Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. ...Additionally, this data-driven paradigm could enable a seamless connection of experimental data probing material responses with numerical simulations at the structural level. Traditionally, these surrogates have just been trained using datasets which map strain inputs to stress outputs for elastic and inelastic materials directly. Recently, artificial neural networks (ANNs) have instead been trained to additionally incorporate the underlying physical laws in the construction of these models. However, ANNs do not offer convergence guarantees from an engineering point of view and are majorly reliant on user-specified parameters. In contrast to ANNs, Gaussian process regression (GPR) is based on nonparametric modeling principles as well as on fundamental statistical knowledge and hence allows for strict convergence guarantees. Motivated by the recent work by Frankel et al. (2021) which is based on rewriting the stress output as a linear combination of an irreducible integrity basis, in this work we present a physics-informed and data-driven constitutive modeling approach for isotropic and anisotropic hyperelastic materials at finite strain. The trained surrogates are able to respect physical principles such as material frame indifference, material symmetry, thermodynamic consistency, stress-free undeformed configuration, and the local balance of angular momentum. Our approach is based on probabilistic machine learning and uniquely can be used in the big data context while maintaining the benefits of GPR. As sampling in the mixed invariant space poses a unique challenge, we additionally present the first sampling approach that directly generates space-filling points in the invariant space corresponding to a bounded domain of the deformation gradient tensor. The sampling technique is based on simulated annealing and provides more efficient and reliable physics-informed constitutive models. Overall, the presented approach is tested on synthetic data from isotropic and anisotropic constitutive laws and shows surprising accuracy even far beyond the limits of the training domain, indicating that the resulting surrogates can efficiently generalize as they incorporate knowledge about the underlying physics.
•We present a generalized method for physics-guided data-driven material models.•Approach relies on tensor function representations of stresses and is applicable to isotropic and anisotropic hyperelasticity.•Local approximate Gaussian process regression allows for big data domain usage.•Space-filling sampling in invariant space makes method more efficient.•Approach offers high accuracy even far outside the training domain.
Hierarchical computational methods for multiscale mechanics such as the FE2 and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the ...process up significantly by enabling to incorporate the effective micromechanical response in macroscale simulations without the need of performing additional computations at each Gauss point explicitly. Traditionally artificial neural networks (ANNs) have been the surrogate modeling technique of choice in the solid mechanics community. However they suffer from severe drawbacks due to their parametric nature and suboptimal training and inference properties for the investigated datasets in a three dimensional setting. These problems can be avoided using local approximate Gaussian process regression (laGPR). This method can allow the prediction of stress outputs at particular strain space locations by training local regression models based on Gaussian processes, using only a subset of the data for each local model, offering better and more reliable accuracy than ANNs. A modified Newton–Raphson approach specific to laGPR is proposed to accommodate for the local nature of the laGPR approximation when solving the global structural problem in a FE setting. Hence, the presented work offers a complete and general framework enabling multiscale calculations combining a data-driven constitutive prediction using laGPR, and macroscopic calculations using an FE scheme that we test for finite-strain three-dimensional hyperelastic problems.
•Introducing Local Approximate Gaussian Process Regression (laGPR) for constitutive modeling.•Thoroughly compare between ANNs and laGPR, for finite deformations and hyperelasticity.•ANNs are often utilized for data driven constitutive modeling, and we highlight their limitations.•Develop a modified Newton–Raphson scheme to use laGPR in structural FE simulations.•We showcase efficient 3D multiscale calculations using an FEM-laGPR coupled scheme.
The flow behaviour of AA2060 Al alloy under warm/hot deformation conditions is complicated because of its dependency on strain rates (ε˙), strain (ε), and deformation modes. Thus, it is crucial to ...reveal and predict the flow behaviours of this alloy at a wide range of temperatures (T) and ε˙ using different constitutive models. Firstly, the isothermal tensile tests were carried out via a Gleeble-3800 thermomechanical simulator at a T range of 100, 200, 300, 400, and 500 °C and ε˙ range of 0.01, 0.1, 1, and 10 s
to reveal the warm/hot flow behaviours of AA2060 alloy sheet. Consequently, three phenomenological-based constitutive models (L-MJC, S1-MJC, S2-MJC) and a modified Zerilli-Armstrong (MZA) model representing physically based constitutive models were developed to precisely predict the flow behaviour of AA2060 alloy sheet under a wide range of T and ε˙. The predictability of the developed constitutive models was assessed and compared using various statistical parameters, including the correlation coefficient (
), average absolute relative error (
), and root mean square error (
). By comparing the results determined from these models and those obtained from experimentations, and confirmed by
,
, and
values, it is concluded that the predicted stresses determined from the S2-MJC model align closely with the experimental stresses, demonstrating a remarkable fit compared to the S1-MJC, L-MJC, and MZA models. This is because of the linking impact between softening, the strain rate, and strain hardening in the S2-MJC model. It is widely known that the dislocation process is affected by softening and strain rates. This is attributed to the interactions that occurred between ε and ε˙ from one side and between ε, ε˙, and T from the other side using an extensive set of constants correlating the constitutive components of dynamic recovery and softening mechanisms.
