A Modified Microplane Model Using Transformation Surfaces to Consider Loading History on Phase Transition in Shape Memory Alloys

2014 ◽  
Author(s):  
Milad Shirani ◽  
Reza Mehrabi ◽  
Masood Taheri Andani ◽  
Mahmoud Kadkhodaei ◽  
Mohammad Elahinia ◽  
...  
Keyword(s):  
Free Energy ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Phenomenological Approach ◽  
Material Point ◽  
Loading History ◽  
Energy Potential ◽  
Microplane Model ◽  
Thermodynamic Driving Force

In most of the existing SMA constitutive models, it is assumed that transformation starts when a thermodynamic driving force reaches a specified amount regardless of loading history. In this work, a phenomenological approach is used to develop an enhanced one-dimensional constitutive model in which loading history is directly considered as one of the main parameters affecting the transformation start conditions. To generalize the model to three-dimensional cases, a microplane formulation based on volumetric-deviatoric is employed. A free energy potential is defined at the microplane level, integrated over all orientations at a material point to provide the macroscopic free energy. Experiments are carried out on Nitinol superelastic tubes to validate the newly proposed constitutive model. In these experiments, interruptions are applied during transformations to show the effects of loading history on transformation start conditions. Numerical results are compared with the experimental data to demonstrate the accuracy of the enhanced model.

scholarly journals Microplane Constitutive Model and Metal Plasticity

2000 ◽  
Vol 53 (10) ◽  
pp. 265-281 ◽  
Author(s):  
Michele Brocca ◽  
Zdeneˇk P. Bazˇant
Keyword(s):  
Constitutive Model ◽  
Plastic Region ◽  
Constitutive Models ◽  
Flow Theory ◽  
Basic Structure ◽  
Steel Tube ◽  
Loading Path ◽  
Microplane Model ◽  
Metal Plasticity ◽  
Path Direction

The microplane model is a versatile constitutive model in which the stress-strain relations are defined in terms of vectors rather than tensors on planes of all possible orientations, called the microplanes, representative of the microstructure of the material. The microplane model with kinematic constraint has been successfully employed in the modeling of concrete, soils, ice, rocks, fiber composites and other quasibrittle materials. The microplane model provides a powerful and efficient numerical tool for the development and implementation of constitutive models for any kind of material. The paper presents a review of the background from which the microplane model stems, highlighting differences and similarities with other approaches. The basic structure of the microplane model is then presented, together with its extension to finite strain deformation. Three microplane models for metal plasticity are introduced and discussed. They are compared mutually and with the classical J2-flow theory for incremental plasticity by means of two examples. The first is the material response to a nonproportional loading path given by uniaxial compression into the plastic region followed by shear (typical of buckling and bifurcation problems). This example is considered in order to show the capability of the microplane model to represent a vertex on the yield surface. The second example is the ‘tube-squash’ test of a highly ductile steel tube: a finite element computation is run using two microplane models and the J2-flow theory. One of the microplane models appears to predict more accurately the final shape of the deformed tube, showing an improvement compared to the J2-flow theory even when the material is not subjected to abrupt changes in the loading path direction. This review article includes 114 references.

scholarly journals A Rheological Model of Sandstones considering Response to Thermal Treatment

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Xingang Wang ◽  
Lei Huang ◽  
Junrong Zhang
Keyword(s):  
Thermal Treatment ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Energy Utilization ◽  
Elastic Response ◽  
Structure Damage ◽  
Rheological Response ◽  
Different Temperatures ◽  
Thermally Treated

