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Electro-active materials are classified as electrostrictive and piezoelectric materials. They deform under the action of an external electric field. Piezoelectric material, as a special class of active materials, can produce an internal electric field when subjected to mechanical stress or strain. In return, there is the converse piezoelectric response, which expresses the induction of the mechanical deformation in the material when it is subjected to the application of the electric field. This work presents a variational-based computational modeling approach for failure prediction of ferromagnetic materials. In order to solve this problem, a coupling between magnetostriction and mechanics is modeled, then the fracture mechanism in ferromagnetic materials is investigated. Furthermore, the failure mechanics of ferromagnetic materials under the magnetostrictive effects is studied based on a variational phase-field model of fracture. Phase-field fracture is numerically challenging since the energy functional may admit several local minima, imposing the global irreversibility of the fracture field and dependency of regularization parameters related discretization size. Here, the failure behavior of a magnetoelastic solid body is formulated based on the Helmholtz free energy function, in which the strain tensor, the magnetic induction vector, and the crack phase-field are introduced as state variables. This coupled formulation leads to a continuity equation for the magnetic vector potential through well-known Maxwell's equations. Hence, the energetic crack driving force is governed by the coupled magneto-mechanical effects under the magneto-static state. Several numerical results substantiate our developments. • Extension of Maxwell's equations towards a coupled magneto-mechanical model to investigate the stress response of the ferromagnetic materials. • Transition rule for the electromagnetic material properties from undamaged to fully damaged states through the fracture phase-field, which acts as a geometric interpolation variable. • Investigation of the magnetostrictive-induced cracking in the ferromagnetic materials by developing a magneto-mechanical model coupled with the phase-field model. • Representation of numerical examples to substantiate our developments in predicting the fracture response of the ferromagnetic material. [ABSTRACT FROM AUTHOR]

To gain better insights into the structural reliability of lithium-ion battery electrodes and the nucleation as well as propagation of cracks during the charge and discharge cycles, it is crucial to enhance our understanding of the degradation mechanisms of electrode particles. This work presents a rigorous mathematical formulation for a fatigue failure theory for lithium-ion battery electrode particles for lithium diffusion induced fracture. The prediction of fatigue cracking for lithium-ion battery during the charge and discharge steps is an particularly challenging task and plays an crucial role in various electronic-based applications. Here, to simulate fatigue cracking, we rely on the phase-field approach for fracture which is a widely adopted framework for modeling and computing fracture failure phenomena in solids. The primary goal here is to describe a variationally consistent energetic formulation for gradient-extended dissipative solids, which is rooted in incremental energy minimization. The formulation has been derived as a coupled system of partial differential equations (PDEs) that governs the gradient-extended elastic-chemo damage response. Additionally, since the damage mechanisms of the lithium-ion battery electrode particles result from swelling and shrinkage, an additive decomposition of the strain tensor is performed. Several numerical simulations with different case studies are performed to demonstrate the correctness of our algorithmic developments. Furthermore, we investigate the effect of randomly distributed micro cavities (voids) and micro notches on fracture resistance. [ABSTRACT FROM AUTHOR]

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples. [ABSTRACT FROM AUTHOR]

In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a Global–Local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and linearized system of equations is solved. Both domains are coupled with Robin-type interface conditions. The fractures inside the local domain are allowed to propagate and consequently, both subdomains change within time. Here, a predictor–corrector strategy is adopted, in which the local domain is dynamically adjusted to the current fracture pattern. The resulting framework is algorithmically described in detail and substantiated with some numerical tests. [ABSTRACT FROM AUTHOR]

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values. [ABSTRACT FROM AUTHOR]

In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws between a porous medium and the fracture. The resulting model is augmented with thermodynamical arguments and then analyzed from a mechanical perspective. The numerical solution is based on a robust semi-smooth Newton approach in which the linear equation systems are solved with a generalized minimal residual method and algebraic multigrid preconditioning. The proposed modeling and algorithmic developments are substantiated with different examples in two- and three dimensions. We notice that for some of these configurations manufactured solutions can be constructed, allowing for a careful verification of our implementation. Furthermore, crack-oriented predictor–corrector adaptivity and a parallel implementation are used to keep the computational cost reasonable. Snapshots of iteration numbers show an excellent performance of the nonlinear and linear solution algorithms. Lastly, for some tests, a computational analysis of the effects of strain-energy splitting is performed, which has not been undertaken to date for similar phase-field settings involving pressure, fluids or non-isothermal effects. • A phase-field fracture model in thermo-poroelasticity and non-isothermal settings is developed. • A detailed analysis from the mechanical point of view is provided. • A series of seven numerical tests is undertaken. [ABSTRACT FROM AUTHOR]

