scholarly journals Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5837
Author(s):  
Tomasz Janiak
Keyword(s):  
Numerical Methods ◽  
Constitutive Model ◽  
Matrix Models ◽  
Constitutive Models ◽  
Computer Software ◽  
Physical Nonlinearity ◽  
Analytical Models ◽  
Hyper Elastic ◽  
Properties Of Materials ◽  
Constitutive Matrix

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

A variable-order viscoelastic constitutive model under constant strain rate

2020 ◽  
Author(s):  
Yao Wang ◽  
Dagang Sun ◽  
Zhanlong Li ◽  
Yuan Qin ◽  
Bao Sun
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Fractional Order ◽  
Viscoelastic Material ◽  
Constitutive Models ◽  
Constant Strain Rate ◽  
Variable Order ◽  
Hyper Elastic ◽  
Material Coefficient ◽  
Viscoelastic Coefficient

The traditional viscoelastic constitutive models encounter the problems of massive parameters and ambiguous physical meanings. A new concept of variable-order viscoelastic constitutive (called VOVC) model is put forward based on the constant fractional-order constitutive model and the viscoelastic theory. The determination methods of the two parameters in the VOVC model, including the material coefficient and the viscoelastic coefficient, are discussed both in the tensile and the resilient processes. The comparisons are made between the VOVC model and the traditional constitutive models i.e. the constant fractional-order Kelvin-Voigt (CFKV) model, the Zhu-wang-tang nonlinear thermo-viscoelastic constitutive (ZWT) model and the Ogden nonlinear hyper-elastic (Ogden) model. The results show that the VOVC model with the constant material coefficient and the variable viscoelastic coefficient predicts the whole evolution of the constitutive behavior of the viscoelastic material under the constant strain rate more precisely. The constant material coefficient in the VOVC model means the stiffness of the viscoelastic material. The variable viscoelastic coefficient in the model means the distribution of the elasticity and viscosity. The VOVC model contains a simpler structure, fewer parameters, clearer physical meanings and higher precision.

scholarly journals Constitutive Models for the Tensile Behaviour of TRM Materials: Literature Review and Experimental Verification

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 700
Author(s):  
Maria Concetta Oddo ◽  
Giovanni Minafò ◽  
Lidia La Mendola
Keyword(s):  
State Of The Art ◽  
Constitutive Models ◽  
Stress Transfer ◽  
Theoretical Models ◽  
Tensile Tests ◽  
Analytical Models ◽  
Tensile Behaviour ◽  
Tensile Response ◽  
Textile Reinforced Mortar ◽  
Inorganic Matrix

In recent years, the scientific community has focused its interest on innovative inorganic matrix composite materials, namely TRM (Textile Reinforced Mortar). This class of materials satisfies the need of retrofitting existing masonry buildings, by keeping the compatibility with the substrate. Different recent studies were addressed to improve the knowledge on their mechanical behaviour and some theoretical models were proposed for predicting the tensile response of TRM strips. However, this task is complex due to the heterogeneity of the constituent materials and the stress transfer mechanism developed between matrix and fabric through the interface in the cracked stage. This paper presents a state-of-the-art review on the existing constitutive models for the tensile behavior of TRM composites. Literature experimental results of tensile tests on TRM coupons are presented and compared with the most relevant analytical models proposed until now. Finally, a new experimental study is presented and its results are used to further verify the reliability of the literature expressions.

scholarly journals Calibration of Finn Model and UBCSAND Model for Simplified Liquefaction Analysis Procedures

2021 ◽  
Vol 11 (11) ◽  
pp. 5283
Author(s):  
Jui-Ching Chou ◽  
Hsueh-Tusng Yang ◽  
Der-Guey Lin
Keyword(s):  
Numerical Simulation ◽  
Constitutive Model ◽  
Structural Damage ◽  
Simulation Analysis ◽  
Constitutive Models ◽  
Soil Liquefaction ◽  
Analysis Procedure ◽  
Liquefaction Resistance ◽  
Simplified Procedure ◽  
Liquefaction Analysis

Soil-liquefaction-related hazards can damage structures or lead to an extensive loss of life and property. Therefore, the stability and safety of structures against soil liquefaction are essential for evaluation in earthquake design. In practice, the simplified liquefaction analysis procedure associated with numerical simulation analysis is the most used approach for evaluating the behavior of structures or the effectiveness of mitigation plans. First, the occurrence of soil liquefaction is evaluated using the simplified procedure. If soil liquefaction occurs, the resulting structural damage or the following mitigation plan is evaluated using the numerical simulation analysis. Rational and comparable evaluation results between the simplified liquefaction analysis procedure and the numerical simulation analysis are achieved by ensuring that the liquefaction constitutive model used in the numerical simulation has a consistent liquefaction resistance with the simplified liquefaction analysis procedure. In this study, two frequently used liquefaction constitutive models (Finn model and UBCSAND model) were calibrated by fitting the liquefaction triggering curves of most used simplified liquefaction analysis procedures (NCEER, HBF, JRA96, and T-Y procedures) in Taiwan via FLAC program. In addition, the responses of two calibrated models were compared and discussed to provide guidelines for selecting an appropriate liquefaction constitutive model in future projects.