The flow behaviors of TC18 titanium alloy are studied in the α+β regime by hot compression tests at the strain rates of 0.001–0.1 s−1 and temperatures of 1033–1123 K. The deformation characteristics ...of this alloy are greatly influenced by deformation conditions. The stress descends with the decreased strain rate or the increased temperature. The dynamic recrystallization behavior becomes weaken, while the dynamic recovery behavior tends to be more obvious with increasing deformation temperature. The deformation storage energy can effectively promote the transformation from α phase into β phase. Meanwhile, the β phases permeate into the lamellar α phases, resulting in the fragmentation and spheroidization of lamellar α phases. Three constitutive models, including the strain-compensated Arrhenius-type, Hensel-Spittel (HS) and artificial neural network (ANN) models, are constructed to depict the flow behaviors of the studied alloy. The correlation coefficients of the measured and predicted results are 0.9866, 0.9739 and 0.9971, respectively, for the constructed strain-compensated Arrhenius-type, HS and ANN models. Also, their average absolute relative errors are 6.51%, 8.30% and 1.68%, respectively. Therefore, three models can well describe the flow behavior of the studied alloy, and the prediction accuracy of ANN model is the best among three constitutive models.
•Phase transformation and flow behaviors of TC18 alloy are studied in α+β regime.•DRX becomes weaken, while DRV tends to be obvious with increasing deformation temperature.•Deformation storage energy can promote the transformation from α phase into β phase.•β phases permeate into lamellar α phases, resulting in the spheroidization of lamellar α phases.•Strain-compensated Arrhenius, Hensel-Spittel and artificial neural network models are constructed.
Viscoelastic dampers (VEDs) have attracted significant attention during the last decades, due to their enormous potential in vibration control for building structures. However, owing to the ...performance of VEDs being significantly affected by temperature and frequency, their wide applicability is hindered. Broadening the damping temperature range of the matrix viscoelastic damping materials (VDMs) is the key to promoting their application. The progress of polymer and nanomaterials provides a new perspective to enhance the damping performance of VDMs. Moreover, various influencing factors should also be considered in calculation models. Thus, state-of-the-art research in the modification technologies of VDMs is critically reviewed in this article. In addition, the linear and nonlinear constitutive models of VDMs are comprehensively summarized. Furthermore, the developments of VDMs are proposed. Finally, the trends and directions of VDMs and VEDs are prospected. This systematic review can encourage the research community to conduct more studies and help engineers facilitate further applications.
Display omitted
•Modification technologies and constitutive models of VDMs are systematically reviewed.•Adding nanomaterials and small organic molecules shows great potential.•Models should account for temperature, frequency, Payne, and Mullins effects.•Research gaps and challenges are discussed and possible strategies are given.
Abstract
Aiming at the typical delamination damage mode of fiber-reinforced composites, the constitutive model and failure criterion of composites that commonly used in dynamic simulation are ...studied, and the principles and characteristics of cohesive element and tiebreak contact algorithm are analyzed.Then the simulation calculation of two fiber-reinforced composite targets anti penetration is take as an example,The accuracy of the cohesive element and the tiebreak contact algorithm are verified respectively, and the protection mechanism of fiber-reinforced composites in the process of anti penetration is revealed, which provides an important reference for the development and design of new composite protection structures and equipment.
This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis ...framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.
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.
We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and ...global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment — but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity of the solution is achieved by ℓp regularization combined with thresholding, which calls for a non-linear optimization scheme. The ensuing fully automated algorithm leverages physics-based constraints for the automatic determination of the penalty parameter in the regularization term. Using numerically generated data including artificial noise, we demonstrate the ability of the approach to accurately discover five hyperelastic models of different complexity. We also show that, if a “true” feature is missing in the function library, the proposed approach is able to surrogate it in such a way that the actual response is still accurately predicted.
•We propose a new approach for data-driven automated discovery of constitutive laws.•The approach is unsupervised, i.e. it needs only displacement and global force data.•The approach is interpretable, i.e. it discovers parsimonious laws through sparse regression.•The approach is one-shot, i.e. it only needs one experimental dataset.•Sparse regression is empowered by domain knowledge.
PDF