Highlights • Non-linear optimization formulation is integrated with Finite Element Analysis. • Characterising intrinsic material properties of coated thin films on substrates that exhibit significant elastic-plastic deformation. • A global optimization approach is employed by perturbing first optimum solution to reach its desired tolerance value. • The proposed method is verified for the HA coating on Ti–6Al–4 V substrate, Al 2 O 3 coating on Al substrate and Cr coating on SS substrate. Abstract Determination of the material properties of coated thin films on substrates has always been complicated due to the influence of the substrate deformation on the thin film behaviour. In this study, indentation tests are used to continuously capture the indentation load, P , as a continuous function of the depth of penetration, h , into the indented specimen. Numerical optimisation schemes are used to extract elastic-plastic material properties of thin film coating materials from an indentation loading–unloading curve. Material parameters with non-linear isotropic hardening are determined by minimizing the least squares error (LSE) between target data and the results obtained from FE analysis of the indentation test. Lagrange linear interpolation polynomial (LLIP) and Cubic B-Spline approach are used for axisymmetric conical model and three-dimensional Berkovich model, respectively, to obtain the relationship between the applied load and penetration depth in the loading–unloading curve. This study also considers a global optimisation approach using a load–displacement curve based on a sharp indenter tip applied to HA coating on Ti–6Al–4 V substrate, Al 2 O 3 coating on Al substrate and Cr coating on SS substrate. Additionally, in order to maintain FE analysis accuracy, multiple starting points are performed to obtain the correct material properties. The proposed optimisation algorithm is shown to achieve excellent convergence even when the initial guess values are much greater or less than the target values and hence is potentially considered for characterising intrinsic material properties of coated thin films on substrates that exhibit significant elastic-plastic deformation. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This work presents a rigorous mathematical formulation for topology optimization of a macro structure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly challenging task and plays an extremely important role in various engineering applications. Here, we rely on the phase-field approach to fracture which is a widely adopted framework for modeling and computing the fracture failure phenomena in solids. The first objective is to optimize the topology of the structure in order to minimize its mass, while accounting for structural damage. To do so, the topological phase transition function (between solid and void phases) is introduced, thus resulting in an extension of all the governing equations. Our second objective is to additionally enhance the fracture resistance of the structure. Accordingly, two different formulations are proposed. One requires only the residual force vector of the deformation field as a constraint, while in the second formulation, the residual force vector of the deformation and phase-field fracture simultaneously have been imposed. An incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. Thereafter, to obtain optimal topology to enhance the structural resistance due to fracture, the level-set-based formulation is formulated. The level-set-based topology optimization is employed to seek an optimal layout with smooth and clear boundaries. Sensitivities are derived using the analytical gradient-based adjoint method to update the level-set surface for both formulations. Here, the evolution of the level-set surface is realized by the reaction–diffusion equation to maximize the strain energy of the structure while a certain volume of design domain is prescribed. Several three-dimensional numerical examples are presented to substantiate our algorithmic developments. [ABSTRACT FROM AUTHOR]

Modified Augmented lagrangian genetic Algorithm (ALGA) and Quadratic Penalty Function genetic Algorithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical examples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications. [ABSTRACT FROM PUBLISHER]

