiskers for whisker volume fractions of 10 percent to 30 percent, and comparison is made with predictions based on a corresponding flow theory of plasticity with isotropic hardening. The predicted trend for composite strengthening with whisker volume fraction is the same for the various matrix material constitutive characterizations. It is found that the crystal model can give rise to shear localization, initiating at the sharp whisker edges. As a consequence of this localization, the stress carrying capacity eventually drops.

A large deformation framework for shape memory polymers: Constitutive modeling and finite element implementation

2012 ◽  
Vol 24 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Mostafa Baghani ◽  
Reza Naghdabadi ◽  
Jamal Arghavani
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Shape Memory ◽  
Finite Deformation ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Small Strain ◽  
Internal Variables

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is adopted. Moreover, employing the mixture rule, the Green–Lagrange strain tensor is related to the rubbery and glassy parts. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. Furthermore, we present the time-discrete form of the proposed constitutive model in the implicit form. Using the finite element method, we solve several boundary value problems, that is, tension and compression of bars and a three-dimensional beam made of shape memory polymers, and investigate the model capabilities as well as its numerical counterpart. The model is validated by comparing the predicted results with experimental data reported in the literature that shows a good agreement.

Optimal Bounds on Plastic Deformations for Bodies Constituted of Temperature-Dependent Elastic Hardening Material

1997 ◽  
Vol 64 (3) ◽  
pp. 510-518 ◽  
Author(s):  
F. Giambanco ◽  
L. Palizzolo
Keyword(s):  
Plastic Material ◽  
The Body ◽  
Internal Variables ◽  
Lagrange Equations ◽  
Temperature Dependent ◽  
Hardening Material ◽  
Plastic Deformations ◽  
Local Character ◽  
Elastic Plastic Material ◽  
Shakedown Limit

Bounds are investigated on the plastic deformations in a continuous solid body produced during the transient phase by cyclic loading not exceeding the shakedown limit. The constitutive model employs internal variables to describe temperature-dependent elastic-plastic material response with hardening. A deformation bounding theorem is proved. Bounds turn out to depend on some fictitious self-stresses and mechanical internal variables evaluated in the whole structure. An optimization problem, aimed to make the bound most stringent, is formulated. The Euler-Lagrange equations related to this last problem are deduced and they show that the relevant optimal bound has a local character, i.e., it depends just on some fictitious plastic deformations produced in the same region of the body where the bounded real plastic deformations are considered. The bounding technique is also generalized to the case of loads arbitrarily varying in a given domain. An application is worked out.

On the Determination of Entropy From a Scalar Potential for Special Inelastic Materials

1999 ◽  
Author(s):  
George C. Johnson ◽  
Ali Imam
Keyword(s):  
Energy Function ◽  
Helmholtz Free Energy ◽  
Scalar Potential ◽  
Deformation Gradient ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Free Energy Function ◽  
Response Functions ◽  
Constitutive Response

Abstract A known version of the second law of thermodynamics embodying the notion of dissipation is employed to obtain restrictions among constitutive response functions for two classes of inelastic bodies. It is shown that for such bodies the entropy function can be determined once the constitutive relation for the Helmholtz free energy function is specified. In addition the internal energy function is shown to depend exclusively on the temperature and the deformation gradient.

scholarly journals Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150755 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Free Energy ◽  
Energy Function ◽  
Kinematic Hardening ◽  
Deformation Gradient ◽  
Gradient Elasticity ◽  
Gradient Term ◽  
Deformation Model ◽  
Finite Width ◽  
Free Energy Function ◽  
Constitutive Material Model

The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.

scholarly journals Analysis of Springback Behaviour in Micro Flexible Rolling of Crystalline Materials

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Feijun Qu ◽  
Zhengyi Jiang ◽  
Xiaogang Wang ◽  
Cunlong Zhou
Keyword(s):  
Stainless Steel ◽  
Voronoi Tessellation ◽  
Constitutive Modelling ◽  
Combined Loading ◽  
304 Stainless Steel ◽  
Isotropic Hardening ◽  
Stress Strain ◽  
Finite Element Program ◽  
Hardening Model ◽  
Average Grain Size

