scholarly journals A Thermodynamically Consistent Model of Quasibrittle Elastic Damaged Materials Based on a Novel Helmholtz Potential and Dissipation Function

Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6323
Author(s):  
Inez Kamińska ◽  
Aleksander Szwed
Keyword(s):  
Pure Shear ◽  
Strain Tensor ◽  
Small Strain ◽  
Damage Parameter ◽  
Dissipation Function ◽  
Mode Interaction ◽  
Dissipation Potential ◽  
Consistent Model ◽  
Tension And Compression ◽  
Damage Condition

In the paper, a thermodynamically consistent model of elastic damaged material in the framework of small strain theory is formulated, describing the process of deterioration in quasibrittle materials, concrete in particular. The main goal is to appropriately depict the distinction between material responses in tension and compression. A novel Helmholtz energy and a dissipation potential including three damage parameters are introduced. The Helmholtz function has a continuous first derivative with respect to strain tensor. Based on the assumed functions, the strain–stress relationship, the damage condition, the evolution laws, and the tangent stiffness tensor are derived. The model’s predictions for uniaxial tension, uniaxial compression, uniaxial cyclic compression–tension, and pure shear tests are calculated using Wolfram Mathematica in order to identify the main features of the model and to grasp the physical meaning of an isotropic damage parameter, a tensile damage parameter, and a compressive damage parameter. Their values can be directly bound to changes of secant stiffness and generalized Poisson’s ratio. An interpretation of damage parameters in association with three mechanisms of damage is given. The considered dissipation potential allows a flexible choice of a damage condition. The influence of material parameters included in dissipation function on damage mode interaction is discussed.

scholarly journals Constitutive Relation for Large Deformations of Fiber-Reinforced Rubberlike Materials with Different Response in Tension and Compression

2016 ◽  
Vol 44 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Qian Li ◽  
David A. Dillard ◽  
Romesh C. Batra
Keyword(s):  
Constitutive Relation ◽  
Large Deformations ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Strain Tensor ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Tension And Compression ◽  
Different Response ◽  
Rubberlike Materials

ABSTRACT Fiber-reinforced rubberlike materials commonly used in tires undergo large deformations and exhibit different responses in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function in terms of the five invariants of the right Cauchy-Green strain tensor and account for different response in tension and compression along the fiber direction. The constitutive relation accounts for both material and geometric nonlinearities and incorporates effects of the fifth strain invariant, I5. It has been shown by Merodio and Ogden that in shear dominated deformations, I5 makes a significant contribution to the stress-strain curve. We have implemented the proposed constitutive relation in the commercial software, LS-DYNA. The numerical solutions of a few boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which part of the solution is assumed and unknowns in the presumed solution are found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. When test data become available, one can modify the form of the strain energy density and replace the proposed constitutive relation by the new one in LS-DYNA.

Thermodynamic Modeling of Ionic Polymer-Metal Composite Beams

2012 ◽  
Author(s):  
Jayavel Arumugam ◽  
Arun Srinivasa
Keyword(s):  
Beam Theory ◽  
Dissipation Function ◽  
Convective Heating ◽  
Metal Composite ◽  
Ionic Polymer Metal Composite ◽  
Ionic Polymer ◽  
Consistent Model ◽  
Electromechanical Responses ◽  
Polymer Metal ◽  
Rate Of Dissipation

A thermodynamically consistent model to simulate the electromechanical response of ionic polymer-metal composite (IPMC) beams has been developed based on Euler-Bernoulli beam theory. Appropriate assumptions have been made and suitable forms for the Helmholtz free energy and the rate of dissipation have been chosen. The governing equations, describing the actuation and sensing behavior of IPMC strips in air, have been formulated using a set of kinematic assumptions, the power theorem, and the maximum rate of dissipation hypothesis, neglecting inertial effects. The model has been extended to solve for large deformations in IPMC cantilevers with certain loading conditions. The model has been shown to simulate the electromechanical responses of both Nafion and Flemion based IPMC strips. This includes the initial overshoot followed by a gradual back-relaxation observed in the tip deflection measurements of Nafion based IPMC strips under the application of a step voltage. It has been shown that a coupled convective heating term in the rate of dissipation function is crucial for simulating this overshoot and the back relaxation.

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.

Effects of alternating strain on the structure of a metal

1953 ◽  
Vol 220 (1141) ◽  
pp. 255-266 ◽  
Keyword(s):  
Fatigue Crack ◽  
Crystalline Structure ◽  
Fatigue Failure ◽  
General Principle ◽  
Small Strain ◽  
Local Deformation ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sharp Distinction ◽  
Tension And Compression

The work is part of researches into the cause of fatigue failure in metals. The effects on the crystalline structure of successive unidirectional tensile strains are compared with the effects of the same strains applied alternately in tension and compression. It is found that X-ray diffraction shows a sharp distinction between the direct and alternating deformation. This is interpreted as showing as a general principle that alternating reversals of a sufficiently small strain do not significantly extend the regions in the grain disturbed by its first application, though they may intensify this local deformation. It is shown that the theory of dislocations could account qualitatively for the localizing of the deformation and the forming of the fatigue crack in the affected regions.

