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Showing papers on "Constitutive equation published in 2021"


Journal ArticleDOI
TL;DR: In this article, the authors propose a new class of data-driven, physics-based, neural networks for constitutive modeling of strain rate independent processes at the material point level, which they define as Thermodynamics-based Artificial Neural Networks (TANNs).
Abstract: Machine Learning methods and, in particular, Artificial Neural Networks (ANNs) have demonstrated promising capabilities in material constitutive modeling. One of the main drawbacks of such approaches is the lack of a rigorous frame based on the laws of physics. This may render physically inconsistent the predictions of a trained network, which can be even dangerous for real applications. Here we propose a new class of data-driven, physics-based, neural networks for constitutive modeling of strain rate independent processes at the material point level, which we define as Thermodynamics-based Artificial Neural Networks (TANNs). The two basic principles of thermodynamics are encoded in the network's architecture by taking advantage of automatic differentiation to compute the numerical derivatives of a network with respect to its inputs. In this way, derivatives of the free-energy, the dissipation rate and their relation with the stress and internal state variables are hardwired in the architecture of TANNs. Consequently, our approach does not have to identify the underlying pattern of thermodynamic laws during training, reducing the need of large datasets. Moreover the training is more efficient and robust, and the predictions more accurate. Finally and more important, the predictions remain thermodynamically consistent, even for unseen data. Based on these features, TANNs are a starting point for data-driven, physics-based constitutive modeling with neural networks. We demonstrate the wide applicability of TANNs for modeling elasto-plastic materials, using both hyper-and hypo-plasticity models. Strain hardening and softening are also considered for the hyper-plastic scenario. Detailed comparisons show that the predictions of TANNs outperform those of standard ANNs. Finally, we demonstrate that the implementation of the laws of thermodynamics confers to TANNs high degrees of robustness to the presence of noise in the training data, compared to standard approaches. TANNs ' architecture is general, enabling applications to materials with different or more complex behavior, without any modification.

147 citations


Journal ArticleDOI
TL;DR: In this paper, a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible hard magnetorheological elastomers (h-MREs) is provided.
Abstract: Hard magnetorheological elastomers ( h -MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h -MREs. Energy dissipates in such hard-magnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto–mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto–mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h -MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h -MREs in terms of their pre-magnetization and the associated self-fields.

56 citations


Journal ArticleDOI
TL;DR: In this paper, a microstructurally-motivated finite strain model is proposed to better understand the magneto-mechanical responses of MAPs and guide their design and manufacturing processes.

53 citations


Journal ArticleDOI
TL;DR: In this article, the nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the non-local modified gradient theory of elasticity, and an equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced.
Abstract: The nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the nonlocal modified gradient theory of elasticity. The equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced. The size-dependent effects of the dilatation gradient, deviatoric stretch gradient, and symmetric rotation gradient in addition to the nonlocality are beneficially captured in the flexure problem of nano-beams. The well posedness of the proposed nonlocal modified gradient problem is demonstrated via analytical examination of the elastostatic flexure and the wave dispersion phenomenon in nano-beams. The dispersive behavior of flexural waves is verified in comparison with the molecular dynamics simulation. The dominant stiffening effect of the gradient characteristic parameters associated with the nonlocal modified gradient elasticity is confirmed. Both the stiffening and softening responses of nano-structured materials are effectively realized in the framework of the introduced augmented elasticity theory. The conceived nonlocal modified gradient elasticity theory can accordingly provide a practical approach for nanoscopic study of the field quantities.

48 citations


Journal ArticleDOI
TL;DR: In this article, a three-dimensional constitutive model for shape memory alloys considering the TRsformation-Induced Plasticity (TRIP) as well as the Two-Way Shape Memory Effect (TWSME) through a large deformation framework is presented.

