A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

2021 ◽  
pp. 1-32
Author(s):  
Ankit Agarwal ◽  
Marcial Gonzalez
Keyword(s):  
Constitutive Model ◽  
Yield Surface ◽  
Finite Deformation ◽  
Large Strain ◽  
Elastic Response ◽  
Rate Equations ◽  
Internal Variables ◽  
Model Parameters ◽  
Stress Strain ◽  
Stress Softening

Abstract We present a constitutive model for particle-binder composites that accounts for finite-deformation kinematics, nonlinear elasto-plasticity without apparent yield, cyclic hysteresis, and progressive stress-softening before the attainment of stable cyclic response. The model is based on deformation mechanisms experimentally observed during quasi-static monotonic and cyclic compression of mock Plastic-Bonded Explosives (PBX) at large strain. An additive decomposition of strain energy into elastic and inelastic parts is assumed, where the elastic response is modeled using Ogden hyperelasticity while the inelastic response is described using yield-surface-free endochronic plasticity based on the concepts of internal variables and of evolution or rate equations. Stress-softening is modeled using two approaches; a discontinuous isotropic damage model to appropriately describe the softening in the overall loading-unloading response, and a material scale function to describe the progressive cyclic softening until cyclic stabilization. A nonlinear multivariate optimization procedure is developed to estimate the elasto-plastic model parameters from nominal stress-strain experimental compression data. Finally, a correlation between model parameters and the unique stress-strain response of mock PBX specimens with differing concentrations of aluminum is identified, thus establishing a relationship between model parameters and material composition.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

Protein Forced Unfolding and Its Effects on the Finite Deformation Stress-Strain Behavior of Biomacromolecular Solids

2005 ◽  
Vol 874 ◽  
Author(s):  
H. Jerry Qi ◽  
Christine Ortiz ◽  
Mary C. Boyce
Keyword(s):  
Constitutive Model ◽  
Single Molecule ◽  
Biological Networks ◽  
Finite Deformation ◽  
State Theory ◽  
Force Extension ◽  
Stress Strain ◽  
Strain Behavior ◽  
Mechanics Model ◽  
Deformation Stress

AbstractMany proteins have been experimentally observed to exhibit a force-extension behavior with a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak (a “saw-tooth” profile) due to successive unfolding of modules during extension. This behavior is speculated to play a governing role in biological and mechanical functions of natural materials and biological networks composed of assemblies of such protein molecules. In this paper, a constitutive model for the finite deformation stress-strain behavior of crosslinked networks of modular macromolecules is developed. The force-extension behavior of the individual modular macromolecule is represented using the Freely Jointed Chain (FJC) statistical mechanics model together with a two-state theory to capture unfolding. The single molecule behavior is then incorporated into a formal continuum mechanics framework to construct a constitutive model. Simulations illustrate a relatively smooth “yield”-like stress-strain behavior of these materials due to activate unfolding in these microstructures.

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.

The Studies of Rock Damage Softening Statistical Constitutive Model under True Triaxial Stress State

2014 ◽  
Vol 580-583 ◽  
pp. 312-315
Author(s):  
Hui Mei Zhang ◽  
Xiang Miao Xie ◽  
Geng She Yang
Keyword(s):  
Constitutive Model ◽  
Strain Curve ◽  
Stress Path ◽  
Complex Stress ◽  
Model Parameters ◽  
Stress Strain ◽  
Deformation And Failure ◽  
True Triaxial ◽  
Complex Stress Path ◽  
The Impact

From the feature of rock micro-unit failure obeys Poisson random distribution, the damage softening statistical constitutive of was established under true triaxial confinement based on D-P criterion, so the impact of the intermediate principal stress on rock deformation and failure was considered in theory, and the actual engineering rock complex stress path evolution was reflected more realistically. Furthermore, according to the geometrical conditions of stress-strain relationship, the theoretical relationship between constitutive model parameters and the stress-strain curve characteristic parameters during the process of rock softening and deforming, which enhance the adaptability of the model. Finally, the rationality of the model verified by the measured data.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

scholarly journals A Constitutive Model of Clay Considering Structural Failure

2021 ◽  
Vol 8 ◽  
Author(s):  
Biaohe Zhou ◽  
Bin Tang ◽  
Jiashuai Kang
Keyword(s):  
Constitutive Model ◽  
Yield Stress ◽  
Failure Process ◽  
Strength Distribution ◽  
Model Parameters ◽  
Structural Failure ◽  
Stress Strain ◽  
Softening Effect ◽  
Undisturbed Soil ◽  
Confining Pressures

Due to the different material composition and deposition conditions, the undisturbed clay presents different degree of structure. Because of the existence of structure, the undisturbed clay has structural yield stress. When the stress level exceeds the structural yield stress, the stress-strain relation of undisturbed clay has typical softening characteristics. To explore the constitutive relation of undisturbed soil, triaxial consolidation, and drainage tests were carried out on undisturbed and remolded soils of structural clay in Zhanjiang Formation in China, and the stress-strain relations under different confining pressures were obtained. By analyzing the structural failure process of undisturbed clay, Weibull distribution was introduced to describe the strength distribution of each point in undisturbed clay, and the structural failure coefficient of undisturbed clay was established during the loading process. Based on the elastic theory and structural failure coefficient, a constitutive model considering the structural failure of clay was proposed, and the method to determine the model parameters was given. The model was used to simulate the experimental data in this paper and the reference, and the validity of the model was verified. The results show that the model can well simulate the softening effect of structural clay during loading.

Study of magnetomechanical non-linear deformation of ferromagnetic materials: Theory and experiment

2004 ◽  
Vol 218 (12) ◽  
pp. 1405-1410 ◽  
Author(s):  
D N Fang ◽  
X Feng ◽  
K C Hwang
Keyword(s):  
Magnetic Field ◽  
Constitutive Model ◽  
Yield Surface ◽  
Remanent Magnetization ◽  
General Structure ◽  
Ferromagnetic Materials ◽  
Internal Variables ◽  
Linear Deformation ◽  
Soft Ferromagnetic ◽  
Non Linear

A robust constitutive model is desirable in order to guide the processing and development of ferromagnetism and for use in the design of ferromagnetic devices. In this paper, a non-linear constitutive model of soft ferromagnets is developed for general magnetomechanical loading histories. The experimental set-up and measured techniques, which were employed to measure the non-linear deformation of both the magnetostrictive materials and the soft ferromagnetic materials subjected to coupled magnetomechanical loading, are introduced. The general structure for the constitutive behaviour of ferromagnets including soft-ferromagnetic and hard-ferromagnetic materials is similar to the classical models of metal plasticity; i.e. a convex yield surface can be identified in a stress-magnetic field space, within which the deformation and magnetization are reversible, and increments of both remanent magnetization and remanent strains are normal to the yield surface. The state of materials is described in terms of the remanent strain and the remanent magnetization that are introduced as internal variables besides stress, strain, magnetic field and magnetization. The one-dimensional model is examined by numerical stimulations and the response of the ferromagnetic materials is discussed in comparison with the measured results. The macroscopic features of ferromagnets, such as hysteresis loop and magnetostrictive hysteresis, are predicted.

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