Compressibility, Damage, and Age-Hardening Effects of Solid Propellants Using Finite Strain Constitutive Model

In this paper, the finite strain viscoelastic constitutive model for particulate composite solid propellants is proposed considering strain rate, large deformation/large strain, thermorheological behavior, stress softening due to microstructural damage, compressibility, and chemical age hardening. The compressible Mooney–Rivlin hyperelastic strain energy density function is used along with the standard model of viscoelasticity. To model the compressibility, the dilatational strain energy is taken as the hyperbolic function of the determinant of deformation gradient. The stress-softening phenomenon during cyclic loading (Mullin's effect) due to microstructural damage is described by an exponential function of the current magnitude of intensity of strain and its previous maximum value. The variation of material properties with time are studied using the isothermal accelerated aging technique through simulation and experimental investigation. The comparison of predictions based on the proposed model with the uniaxial experimental data demonstrates that the proposed model successfully captures the observed behavior of the solid propellants.

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A Directional Damage Constitutive Model for Stress-Softening in Solid Propellant

Volume 12: Mechanics of Solids, Structures, and Fluids ◽

10.1115/imece2020-24285 ◽

2020 ◽

Author(s):

Yang Chen ◽

Vahid Morovati ◽

Roozbeh Dargazany

Keyword(s):

Constitutive Model ◽

Mechanical Model ◽

Solid Propellant ◽

Network Evolution ◽

Elastic Behavior ◽

Plastic Behavior ◽

Solid Propellants ◽

Softening Effect ◽

Stress Softening ◽

Highly Nonlinear

Abstract Solid propellants are particulate composite with a light cross-linked elastomeric binder filled with a high concentration of energetic, solid aggregates. Solid propellants are often considered as highly nonlinear elastomeric materials, with elastic behavior resulted from its binder and plastic behavior from its energetic particles. The study of the micro-structure and mechanical properties of solid propellant is crucial for its design, safety evaluation, and lifetime prediction of solid fuel carriers. The constitutive model proposed for rubber-like material can often be generalized to predict the nonlinear behavior of solid propellant due to the dependency on the mechanical behavior of solid propellant on its elastomeric binder material. This paper focuses on developing a model that predicts the stress softening and strain-residual mechanism of the solid propellant. This micro-mechanical model for solid propellant was proposed based on the network evolution theory. The motivation of this study is the lack of a micro-mechanical model that can describe both the stress softening effect and strain residual in the quasi-static behavior of propellants. The simplified network-evolution model with only five parameters is a simple micro-mechanical model that captures both the stress softening effect and strain residual. Besides the simplicity and reduced fitting procedure, the model was validated against several experimental data and illustrated good agreement in small and large deformations, making the proposed model a suitable option for commercial and other applications.

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Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient

Theoretical and Applied Mechanics ◽

10.2298/tam0229379v ◽

2002 ◽

pp. 379-399 ◽

Cited By ~ 33

Author(s):

L. Vujosevic ◽

V.A. Lubarda

Keyword(s):

Free Energy ◽

Elastic Strain ◽

Strain Energy ◽

Finite Strain ◽

Helmholtz Free Energy ◽

Deformation Gradient ◽

Elastic Strain Energy ◽

Multiplicative Decomposition ◽

Latent Heats ◽

Constitutive Formulation

The constitutive formulation of the finite-strain thermoelasticity is revisited within the thermodynamic framework and the multiplicative decomposition of the deformation gradient into its elastic and thermal parts. An appealing structure of the Helmholtz free energy is proposed. The corresponding stress response and the entropy expressions are derived. The results are specified in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. The specific and latent heats are discussed, and the comparison with the results of the classical thermoelasticity are given. .

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A Novel Damage Model for Strata Layers and Coal Mass

Energies ◽

10.3390/en13081928 ◽

2020 ◽

Vol 13 (8) ◽

pp. 1928 ◽

Cited By ~ 2

Author(s):

Faham Tahmasebinia ◽

Chengguo Zhang ◽

Ismet Canbulat ◽

Samad Sepasgozar ◽

Serkan Saydam

Keyword(s):

Constitutive Model ◽

Strain Energy ◽

Damage Model ◽

Rock Joint ◽

Coal Mass ◽

Stored Energy ◽

Rock Interaction ◽

Geological Factors ◽

Coal Rock ◽

Joint Quality

Coal burst occurrences are affected by a range of mining and geological factors. Excessive slipping between the strata layers may release a considerable amount of strain energy, which can be destructive. A competent strata is also more vulnerable to riveting a large amount of strain energy. If the stored energy in the rigid roof reaches a certain level, it will be released suddenly which can create a serious dynamic reaction leading to coal burst incidents. In this paper, a new damage model based on the modified thermomechanical continuum constitutive model in coal mass and the contact layers between the rock and coal mass is proposed. The original continuum constitutive model was initially developed for the cemented granular materials. The application of the modified continuum constitutive model is the key aspect to understand the momentum energy between the coal–rock interactions. The transformed energy between the coal mass and different strata layers will be analytically demonstrated as a function of the rock/joint quality interaction conditions. The failure and post failure in the coal mass and coal–rock joint interaction will be classified by the coal mass crushing, coal–rock interaction damage and fragment reorganisation. The outcomes of this paper will help to forecast the possibility of the coal burst occurrence based on the interaction between the coal mass and the strata layers in a coal mine.

