Showing papers on "Constitutive equation published in 2022"

Additive manufacturing – A review of hot deformation behavior and constitutive modeling of flow stress

Abstract: Hot working, as an important group of post-processing routes for additive manufacturing technology (3D printing), is used to reduce the solidification/processing defects and anisotropy of properties, grain refinement, improvement of mechanical properties, processing of pre-formed parts, and increasing the applicability domain. Accordingly, the present state of the art of the elevated temperature deformation behavior and constitutive description of flow stress during thermomechanical processing of additively manufactured parts is summarized in this monograph. Besides the effects of temperature and strain rate (represented by the Zener-Hollomon parameter), the significance of initial phases and the type of additive manufacturing process on the hot deformed microstructure, restoration processes of dynamic recovery (DRV) and dynamic recrystallization (DRX), flow stress, workability, and hot deformation activation energy is critically discussed. In this regard, the α'-martensite in Ti-6Al-4V titanium alloy produced by selective laser melting (SLM), the precipitates in aluminum alloys (such as 2219 Al alloy) produced by wire and arc additive manufacturing (WAAM), and the Laves phase in Inconel 718 superalloy produced by laser metal deposition (LMD) are remarkable examples. The utilization of innovative methods with in situ hot working effects such as additive friction stir deposition (AFSD) is also enlightened. Regarding the constitutive equations for modeling and prediction of hot flow stress, the reports on the strain-compensated Arrhenius model, artificial neural network (ANN) approach, DRX/DRV kinetics models, Johnson-Cook equation, and Fields-Backofen formula are presented, and the potentials of the modified, simplified, and physically-based approaches are discussed. Finally, the future prospects in this research field such as the hybridization of additive manufacturing with hot forming processes, work-hardening analysis for obtaining the onset of DRX, unraveling the effects of as-built microstructure, developing processing maps, proposing some physical-based unified constitutive models, and investigation of novel and/or widely-used alloys such as austenitic stainless steels, high-entropy alloys, and aluminum alloys (e.g. AlSi10Mg alloy) are proposed.

Unloading and reloading stress-strain relationship of recycled aggregate concrete reinforced with steel/polypropylene fibers under uniaxial low-cycle loadings

Abstract: To solve the key scientific problems such as low toughness and easy cracking of recycled aggregate concrete (RAC), A new sustainable material (fiber-reinforced recycled aggregate concrete - FRAC) was obtained by adding steel fiber (SF) and polypropylene fiber (PPF) into RAC matrix. Few experimental results were reported for the material under uniaxial low-cycle loading, and consequently, there is a gap in constitutive propositions to predict its behavior. Thus, one purpose of this research is to provide experimental results for FRAC characterizing damage growth and residual strain during cyclic compression in low-cycle tests with increasing strain amplitudes. Another purpose is to present a constitutive model to predict this behavior of FRAC accounting for fiber content. It is worth noting that the present results are relevant to displacement-controlled tests. The development law of residual strain (permanent strain) is explored, and the relationships between residual strain and unloading strain/reloading strain are proposed. The unloading stress-strain/reloading stress-strain equations are given. The damage evolution law of FRAC is revealed. Also, a new damage model represented by residual strain is suggested accounting for the fiber content. Furthermore, a stress-strain constitutive model coupling damage for FRAC is proposed. The model predicted with accuracy the unloading path, reloading path, residual strain development, and damage evolution for the composite accounting for fiber content.

Polyconvex anisotropic hyperelasticity with neural networks

Abstract: In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups.

Polyconvex anisotropic hyperelasticity with neural networks

Abstract: In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups.

On the analytical and meshless numerical approaches to mixture stress gradient functionally graded nano-bar in tension

Abstract: The mixture stress gradient theory of elasticity is conceived via consistent unification of the classical elasticity theory and the stress gradient theory within a stationary variational framework. The boundary-value problem associated with a functionally graded nano-bar is rigorously formulated. The constitutive law of the axial force field is determined and equipped with proper non-standard boundary conditions. Evidences of well-posedness of the mixture stress gradient problems, defined on finite structural domains, are demonstrated by analytical analysis of the axial displacement field of structural schemes of practical interest in nano-mechanics. An effective meshless numerical approach is, moreover, introduced based on the proposed stationary variational principle while employing autonomous series solution of the kinematic and kinetic field variables. Suitable mathematical forms of the coordinate functions are set forth in terms of the modified Chebyshev polynomials, satisfying the required classical and non-standard boundary conditions. An excellent agreement between the numerical results of the axial displacement field of the functionally graded nano-bar and the analytical solution counterpart is confirmed on the entire span of the nano-sized bar, in terms of the mixture parameter and the stress gradient characteristic parameter. The effectiveness of the established meshless numerical approach, demonstrating a fast convergence rate and an admissible convergence region, is hence ensured. The established mixture stress gradient theory can effectively characterize the peculiar size-dependent response of functionally graded structural elements of advanced ultra-small systems.