Constitutive Modeling for Flow Stress Behavior of Nimonic 80A Superalloy During Hot Deformation Process

2016 ◽  
Vol 35 (3) ◽  
pp. 327-336 ◽  
Author(s):  
Sendong Gu ◽  
Liwen Zhang ◽  
Chi Zhang ◽  
Wenfei Shen
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Hot Deformation ◽  
Critical Strain ◽  
Volume Fraction ◽  
Constitutive Models ◽  
Avrami Equation ◽  
Peak Strain ◽  
Compression Tests ◽  
Nimonic 80A

AbstractThe hot deformation characteristics of nickel-based alloy Nimonic 80A were investigated by isothermal compression tests conducted in the temperature range of 1,000–1,200°C and the strain rate range of 0.01—5 s–1on a Gleeble-1500 thermomechanical simulator. In order to establish the constitutive models for dynamic recrystallization (DRX) behavior and flow stress of Nimonic 80A, the material constantsα,nand DRX activation energyQin the constitutive models were calculated by the regression analysis of the experimental data. The dependences of initial stress, saturation stress, steady-state stress, dynamic recovery (DRV) parameter, peak strain, critical strain and DRX grain size on deformation parameters were obtained. Then, the Avrami equation including the critical strain for DRX and the peak strain as a function of strain was established to describe the DRX volume fraction. Finally, the constitutive model for flow stress of Nimonic 80A was developed in DRV region and DRX region, respectively. The flow stress values predicted by the constitutive model are in good agreement with the experimental ones, which indicates that the constitutive model can give an accurate estimate for the flow stress of Nimonic 80A under the deformation conditions.

scholarly journals Simultaneous Characterization of Relaxation, Creep, Dissipation, and Hysteresis by Fractional-Order Constitutive Models

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Jun-Sheng Duan ◽  
Di-Chen Hu ◽  
Yang-Quan Chen
Keyword(s):  
Constitutive Model ◽  
Storage Modulus ◽  
Loss Factor ◽  
Creep Compliance ◽  
Loss Modulus ◽  
Constitutive Models ◽  
Stationary Points ◽  
Logarithmic Scale ◽  
Zener Model ◽  
Fractional Zener Model

We considered relaxation, creep, dissipation, and hysteresis resulting from a six-parameter fractional constitutive model and its particular cases. The storage modulus, loss modulus, and loss factor, as well as their characteristics based on the thermodynamic requirements, were investigated. It was proved that for the fractional Maxwell model, the storage modulus increases monotonically, while the loss modulus has symmetrical peaks for its curve against the logarithmic scale log(ω), and for the fractional Zener model, the storage modulus monotonically increases while the loss modulus and the loss factor have symmetrical peaks for their curves against the logarithmic scale log(ω). The peak values and corresponding stationary points were analytically given. The relaxation modulus and the creep compliance for the six-parameter fractional constitutive model were given in terms of the Mittag–Leffler functions. Finally, the stress–strain hysteresis loops were simulated by making use of the derived creep compliance for the fractional Zener model. These results show that the fractional constitutive models could characterize the relaxation, creep, dissipation, and hysteresis phenomena of viscoelastic bodies, and fractional orders α and β could be used to model real-world physical properties well.

A Generalized Elasto-Plastic Micro-Polar Constitutive Model

2015 ◽  
Vol 798 ◽  
pp. 505-509 ◽  
Author(s):  
Lapo Gori ◽  
Roque Luiz da Silva Pitangueira ◽  
Samuel Silva Penna ◽  
Jamile Salim Fuina
Keyword(s):  
Structural Analysis ◽  
Constitutive Model ◽  
Numerical Method ◽  
Strain Localization ◽  
Continuum Model ◽  
Constitutive Models ◽  
Localization Problem ◽  
Polar Model ◽  
Basic Characteristics ◽  
Analysis Environment

This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.