47 citations


Journal ArticleDOI
TL;DR: In this article, a piecewise constitutive model based on the characteristics of compaction and post-compaction stages of the stress-strain curve was proposed using a statistical compaction model in combination with the conventional statistical damage mechanics model with the strain equivalence hypothesis.

46 citations


Journal ArticleDOI
TL;DR: In this article, an artificial neural network (ANN) was constructed to replace the nonlinear stress-integration scheme conducted in the conventional theoretical constitutive model under isotropic hardening and associated flow rule.

44 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the incompressible hydromagnetic flow of Maxwell nanofluid and obtained the dimensionalized form of flow equations by elaborating appropriate similarity functions using Runge-Kutta-Fehlberg (RKF) shooting technique.

38 citations


Journal ArticleDOI
TL;DR: In this paper, both of the conventional and improved Arrhenius constitutive equations were developed to predict the flow characteristics, and the 3D activation energy maps were constructed to propose the optimal deformation conditions and reveal the effects of deformation parameters on microstructure evolution.

38 citations


Journal ArticleDOI
TL;DR: In this article, the wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) with regard to the influences of small scale in the context of the so-called nonlocal strain gradient theory (NSGT) of elasticity are investigated.
Abstract: Present manuscript undergoes with the investigation of the wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) with regard to the influences of small scale in the context of the so-called nonlocal strain gradient theory (NSGT) of elasticity. The under observation continuous system, i.e. a thin-type one, is modeled via the Kirchhoff-Love theorem incorporated with the dynamic form of the principle of virtual work considering the impacts of both thermal and viscose losses on the dispersion characteristics of the nanostructure. Once the modified size-dependent constitutive equations are inserted into the motion equations, the final governing equations of the problem are attained. Thereafter, an analytical dispersion solution will be employed for the purpose of solving the dynamic problem to extract the wave response of the system. In order to examine the accuracy of the presented results, the natural frequencies obtained from this methodology are compared with those reported in the open literature. According to the presented illustrations, it can be declared that the magnetostriction can affect the dispersion responses of the smart nanoplate in low wave numbers.

35 citations


Journal ArticleDOI
TL;DR: In this article, a physics-driven machine learning (PD-ML) algorithm is proposed to map the temperature, stress and rate-dependent deformation in Li-metal anode.
Abstract: Precise understanding on the temperature and time-dependent deformation in lithium-metal anode is of compelling need for durable service of Li-based batteries. Due to both temporal and spatial intertwined thermal agitations and the scarcity of experiments, faithful deformation map of Li-metal covering a broad range of service condition is still lacking. Here we design a physics-driven machine learning (PD-ML) algorithm to map the temperature, stress and rate-dependent deformation in Li-metal. We demonstrate that the PD-ML model, fed with limited experimental results, can predict the mechanical response of Li-metal in a wide span of temperature and deformation rate, and help to realize a deformation map of Li-metal with high fidelity. A finite element (FE) procedure based on the PD-ML constitutive model is then developed. The integration of PD-ML with FE procedure inherits the power of FE analysis and the accuracy originated from PD-ML in describing temperature, stress and rate-dependent mechanical response of Li-metal. The method introduced here paves a new way for constitutive modelling to capture the complex deformation in solids involving multi-field and multiscale mechanics.

Journal ArticleDOI
TL;DR: In this paper, a dislocation density-based constitutive model, which considers geometrically necessary dislocations (GNDs) and the back stress induced by internal heterogeneous deformation, is developed for describing the deformation of hetero-structured laminate materials.

Journal ArticleDOI
TL;DR: Comparisons of various models used in finite element analysis to assess the structural performance of composite materials will allow comparing various models for their capabilities and application domains for researchers and industry practitioners developing components using composite materials.

Journal ArticleDOI
TL;DR: Various research works demonstrate that the I-integral is a most accurate and reliable approach to extracting the individual SIFs and T-stress for the materials obeying linear constitutive law or the materials with limited nonlinear effect.