A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and spatial quantities (of different phases in the geometrical domain) are assumed to be homogeneous and deterministic. This is unlike the lower scale with strong fluctuation in the material and geometrical properties. Such a response is approximated through some uncertainty in the model problem. The presented contribution is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure. Hereby, the proposed model employs various representative volume elements with random distribution of stiff inclusions and voids within the composite structure. We develop an allocating strategy to allocate the heterogeneities and generate the corresponding meshes in two- and three-dimensional cases. Then the Monte Carlo Finite Element Method (MC-FEM) is employed for solving the stochastic PDE-based model and approximate the expectation and the variance of the solution field of brittle/ductile failure by evaluating a large number of samples. For the prediction of failure mechanisms, we rely on the phase-field approach which is a widely adopted framework for modeling and computing the fracture phenomena in solids. Incremental perturbed minimization principles for a class of gradient-type dissipative materials are used to derive the perturbed governing equations. This analysis enables us to study the highly heterogeneous microstructure and monitor the uncertainty in failure mechanics. Several numerical examples are given to examine the efficiency of the proposed method. • Stochastic phase-field fracture modeling through uncertainties quantification. • Monte Carlo FEM for stochastic failure mechanisms with complex micro-structures. • Random distribution of the heterogeneities in brittle and ductile materials. • Numerical examples in one- , two- and three-dimensional setting. [ABSTRACT FROM AUTHOR]

This paper presents a novel variational phase-field model for different fracture processes in fully saturated porous media. As a key feature, the model employs a micromechanics-based theory for the description of brittle-tensile and compressive–ductile fracture. As such, the field variables are linked to physical mechanisms at the microcrack level, with damage emerging as the consequence of microcrack growth. Similarly, plasticity emerges as a consequence of the frictional sliding of closed microcracks. In this way, the evolution of opening microcracks in tension leads to (mode I) brittle fracture, while the evolution of closed microcracks in compression/shear leads to (mode II) ductile fracture. These failure mechanisms are coupled to fluid flow, resulting in a Darcy–Biot–type hydromechanical model. Therein, in the tensile regime, plasticity naturally vanishes, while damage is driven by poroelastic energy, accounting for the pressure in fluid-filled opening microcracks. On the other hand, in the compressive/shear regime, the plastic driving force naturally follows as a Terzaghi-type effective stress in terms of the local stress field acting on the microcrack surfaces, while damage is solely driven by the frictionally blocked free energy. As another important feature, the model includes a non-associative frictional plasticity law. Nevertheless, a thermodynamically consistent variational framework is employed, for which different energetic principles are discussed. Finally, the numerical simulations show that the model captures relevant hydromechanical coupling effects in benchmark problems, including mechanically induced shear fracture and hydraulically induced tensile fracture. [Display omitted] • Mode I/II fracture coupled to fluid flow is described under saturated conditions. • Micromechanical arguments are explicitly considered in the model. • Brittle (ductile) fracture is linked to opening (sliding) microcracks. • Distinct behavior in tension/compression is captured without ad hoc energy splits. • The model is variational, with a delicate treatment for non-associative plasticity. [ABSTRACT FROM AUTHOR]

This paper outlines a rigorous variational-based multilevel Global–Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global–Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic–plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic–plastic fracturing response. (ii) The main objective of the second approach is to introduce an adoption of the Global–Local model toward the multilevel local setting. In (ii), an elastic–plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic–plastic material and the second local domain is modeled due to the fractured state. To further reduce the computational cost, predictor–corrector adaptivity within the Global–Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic–plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting in a two-way adaptivity procedure. The overall response of the Global–Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples. • An extension of the Global–Local approach for a ductile phase-field fracture. • A multilevel of the Global–Local formulation through two distinct local domains. • One way adaptivity scheme based on evolution of global plastic flow. • Two-way adaptivity procedure through the information of global hardening flow along with local crack phase-field state. • Compact open-source code for the Global–Local approach: One-dimensional Elasticity. [ABSTRACT FROM AUTHOR]

In this work, we employ a Bayesian inversion framework to fluid-filled phase-field fracture. We develop a robust and efficient numerical algorithm for hydraulic phase-field fracture toward transversely isotropic and orthotropy anisotropic fracture. In the fluid-driven coupled problem, three primary fields for pressure, displacements, and the crack phase-field are solved while direction-dependent responses (due to the preferred fiber orientation) are enforced via penalty-like parameters. A new crack driving state function is introduced by avoiding the compressible part of anisotropic energy to be degraded. Next, we use a successful extension of the anisotropic hydraulic phase-field fracture as a departure point for Bayesian inversion to estimate material parameters. To this end, we employ the delayed rejection adaptive Metropolis–Hastings (DRAM) algorithm to identify the parameters. The focus is on uncertainties arising from different variables, including elasticity modulus, Biot's coefficient, Biot's modulus, dynamic fluid viscosity and Griffith's energy release rate in the case of the isotopic hydraulic fracture while in the anisotropic setting, we will have additional penalty-like parameters to be identified. Several numerical examples substantiate our algorithmic developments. • Development of a Bayesian inversion framework for phase-field fracture. • Hydraulic phase-field fracture model including orthotropy anisotropy. • Parameter estimation for fluid-filled phase-field fractures in porous media. • Estimating six different material parameters and penalty-like coefficients [ABSTRACT FROM AUTHOR]