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 Constitutive Model for Concrete: An Overview

2015 ◽  
Vol 10 (Special-Issue1) ◽  
pp. 782-788 ◽  
Author(s):  
Mehdi Shekarbeigi ◽  
Hasan Sharafi
Keyword(s):  
Constitutive Model ◽  
Damage Mechanics ◽  
Constitutive Models ◽  
Continuum Damage Mechanics ◽  
Constitutive Modelling ◽  
Continuum Damage ◽  
Endochronic Theory ◽  
Small Deformations

In the last three decades, the constitutive modelling of concrete evolved considerably. This paper describes various developments in this field based on different approaches such anelasticity, plasticity, continuum damage mechanics, plastic fracturing, endochronic theory, microplane models, etc. In this article the material is assumed to undergo small deformations. Only time independent constitutive models and the issues related to their implementation are discussed

scholarly journals Identification of orthotropic material parameters for acute, necrotic, fibrotic and remodelling myocardial infarcts in the rat

2019 ◽  
Author(s):  
Mazin S. Sirry ◽  
Laura Dubuis ◽  
Neil H. Davies ◽  
Jun Liao ◽  
Thomas Franz
Keyword(s):  
Constitutive Model ◽  
Orthotropic Material ◽  
Constitutive Models ◽  
Biaxial Stress ◽  
Percentage Error ◽  
Fe Model ◽  
Stress Strain ◽  
Material Parameters ◽  
Strain Data ◽  
Tensile Experiment

AbstractFinite element (FE) models have been effectively utilized in studying biomechanical aspects of myocardial infarction (MI). Although the rat is a widely used animal model for MI, there is a lack of material parameters based on anisotropic constitutive models for rat myocardial infarcts in literature. This study aimed at employing inverse methods to identify the parameters of an orthotropic constitutive model for myocardial infarcts in the acute, necrotic, fibrotic and remodelling phases utilizing the biaxial mechanical data developed in a previous study. FE model was developed mimicking the setup of the biaxial tensile experiment. The orthotropic case of the generalized Fung constitutive model was utilized to model the material properties of the infarct. The parameters of Fung model were optimized so that the FE solution best fitted the biaxial experimental stress-strain data. A genetic algorithm was used to minimize the objective function. Fung orthotropic material parameters for different infarct stages were identified. The FE model predictions best approximated the experimental data of the 28 days infarct stage with 3.0% mean absolute percentage error. The worst approximation was for the 7 days stage with 3.6% error. This study demonstrated that the experimental biaxial stress-strain data of healing rat infarcts could be successfully approximated using inverse FE methods and genetic algorithms. The material parameters identified in this study will provide an essential platform for FE investigations of biomechanical aspects of MI and the development of therapies.

Experimental and Numerical Study of Soft Tissue Surrogate Behavior Under Ballistic Loading

2012 ◽  
Author(s):  
Ericka K. Amborn ◽  
Karim H. Muci-Küchler ◽  
Brandon J. Hinz
Keyword(s):  
Soft Tissue ◽  
Constitutive Model ◽  
High Strain Rate ◽  
Strain Rate ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Numerical Study ◽  
Constitutive Models ◽  
Material Behavior ◽  
Good Representation

Studying the high strain rate behavior of soft tissues and soft tissue surrogates is of interest to improve the understanding of injury mechanisms during blast and impact events. Tests such as the split Hopkinson pressure bar have been successfully used to characterize material behavior at high strain rates under simple loading conditions. However, experiments involving more complex stress states are needed for the validation of constitutive models and numerical simulation techniques for fast transient events. In particular, for the case of ballistic injuries, controlled tests that can better reflect the effects induced by a penetrating projectile are of interest. This paper presents an experiment that tries to achieve that goal. The experimental setup involves a cylindrical test sample made of a translucent soft tissue surrogate that has a small pre-made cylindrical channel along its axis. A small caliber projectile is fired through the pre-made channel at representative speeds using an air rifle. High speed video is used in conjunction with specialized software to generate data for model validation. A Lagrangian Finite Element Method (FEM) model was prepared in ABAQUS/Explicit to simulate the experiments. Different hyperelastic constitutive models were explored to represent the behavior of the soft tissue surrogate and the required material properties were obtained from high strain rate test data reported in the open literature. The simulation results corresponding to each constitutive model considered were qualitatively compared against the experimental data for a single projectile speed. The constitutive model that provided the closest match was then used to perform an additional simulation at a different projectile velocity and quantitative comparisons between numerical and experimental results were made. The comparisons showed that the Marlow hyperelastic model available in ABAQUS/Explicit was able to produce a good representation of the soft tissue surrogate behavior observed experimentally at the two projectile speeds considered.

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