Journal ArticleDOI
TL;DR: An analytical method for the linear vibrations and buckling of nano-plates in a hygro-thermal environment is presented in this article, where nonlinear von Karman terms are included in the plate kinematics in order to consider the instability phenomena.
Abstract: An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Karman terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

Journal ArticleDOI
TL;DR: In this article, a new analytical solution for deep circular tunnels in rock with consideration of disturbed zone, 3D strength and large strain is presented, where the rock is assumed to be elastic-brittle-plastic and governed by a 3D Hoek-Brown yield criterion.
Abstract: This paper presents a new analytical solution for deep circular tunnels in rock with consideration of disturbed zone, 3D strength and large strain. The rock is assumed to be elastic–brittle–plastic and governed by a 3D Hoek–Brown yield criterion. To take the large displacement around a tunnel into account, the large-strain theory is adopted to determine the displacement of rock in the plastic zone. Based on the equilibrium equation, constitutive law and large-strain theory, the governing equations for the stresses and radial displacement around the tunnel were derived and solved by using MATLAB. The proposed solution was validated by using it to analyze a tunnel and comparing the results with those from numerical analysis using a finite difference code. Finally, extensive parametric studies were performed on tunnels in both poor-quality and good-quality rock masses with respect to stresses and radial displacement. The results indicate that the disturbed zone and the flow rule both have significant effects on the stress and displacement distributions around the tunnel.

Journal ArticleDOI
TL;DR: The CEL approach combined with the proposed constitutive model can simulate material side flow, which results in a larger width of chip compared to the width of cut, and in the formation of lateral burr on the workpiece.

Journal ArticleDOI
TL;DR: A neural network representing a region to point mapping to describe a nonlocal constitutive model that learns the embedded submodel without using data from that level, thanks to its interpretable mathematical structure, which makes it a promising alternative to traditional non local constitutive models.

Journal ArticleDOI
TL;DR: In this article, a micro-elastoplastic constitutive model considering the post-peak stage of rock mass under compression loading is proposed, and the loading-unloading path in the post peak stage of the rock is considered.

Journal ArticleDOI
TL;DR: In this paper, the second normal-stress difference (N2) is defined as the variation with shear rate of the shear viscosity and the so-called first and second normal stress differences.
Abstract: Shear flow is ubiquitous. Not only is it arguably the most widely-used deformation type to characterise complex fluids in rheological studies but also, in practice, the deformation most likely to occur in the great majority of flows, e.g. involving fluid transport through pipes or conduits. In steady simple shear flow the rheological properties of a complex fluid are completely characterised in just three material functions; the variation with shear rate of the shear viscosity and the so-called first and second normal-stress differences. Despite requiring only three material functions to be completely characterised, most shear-flow rheological characterisations are usually restricted simply to the shear viscosity and, at best, the variation of the first normal-stress difference N1 with shear rate. The second normal-stress difference N2 remains very much neglected. For dilute polymer solutions where this quantity may be negligibly small in comparison to the first normal-stress difference, such neglect is justified but for a whole range of complex fluids – indeed even polymer solutions outside of the dilute regime and especially melts – it is not clear that N2 may be safely disregarded. Indeed, in this review article we spotlight a number of flows where second normal-stress differences are of importance and potentially major consequence. Following this attention, we review the many experimental techniques which have been proposed for its measurement and survey the available literature for measurements of this quantity for various complex fluids including the aforementioned polymeric solutions, melts, liquid crystals, dense non-Brownian suspensions (both with Newtonian and complex fluid bases), semi-dilute wormlike micellar fluids and magnetorheological fluids. Theoretical predictions for N2 from various commonly-used continuum constitutive equations – primarily from the polymer literature – are also given and their asymptotic predictions at low and high shear rates compared. Finally, we end with a brief summary and outlook.