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

Polymers ◽

10.3390/polym13091393 ◽

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.

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Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01475-0 ◽

2021 ◽

Vol 72 (2) ◽

Author(s):

Mircea Bîrsan

Keyword(s):

Energy Density ◽

Constitutive Model ◽

Strain Energy Density ◽

Strain Energy ◽

Shell Theory ◽

Constitutive Relations ◽

Three Dimensional ◽

Classical Shell Theory ◽

Three Dimensional Elasticity ◽

General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability

Journal of Biomechanics ◽

10.1016/s0021-9290(99)00201-8 ◽

2000 ◽

Vol 33 (4) ◽

pp. 475-482 ◽

Cited By ~ 380

Author(s):

M.L. Raghavan ◽

David A. Vorp

Keyword(s):

Abdominal Aortic Aneurysm ◽

Aortic Aneurysm ◽

Constitutive Model ◽

Finite Strain ◽

Abdominal Aortic

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The Constitutive Model for High Temperature Flow Behavior of SiC/6168Al Composite

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1089.37 ◽

2015 ◽

Vol 1089 ◽

pp. 37-41

Author(s):

Jiang Wang ◽

Sheng Li Guo ◽

Sheng Pu Liu ◽

Cheng Liu ◽

Qi Fei Zheng

Keyword(s):

Constitutive Model ◽

Hot Deformation ◽

Flow Behavior ◽

Type Equation ◽

Strain Rate Range ◽

Compression Tests ◽

Stress Strain ◽

Hollomon Parameter ◽

Proposed Model ◽

Relationship Of

The hot deformation behavior of SiC/6168Al composite was studied by means of hot compression tests in the temperature range of 300-450 °C and strain rate range of 0.01-10 s-1. The constitutive model was developed to predict the stress-strain curves of this composite during hot deformation. This model was established by considering the effect of the strain on material constants calculated by using the Zenter-Hollomon parameter in the hyperbolic Arrhenius-type equation. It was found that the relationship of n, α, Q, lnA and ε could be expressed by a five-order polynomial. The stress-strain curves obtained by this model showed a good agreement with experimental results. The proposed model can accurately describe the hot flow behavior of SiC/6168Al composite, and can be used to numerically analyze the hot forming processes.

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Modeling of Shear Rheological Behavior of Uncured Rubber Melt

Applied Rheology ◽

10.1515/arh-2020-0111 ◽

2020 ◽

Vol 30 (1) ◽

pp. 130-137

Author(s):

Hengxiao Yang ◽

Qimian Mo ◽

Hengyu Lu ◽

Shixun Zhang ◽

Wei Cao ◽

...

Keyword(s):

Shear Rate ◽

Constitutive Model ◽

Incompressible Fluid ◽

Rheological Behavior ◽

Rheological Characteristics ◽

One Dimensional ◽

Ptt Model ◽

Rate Region ◽

Proposed Model ◽

Rheological Experiments

AbstractTo describe uncured rubber melt flow, a modified Phan–Thien–Tanner (PTT) model was proposed to characterize the rheological behavior and a viscoelastic one-dimensional flow theory was established in terms of incompressible fluid. The corresponding numerical method was constructed to determine the solution. Rotational rheological experiments were conducted to validate the proposed model. The influence of the parameters in the constitutive model was investigated by comparing the calculated and experimental viscosity to determine the most suitable parameters. The uncured rubber viscosity was 3–4 orders larger than that of plastic and did not have a visible Newtonian region. Compared with the Cross-Williams-Landel-Ferry (Cross-WLF) and original PTT models, the modified PTT model can describe the rheological characteristics in the entire shear-rate region if the parameters are set correctly.

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Study on the generalized k-Hilfer–Prabhakar fractional viscoelastic–plastic model

Mathematics and Mechanics of Solids ◽

10.1177/10812865211025813 ◽

2021 ◽

pp. 108128652110258

Author(s):

Yi-Ying Feng ◽

Xiao-Jun Yang ◽

Jian-Gen Liu ◽

Zhan-Qing Chen

Keyword(s):

Constitutive Model ◽

Three Dimensional ◽

Sensitivity Analyses ◽

Creep Process ◽

Fractional Operator ◽

Modified Model ◽

Proposed Model ◽

Accelerated Creep ◽

The Laplace Transform ◽

Classical Models

The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic–plastic constitutive model with the sense of the k-Hilfer–Prabhakar ( k-H-P) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element [Formula: see text] is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order [Formula: see text] and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.

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