This paper presents a constitutive modelling of the polycrystalline thin metal strip under a state of combined loading in microflexible rolling. The concept of grained inhomogeneity is incorporated into the classic Chaboche hardening model that accounts for the Bauschinger effect, in order to provide more precise description and analysis of the springback mechanism in the particular forming operation. The model is first implemented in the finite element program ABAQUS to numerically predict the stress-strain relationship of 304 stainless steel specimens over a range of average grain sizes. After validation of the developed model by comparison of predicted curves and actual stress-strain data points, it is further applied to predict the thickness directional springback in microflexible rolling of 304 stainless steel strips with initial thickness of 250 µm and reduction changing from 5 to 10%. The model predictions show a reasonable agreement with the experimental measurements and have proven to be more accurate than those obtained from the conventional multilinear isotropic hardening model in combination with the Voronoi tessellation technique. In addition, the variation of thickness directional springback along with the scatter effect is compared and analysed in regard to the average grain size utilising both qualitative and quantitative approaches in respect of distinct types of data at different reductions.

scholarly journals Fractional calculus for continuum mechanics – anisotropic non-locality

2016 ◽  
Vol 64 (2) ◽  
pp. 361-372 ◽  
Author(s):  
W. Sumelka
Keyword(s):  
Fractional Calculus ◽  
Continuum Mechanics ◽  
General Framework ◽  
Deformation Gradient ◽  
Theoretical Discussion ◽  
Geometrical Meaning ◽  
Numerical Examples ◽  
Non Local ◽  
Fractional Continuum ◽  
Non Locality

Abstract In this paper, a generalisation of previous author’s formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction.

The Modified Cam-Clay Model and the Constitutive Relation Principle of Thermodynamics with Internal Variables

2013 ◽  
Vol 353-356 ◽  
pp. 837-841 ◽  
Author(s):  
Jing Yu Chen ◽  
Ying Hai
Keyword(s):  
Free Energy ◽  
Constitutive Relation ◽  
Energy Function ◽  
Yield Function ◽  
Dissipation Function ◽  
Saturated Soils ◽  
Internal Variables ◽  
Free Energy Function ◽  
Modified Cam Clay ◽  
Cam Clay

According the theory of thermodynamics with internal variables, the relation between yield function and dissipation function and the condition of associated flow rule in stress space are presented; the elastoplastic matrix of the incremental form of the material constitutive equation is given out, this matrix is determined by the free energy function and the yield function. The Gibbs free energy function of solid phase of saturated soils subjected triaxial compression stress state is presented, and using the constitutive theory of thermodynamics with internal variables, yield function and stress-strain relation of the modified Cam-Clay model is obtained by the free energy function and the dissipation function. These results prove the correctness and feasibility for this constitutive theory to construct elastoplastic constitutive relation of saturated soils.

Simulation of Electromagnetic Forming of a Cross-Shaped Cup by Means of a Viscoplasticity Model Coupled with Damage at Finite Strains

2013 ◽  
Vol 554-557 ◽  
pp. 2363-2368 ◽  
Author(s):  
Yalin Kiliclar ◽  
O. Koray Demir ◽  
Ivaylo N. Vladimirov ◽  
Lukas Kwiatkowski ◽  
Stefanie Reese ◽  
...  
Keyword(s):  
Finite Element ◽  
Deep Drawing ◽  
High Speed ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Deformation Gradient ◽  
Electromagnetic Forming ◽  
Isotropic Hardening ◽  
Order Structure ◽  
Forming Process

In the field of sheet metal forming traditional forming processes are used. However, a quasi-static forming process combined with a high speed forming process can enhance the forming limits of a single one. In this paper, the investigation of the process chain quasi-static deep drawing – electromagnetic forming by means of a new coupled damage-viscoplasticity model for large deformations is performed. The finite strain constitutive model, used in the finite element simulation combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. The anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. Hill-type plastic anisotropy is modelled by expressing the yield surface as a function of second-order structure tensors as additional tensor-valued arguments. The coupling of damage and plasticity is carried out in a constitutive manner according to the effective stress concept. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package of LS-Dyna with the electromagnetical modul. Aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming process.

scholarly journals Incompressible limit for a magnetostrictive energy functional

2013 ◽  
Vol 61 (4) ◽  
pp. 1025-1030
Author(s):  
B. Gambin ◽  
W. Bielski
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Elastic Behaviour ◽  
Incompressible Limit ◽  
Elastic Deformations ◽  
Energy Functionals ◽  
Second Gradient ◽  
Non Local ◽  
Γ Convergence ◽  
Non Locality

Abstract The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

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