A fabric tensor based small strain constitutive law for the elastoplastic behavior of snow

2021 ◽  
pp. 104182
Author(s):  
Anurag K. Singh ◽  
P.K. Srivastava ◽  
N. Kumar ◽  
P. Mahajan
Keyword(s):  
Small Strain ◽  
Constitutive Law ◽  
Fabric Tensor ◽  
Elastoplastic Behavior

A New Elasto-Plastic Critical State Model RU+MCC for Overconsolidated Soil

2016 ◽  
Vol 837 ◽  
pp. 68-74
Author(s):  
Rafal Uliniarz
Keyword(s):  
Critical State ◽  
Soil Mechanics ◽  
Small Strain ◽  
Computer Code ◽  
Constitutive Law ◽  
Isotropic Hardening ◽  
Loading Test ◽  
Modified Cam Clay ◽  
Soil Behaviour ◽  
Cam Clay

The paper presents a reasonably advanced constitutive law for soil – a hybrid of the Modified Cam Clay and a new RU development. The Modified Cam Clay model is an isotropic hardening elasto – plastic model originated by Burland in 1967 [1] within the critical state soil mechanics. This model describes realistically mechanical soil behaviour in normal consolidation states. The other one is designed to ensure more adequate soil responses to reloading paths, particularly in the range of small strains. The RU+MCC model has been implemented in the FEM computer code Z_SOIL.pc. To test the influence of the small strain nonlinearity on soil – structure interaction as well as to exhibit the ability of the proposed model to simulate realistically this effect, a comparative study based on the FEM solution has been carried out. As a benchmark a trial loading test of strip footing was used.

A Comprehensive Energy Formulation for General Nonlinear Material Continua

1997 ◽  
Vol 64 (2) ◽  
pp. 353-360 ◽  
Author(s):  
A. Carini ◽  
O. De Donato
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Strain ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Total Potential ◽  
Initial Boundary Value ◽  
Energy Formulation ◽  
The Continuum

By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.

On the Development of Creep Laws for Rubber in the Parallel Rheological Framework

2019 ◽  
Vol 47 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Gautam Sagar ◽  
Dong Zheng ◽  
Anuwat Suwannachit ◽  
Maik Brinkmeier ◽  
Kristin Fietz ◽  
...  
Keyword(s):  
Complex Modulus ◽  
Dynamic Stiffness ◽  
Viscoelastic Model ◽  
American Chemical Society ◽  
Small Strain ◽  
Chemical Society ◽  
Material Behavior ◽  
Constitutive Law ◽  
Rate Dependency ◽  
Linear Viscoelastic

ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

A Finite Element Study of Stable Crack-Growth in Superelastic Shape Memory Alloys

2012 ◽  
Author(s):  
Antonino Parrinello ◽  
Theocharis Baxevanis ◽  
Dimitris Lagoudas ◽  
Austin Cox
Keyword(s):  
Finite Element ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Crack Growth ◽  
Small Strain ◽  
Stable Crack Growth ◽  
Constitutive Law ◽  
Scale Transformation ◽  
Small Scale ◽  
Element Analysis

A finite-element analysis of stable crack growth in superelastic Shape Memory Alloys (SMAs) is carried out for plane strain, mode I loading. The small-scale transformation assumption is employed in the calculations using displacement boundary conditions on a circular region that encloses the stress-induced phase transformation zone. The constitutive law adopts the classical rate-independent small-strain flow theory for the evolution equation of the transformation strains. The crack is assumed to propagate quasi-statically with the energy release rate maintained at a critical value; the analysis is accomplished by means of the Virtual Crack Closure Technique (VCCT). Resistance curves, obtained for a range of thermomechanical parameters, show enhanced fracture toughness.

scholarly journals Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3667
Author(s):  
Yevgeniya Filanova ◽  
Johannes Hauptmann ◽  
Frank Längler ◽  
Konstantin Naumenko
Keyword(s):  
Experimental Data ◽  
Strain Rate ◽  
Axial Strain ◽  
Equivalent Stress ◽  
Small Strain ◽  
Composite Model ◽  
Constitutive Law ◽  
Flow Rule ◽  
Inelastic Behavior ◽  
Temperature Ranges