Neutron Diffraction Study of Duplex Stainless Steel during Loading at 200°C

2008 ◽  
Vol 571-572 ◽  
pp. 175-180
Author(s):  
Rim Dakhlaoui ◽  
Andrzej Baczmanski ◽  
Chedly Braham ◽  
Sebastian Wroński ◽  
Krzysztof Wierzbanowski ◽  
...  
Keyword(s):  
Neutron Diffraction ◽  
Room Temperature ◽  
Compressive Loading ◽  
Diffraction Method ◽  
Neutron Diffraction Study ◽  
Shear Stresses ◽  
Duplex Steel ◽  
Consistent Model ◽  
Influence Of Temperature On ◽  
Tension And Compression

In this work, the influence of temperature on the mechanical properties of duplex steel is studied by performing monotonic “in situ” tension and compression at 200oC. The lattice strains in both phases were measured using the time-of-flight neutron diffraction method (at the ISIS spallation neutron source, STFC Rutherford Appleton Laboratory, UK). A thermal-elastic selfconsistent model was used to predict the expansion of the interplanar spacings during heating to 200°C. Subsequently, the variation of phase stresses during tensile and compressive loading at room temperature (20°C) and at 200°C were theoretically calculated by the elastoplastic self-consistent model. Comparing the model data with experimental results the critical resolved shear stresses and work hardening parameters were determined individually in each phase of the DSS. Finally, the yield stresses in each phase of the studied steel have been estimated. It was found that both yield points (of austenite and ferrite) are lower at 200°C than those at room temperature.

The Effect of Compressive Damage on Tensile Loading Failure of Titanium 6Al-4V

2012 ◽  
Author(s):  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
John Wertz ◽  
Casey Holycross
Keyword(s):  
Strain Energy ◽  
Tensile Loading ◽  
Damage Parameter ◽  
Total Strain ◽  
Tensile Fracture ◽  
Half Cycle ◽  
Physical Damage ◽  
Total Strain Energy ◽  
Tension And Compression ◽  
Compressive Damage

In order to explore the belief that total strain energy accumulation during monotonic tensile fracture is a universal damage parameter, the effect of compressive preloads on specimens failed via tensile loading is analyzed. The motivation behind this analysis is due to the theory of an energy-based life prediction model, which states that the total strain energy required for monotonic tensile fracture is defined as the physical damage quantity for the fatigue lifing model. Two things are observed in order to determine the effects of a compressive preload on tensile monotonic fracture. First, the compressive work is viewed as accumulated damage, thus adding to the total work necessary for failure. Second, tensile works of fractured specimens with and without stored compressive energy are compared to see if the damage parameter is affected. The analysis is conducted through experimental data acquisition from round stock Titanium 6Al-4V dogbone specimens. The results from this study show that compressive damage has a negligible effect on monotonic tensile work to fracture, and combined half-cycle tension and compression preloads have an unnoticeable effect on the tensile work of the final pull to fracture. These results contradict the theory and research validations of the energy-based predictions; however, they provide a platform for future efforts to understand the strain energy correlation between monotonic, low cycle and high cycle failures.

Two-Dimensional Geometrically Nonlinear Finite Element Formulation for Analysis of Straight Pipes

2020 ◽  
Author(s):  
Saher Attia ◽  
Magdi Mohareb ◽  
Michael Martens ◽  
Nader Yoosef Ghodsi ◽  
Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Strain Tensor ◽  
Structural Response ◽  
Small Strain ◽  
Nonlinear Finite Element ◽  
Finite Element Formulation ◽  
Single Element ◽  
Element Formulation ◽  
Geometrically Nonlinear

Abstract The paper presents a new and simple geometrically nonlinear finite element formulation to simulate the structural response of straight pipes under in-plane loading and/or internal pressure. The formulation employs the Green-Lagrange strain tensor to capture finite deformation-small strain effects. Additionally, the First Piola-Kirchhoff stress tensor and Saint Venant-Kirchhoff constitutive model are adopted within the principle of virtual work framework in conjunction with a total Lagrangian approach. The formulation is applied for a cantilever beam under three loading conditions. Results are in good agreement with shell models in ABAQUS. Although the solution is based on a single element, the formulation provides reasonable displacement and stress predictions.

scholarly journals 2-D finite displacements and strain from particle imaging velocimetry (PIV) analysis of tectonic analogue models with TecPIV

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1123-1139 ◽  
Author(s):  
David Boutelier ◽  
Christoph Schrank ◽  
Klaus Regenauer-Lieb
Keyword(s):  
Software Package ◽  
Finite Strain ◽  
Deformation Gradient ◽  
Strain Tensor ◽  
Small Strain ◽  
Time Lapse ◽  
Image Correlation ◽  
Strain Rate Tensor ◽  
Analogue Models ◽  
Finite Displacements

Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.

Self-Consistent Determination of Time-Dependent Behavior of Metals

1981 ◽  
Vol 48 (1) ◽  
pp. 41-46 ◽  
Author(s):  
G. J. Weng
Keyword(s):  
Driving Forces ◽  
Pure Shear ◽  
Time Dependent ◽  
Hardening Law ◽  
Dependent Behavior ◽  
Consistent Model ◽  
Self Consistent ◽  
The Matrix ◽  
Latent Hardening

Though Kro¨ner’s self-consistent model is not fully consistent in the elastic-plastic deformation of polycrystals, it is found to be perfectly consistent in the time-dependent deformation of such materials. Hill’s model, on the other hand, should be used with a modified constraint tensor containing the elastic moduli of the matrix in that case. Kro¨ner’s model is supplemented with a physically consistent constitutive equation for the slip system; these, together with Weng’s inverse method, form the basis of a self-consistent determination of time-dependent behavior of metals. The kinematic component of the latent hardening law and the residual stress introduced in more favorably oriented grains are the two major driving forces for recovery and the Bauschinger effect in creep. The proposed method was applied to predict the creep and recovery strains of a 2618-T61 Aluminum alloy under pure shear, step and nonradial loading. The predicted results are seen to be in generally good agreement with the test data.

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