Time-dependent rheological response of geomaterials to thermal treatment is a crucial issue in geothermal energy utilization and deep mineral mining. This response, however, has not yet been fully considered in the existing rheological constitutive models for sandstones. In order to experimentally investigate such responses and establish the associated rheological constitutive model, this study considers the sandstone specimens which have been thermally treated under different temperatures. The triaxial rheological test in conjunction with the scanning electron microscope is employed in the investigation to observe the mechanically and macro-/micromorphologically rheological response. Investigation results show that the thermal treatment induces microcracks and microdefects, and subsequently, they propagate during the creep. As a consequence, the heterogeneous deformation occurs, and macrocracks are present, leading to the irregular fluctuation and mutation in strain over time. A higher temperature contributes to a more severe structure damage and in turn reduces the intactness of sandstones and elevates the rheological response. The investigation allows successful establishment of a three-dimensional constitutive equation considering the instantaneous elastic response to thermal treatment. Based on the equation, a nonlinear visco-elastoplastic rheological constitutive model is developed for sandstones. Comparison with three existing rheological models shows that the model developed in this study could well represent the rheological process of the thermally treated sandstones.

Modeling of the impact of rigid ellipsoidal blocks by means of an elastic-visco-plastic constitutive model 

2021 ◽  
Author(s):  
Giuseppe Dattola ◽  
Giovanni Battista Crosta ◽  
Claudio Giulio di Prisco
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
Impact Angle ◽  
Material Point ◽  
Lumped Mass ◽  
Mountain Areas ◽  
Block Motion ◽  
The Impact ◽  
Constitutive Parameters

<p>Rockfall is one of the most common hazards in mountain areas causing severe damages to structures/infrastructures and, human lives. For this reason, numerous are the papers published in the last decades on this subject, both introducing reliable approaches to simulate the boulder trajectory and defining design methods for sheltering structures. As is well known, the most popular strategy to simulate the block trajectory and velocity is based on the lumped mass material point approach. This is capable of describing the block trajectory, before either its natural arrest or impact against an artificial/natural obstacle, by suitably considering its interaction with soil/rock materials, interaction always dynamic, very often highly dissipative and defined, according to its nature, as sliding, rolling or impact.</p><p>In this framework, this study focusses on impacts and, in particular, on the role of block geometry in affecting the block kinematic response. The problem is approached numerically; by modifying a previously conceived elastic-viscoplastic constitutive model, based on the macro-element concept. and capable of satisfactorily simulating impacts of spherical blocks.</p><p>The modified constitutive model relaxes the assumption of spherical block by assuming an ellipsoidal shape and by allowing for the boulder rotation. These two changes make the problem more complex but allow to model more realistically the impact. For the sake of simplicity, the results shown in this work consider the block motion to be planar, but the model already allows to include general three dimensional conditions.</p><p>In this work, the model is briefly outlined and the procedure for calibrating the model constitutive parameters described. Then, the results of an extensive parametric analysis, employing constitutive parameters calibrated on experimental data taken from the literature, are discussed. In particular, the role of (i) the inner block orientation, and (ii) the inner impact angle is considered in terms of both kinematic variables and restitution coefficients. Finally, interpolation functions to compute restitution coefficients, once both block shape and inner impact block orientation are known, are provided.</p>

Non-Coaxial Plasticity Constitutive Modeling of Sands

2013 ◽  
Vol 684 ◽  
pp. 150-153 ◽  
Author(s):  
Ping Hu ◽  
Mao Song Huang ◽  
Deng Gao Wu
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Principal Stress ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Strain Increment ◽  
Stress Axis ◽  
Shear Tests ◽  
Plastic Strain Increment ◽  
Principal Axes

Classical coaxial plasticity constitutive models implicate an inevitable limitation that directions for principal stress and that for principal plastic strain increment are always coaxial. They are not capable of simulating non-coaxial phenomena during the rotation of principal stress axis. In this paper, a three-dimensional, non-coaxial plasticity constitutive model for sands with a modification of Lade angle dependent shape function is introduced to describe the non-coaxial behavior under principal axes rotation. A series of numerical simulations of hollow cylindrical torsional shear tests are performed. The results show that the proposed constitutive model can predict the variations of principal plastic strain increment directions with principal stress directions reasonably.

Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity

1996 ◽  
Vol 69 (5) ◽  
pp. 781-785 ◽  
Author(s):  
Mary C. Boyce
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Rubber Elasticity ◽  
Elastic Materials ◽  
Material Constants ◽  
Salient Features

Abstract The Arruda and Boyce eight-chain network constitutive model for rubber elastic materials is compared to the new Gent constitutive model for rubber elasticity. The salient features of each of the two models are compared. The ability of both models to predict three dimensional large strain deformation is demonstrated showing the near equivalence of these two model constructions as well as their abilities to predict complex three-dimensional deformation with only two material constants.

scholarly journals An investigation of stress inaccuracies and proposed solution in the material point method

2019 ◽  
Vol 65 (2) ◽  
pp. 555-581 ◽  
Author(s):  
José Leόn González Acosta ◽  
Philip J. Vardon ◽  
Guido Remmerswaal ◽  
Michael A. Hicks
Keyword(s):  
Shape Function ◽  
Time Integration ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Implicit Time ◽  
Integration Scheme ◽  
Time Integration Scheme

AbstractStress inaccuracies (oscillations) are one of the main problems in the material point method (MPM), especially when advanced constitutive models are used. The origins of such oscillations are a combination of poor force and stiffness integration, stress recovery inaccuracies, and cell crossing problems. These are caused mainly by the use of shape function gradients and the use of material points for integration in MPM. The most common techniques developed to reduce stress oscillations consider adapting the shape function gradients so that they are continuous at the nodes. These techniques improve MPM, but problems remain, particularly in two and three dimensional cases. In this paper, the stress inaccuracies are investigated in detail, with particular reference to an implicit time integration scheme. Three modifications to MPM are implemented, and together these are able to remove almost all of the observed oscillations.

NUMERICAL SIMULATION OF HUMAN HEAD IMPACT USING THE MATERIAL POINT METHOD

2013 ◽  
Vol 10 (04) ◽  
pp. 1350014 ◽  
Author(s):  
SHUANGZHEN ZHOU ◽  
XIONG ZHANG ◽  
HONGLEI MA
Keyword(s):  
Constitutive Model ◽  
Brain Tissue ◽  
Three Dimensional ◽  
Material Point Method ◽  
Human Head ◽  
Material Point ◽  
Point Method ◽  
Skull Bone ◽  
Ball Impact ◽  
The Impact

In this paper, a three-dimensional material point human head model is constructed from the computed tomography (CT) scanned images of an adult male volunteer, and used to study the dynamic response of human head under the impact of a three-dimensional cylindrical lead projectile with a speed of 6.4 m/s. The model consists of skull bone, brain tissue and membrane of human head, which is close to the real one. The skull and membrane are modeled by an elastic constitutive model, and the brain tissue is modeled by an anisotropic viscoelastic constitutive model. These constitutive models have been implemented in our three-dimensional explicit material point method code, MPM3D, and is verified by comparing its numerical results for a ball impact problem with those obtained by LS-DYNA. The simulation results help illustrate the response of skull bone, membrane and brain tissues subjected to impact, which contributes to the understanding of the biomechanics and mechanisms of head injury.

Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus

2007 ◽  
Vol 129 (5) ◽  
pp. 632-641 ◽  
Author(s):  
Ferhun C. Caner ◽  
Zaoyang Guo ◽  
Brian Moran ◽  
Zdeněk P. Bažant ◽  
Ignacio Carol
Keyword(s):  
Experimental Data ◽  
Soft Tissue ◽  
Constitutive Model ◽  
Annulus Fibrosus ◽  
Constitutive Models ◽  
Coupling Model ◽  
Microplane Model ◽  
Composite Effect ◽  
Matrix Interaction ◽  
Fiber Matrix

In a recent paper, Peng et al. (2006, “An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis,” ASME J. Appl. Mech., 73(5), pp. 815–824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, “A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis,” J. Mech. Phys. Solids, 54(9), pp. 1952–1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, “Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue,” ASME J. Biomech. Eng., 128(3), pp. 419–427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.

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