NN-EUCLID: deep-learning hyperelasticity without stress data

Abstract: We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the scope of our recent framework for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID) and we denote it as NN-EUCLID. The absence of stress labels is compensated for by leveraging a physics-motivated loss function based on the conservation of linear momentum to guide the learning process. The constitutive model is based on input-convex neural networks, which are capable of learning a function that is convex with respect to its inputs. By employing a specially designed neural network architecture, multiple physical and thermodynamic constraints for hyperelastic constitutive laws, such as material frame indifference, (poly-)convexity, and stress-free reference configuration are automatically satisfied. We demonstrate the ability of the approach to accurately learn several hidden isotropic and anisotropic hyperelastic constitutive laws - including e.g., Mooney-Rivlin, Arruda-Boyce, Ogden, and Holzapfel models - without using stress data. For anisotropic hyperelasticity, the unknown anisotropic fiber directions are automatically discovered jointly with the constitutive model. The neural network-based constitutive models show good generalization capability beyond the strain states observed during training and are readily deployable in a general finite element framework for simulating complex mechanical boundary value problems with good accuracy.

Assessment of Diagonal Macrocrack-Induced Debonding Mechanisms in FRP-Strengthened RC Beams

Abstract: This study presents a numerical model to characterize the fracture process of a reinforced concrete (RC) beam strengthened with fiber-reinforced polymer (FRP) in detail. A numerical model based on the application of cohesive elements was developed. Mixed-mode constitutive models were proposed to characterize the mechanical behavior of the FRP–concrete interface, the concrete potential fracture surfaces, and the rebar–concrete interface. The normal separation of the interface and its coupling effect on the shear behavior were considered in the constitutive model. In addition, the friction effect was explicitly considered in the constitutive model. Three different typical cases of FRP-strengthened RC from other experimental research were selected to validate the numerical model developed in this paper. Finally, the influence of different constitutive models on the simulation accuracy was analyzed.

SANISAND-MSf: a sand plasticity model with memory surface and semifluidised state

Abstract: A new constitutive model for sand is formulated by incorporating two new constitutive ingredients into the platform of a reference critical state compatible bounding surface plasticity model with kinematic hardening, in order to address primarily the undrained cyclic response. The first ingredient is a memory surface for more precisely controlling stiffness affecting the plastic deviatoric and volumetric strains and ensuing excess pore pressure development in the pre-liquefaction stage. The second ingredient is the concept of a semifluidised state and the related formulation of stiffness and dilatancy degradation, aiming at modelling large shear strain development in the post-liquefaction stage. In parallel, a modified flow rule aimed at providing a better description of non-proportional monotonic and cyclic loading is introduced. With a single set of constants, for which a detailed calibration procedure is provided, this new model successfully simulates undrained cyclic torsional and triaxial tests with different cyclic stress ratios, separately for the pre- and post-liquefaction stages, as well as liquefaction strength curves based on [Formula: see text] and shear strain criteria for initial liquefaction. The successful reproduction of the sand element response under undrained cyclic shearing contributes to future applications in realistic and thorough seismic site response analysis.

A state‐of‐the‐art review on creep damage mechanics of rocks

Abstract: In many major rock projects, services have spanned decades or even hundreds of years. For engineering design, it is necessary not only to ensure the safety of personnel during construction but also to ensure the safety of long-term use and operation in the future. Therefore, it is indispensable to study the creep damage mechanical properties of rocks before the construction of the project. For a long time, rock creep has been an important reason for large deformation and even instability in building foundations, underground tunnels, and slopes. Moreover, the surrounding rock generally exhibits obvious creep damage characteristics under an environment of high stress, high temperature, and high water-pressure. Under certain geological conditions, this creep damage behavior is extremely prominent. Therefore, the study of rock creep damage mechanics is very important. This paper reviews the advancement of rock creep damage mechanics from the aspects of mechanisms, research methods, constitutive models, and so forth. Rock creep is a process of interaction between structural damage and the hardening effect. The structural damage and hardening effect are opposite to each other, but they exist in the same physical process. The creep research method introduces mainly the research objects, influencing factors, monitoring methods, and experimental methods. Creep constitutive models introduce mainly empirical models, linear element combination models, nonlinear combination models, and other nonlinear models based on new theory. Finally, based on the current research progress, several important research directions in rock creep damage mechanics are pointed out.