The aim of this paper is to present experimental data and the constitutive model for the inelastic behavior of polyoxymethylene in wide strain rate and temperature ranges. To capture the non-linearity of the stress responses for both loading and unloading regimes, the composite model of inelastic deformation is utilized and further developed. The equivalent inelastic strain rate is described by the Prandtl–Eyring law, while the temperature dependence is characterized by the modified Arrhenius-type law. Generalized equivalent stress and the flow rule are formulated to capture pressure sensitivity, transverse strain and volumetric strain responses. The results obtained by the constitutive law are compared with experimental data for stress vs. axial strain from standard tension tests as well as with axial and transverse strains measured by digital image correlation. The developed composite model is able to capture the non-linearity of stress–strain curves for complex loading paths within the small strain regime. For higher strains, apart from geometrically non-linear theory, evolution laws for the volume fraction of the constituents should be modified and calibrated. For the small strain regime, the inelastic dilatation is negligible. For higher axial strain values, a decrease in Poisson’s ratio under tension and increase in it under compression are observed. The Drucker–Prager-type equivalent stress and the developed flow rule provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules.

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Sensitive Mechanocontrolled Luminescence in Cross-Linked Polymer Films

2019 ◽  
Author(s):  
Ayumu Karimata ◽  
Pradnya Patil ◽  
Eugene Khaskin ◽  
Sébastien Lapointe ◽  
robert fayzullin ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Polymer Films ◽  
Soft Matter ◽  
Small Strain ◽  
Visual Methods ◽  
Photoluminescence Intensity ◽  
Stimuli Responsive ◽  
Responsive Materials ◽  
Highly Sensitive ◽  
Mechanical Stretching

Direct translation of mechanical force into changes in chemical behavior on a molecular level has important implication not only for the fundamental understanding of mechanochemical processes, but also for the development of new stimuli-responsive materials. In particular, detection of mechanical stress in polymers via non-destructive methods is important in order to prevent material failure and to study the mechanical properties of soft matter. Herein, we report that highly sensitive changes in photoluminescence intensity can be observed in response to the mechanical stretching of cross-linked polymer films when using stable, (pyridinophane)Cu-based dynamic mechanophores. Upon stretching, the luminescence intensity increases in a fast and reversible manner even at small strain (< 50%) and applied stress (< 0.1 MPa) values. Such sensitivity is unprecedented when compared to previously reported systems based on organic mechanophores. The system also allows for the detection of weak mechanical stress by spectroscopic measurements or by direct visual methods.<br>

Mathematical model to predict the characteristics of polarization in dielectric materials: The concept of piezoelectrcity and electrostriction

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Mathematical Model ◽  
Electric Field ◽  
Lead Zirconate Titanate ◽  
Dielectric Material ◽  
Strain Curve ◽  
Dielectric Materials ◽  
Lead Zirconate ◽  
Simulation Software ◽  
Constitutive Law ◽  
Basic Material

Model was developed for the prediction of polarization characteristics in a dielectric material exhibiting piezoelectricity and electrostriction based on mathematical equations and MATLAB computer simulation software. The model was developed based on equations of polarization and piezoelectric constitutive law and the functional coefficient of Lead Zirconate Titanate (PZT) crystal material used was 2.3×10-6 m (thickness), the model further allows the input of basic material and calculation of parameters of applied voltage levels, applied stress, pressure, dielectric material properties and so on, to generate the polarization curve, strain curve and the expected deformation change in the material length charts. The mathematical model revealed that an application of 5 volts across the terminals of a 2.3×10-6 m thick dielectric material (PZT) predicted a 1.95×10-9 m change in length of the material, which indicates piezoelectric properties. Both polarization and electric field curve as well as strain and voltage curve were also generated and the result revealed a linear proportionality of the compared parameters, indicating a resultant increase in the electric field yields higher polarization of the dielectric materials atmosphere.

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