Journal ArticleDOI
TL;DR: Anssari-Benam and Bucchi as discussed by the authors proposed a two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials.
Abstract: In a recent paper in this journal by Anssari-Benam and Bucchi (2021), the authors have proposed a new two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials. The model reflects the limiting chain extensibility characteristic of non-Gaussian molecular models for rubber. A major contribution of Anssari-Benam and Bucchi (2021) is in showing that the model proposed there is superior to the well-known two-parameter Gent model when fitting with a large variety of experimental data for rubber for the homogeneous deformations of uniaxial, equi-biaxial and pure shear. Moreover, for all of these deformations, a fitting with data is achieved with a single set of values for the parameters with a narrow range of variation. In the present note, we establish a simple direct relation between the new model and the classical Gent model. The large body of research results on the mechanical behavior of rubber-like materials based on the latter model are thus readily applicable to the new model. Some other directions for widening the applicability of the new model are also suggested.

Journal ArticleDOI
TL;DR: In this article, the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods was constructed.
Abstract: We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.

Journal ArticleDOI
TL;DR: In this paper, a physically-based constitutive model is developed for additive manufacturing (AM) Al-Si-Mg alloys, which is based on in-situ neutron diffraction.

Journal ArticleDOI
TL;DR: The constitutive behavior of a near α Ti3Al2.5V alloy, conceived for impact resistant turbine engine containment applications, is characterized at quasi-static, medium, and high strain rates ranging from 10−3 [s−1] to 106 [s −1] by using the cylindrical compression specimen and shear compression specimen.

Journal ArticleDOI
TL;DR: In this paper, a nominal finite element solver is proposed for data-driven finite strain elasticity, bypassing the need for a constitutive model by considering a database of deformation gradient/first Piola-Kirchhoff stress tensors pairs.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the dynamic behavior of functionally graded saturated porous rotating thick truncated cone for the first time, where porosity distributions along the thickness are assumed that symmetric nonlinear, nonlinear asymmetric and uniform distributions.
Abstract: In the current article, dynamic behavior of functionally graded saturated porous rotating thick truncated cone is investigated for the first time. It is assumed that porosity distributions along the thickness are (1) symmetric nonlinear, (2) nonlinear asymmetric and (3) uniform distributions. The Biot poroelastic law instead of Hooke’s law is used to model the constitutive equations. Also, 2D axisymmetric theory of elasticity instead of simple shell theories is used for the governing motion equations. Graded finite element and Newmark methods have been used to solve the governing motion equations. First, natural frequencies of stationary functionally graded saturated porous cone are obtained, and then by considering the effect of centrifugal force and spin softening effect, dynamic response of porous cone in an undrained condition for different variables such as porosity and Skempton coefficients, rotational velocity, semi vertex angle of the cone and different distribution of porosity has been investigated. Obtained results denote that by increasing Skempton coefficient, natural frequencies are increased, and natural frequencies of PUD distribution are lower than other distributions. Also, rotational velocity and semi-vertex angle have significant effect on the displacement and stress field.

Journal ArticleDOI
TL;DR: In this paper, numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections and the assumed geometry imperfections.
Abstract: Numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections

Journal ArticleDOI
TL;DR: In this paper, a computational approach to simulating the deformation response of additively manufactured aluminum alloys is presented, where a three-dimensional microstructure with the grain geometry typical for aluminum alloy produced by selective laser melting is generated by the method of step-by-step packing.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a two-way coupling technique between a total Lagrangian smoothed particle hydrodynamics (SPH) method for solid mechanics and the explicit incompressible SPH (EISPH) to simulate fluid-structure interaction problems.

Journal ArticleDOI
TL;DR: In this paper, a study on nanoindentation of PMMA thin films via instrumented indentation testing and numerical simulation to determine its constitutive behavior is presented. And the results of finite element analysis show that the time-dependent elastic-plastic deformation of the unloading curves becomes more conspicuous when the quadratic viscosity term of the Oyen-Cook constitutive equation is decreased.