In this work, thermodynamically consistent phase-field fracture frameworks for transversely isotropic and orthotropic settings are proposed. We formulate an anisotropic crack phase-field via a penalization approach for each family of fibers. The resulting model is augmented with thermodynamical arguments and then carefully analyzed from a mechanical perspective. The fracture dissipation inequality to prevent crack healing is imposed via a primal–dual active set strategy. Predictor–corrector mesh adaptivity allows to work with small length-scale parameters at a reasonable computational cost. Due to the importance of laminated structures for industrial applications, fracture responses for transversely isotropic and orthotropic materials are performed. Therein, several studies are conducted that include comparisons of anisotropic formulations with Griffith's critical elastic energy release rate and with specific critical fracture energy formulations, as well as non-split and split approaches. • Anisotropic crack phase-field formulation. • Orthotropic materials with two families of fibers. • Consistent additive split for the bulk anisotropic contribution. • Analysis for the thermodynamical consistency. • Formulation within a quasi-monolithic approach with predictor–corrector adaptivity. [ABSTRACT FROM AUTHOR]

This work addresses an efficient Global–Local approach supplemented with predictor–corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on the anisotropic/non-uniform local state in the regularized concept. To resolve the crack phase-field by a given single preferred direction, second-order structural tensors are imposed to both the bulk and crack surface density functions Accordingly, a split in tension and compression modes in anisotropic materials is considered. A Global–Local formulation is proposed, in which the full displacement/phase-field problem is solved on a lower (local) scale, while dealing with a purely linear elastic problem on an upper (global) scale. Robin-type boundary conditions are introduced to relax the stiff local response at the global scale and enhancing its stabilization. Another important aspect of this contribution is the development of an adaptive Global–Local approach, where a predictor–corrector scheme is designed in which the local domains are dynamically updated during the computation. To cope with different finite element discretizations at the interface between the two nested scales, a non-matching dual mortar method is formulated. Hence, more regularity is achieved on the interface. Several numerical results substantiate our developments. • A phase-field formulation of fracture in anisotropic solids. • A Global–Local approach to capture the full local resolution at the global level. • Robin-type boundary conditions between the local and the global domains. • Non-matching FE discretization to obtain sufficient regularity along interface. • Predictor–corrector adaptive scheme for dynamically updated of the local domains. [ABSTRACT FROM AUTHOR]

In this work, a method for automatic hyper-parameter tuning of the stacked asymmetric auto-encoder is proposed. In previous work, the deep learning ability to extract personality perception from speech was shown, but hyper-parameter tuning was attained by trial-and-error, which is time-consuming and requires machine learning knowledge. Therefore, obtaining hyper-parameter values is challenging and places limits on deep learning usage. To address this challenge, researchers have applied optimization methods. Although there were successes, the search space is very large due to the large number of deep learning hyper-parameters, which increases the probability of getting stuck in local optima. Researchers have also focused on improving global optimization methods. In this regard, we suggest a novel global optimization method based on the cultural algorithm, multi-island and the concept of parallelism to search this large space smartly. At first, we evaluated our method on three well-known optimization benchmarks and compared the results with recently published papers. Results indicate that the convergence of the proposed method speeds up due to the ability to escape from local optima, and the precision of the results improves dramatically. Afterward, we applied our method to optimize five hyper-parameters of an asymmetric auto-encoder for automatic personality perception. Since inappropriate hyper-parameters lead the network to over-fitting and under-fitting, we used a novel cost function to prevent over-fitting and under-fitting. As observed, the unweighted average recall (accuracy) was improved by 6.52% (9.54%) compared to our previous work and had remarkable outcomes compared to other published personality perception works. [ABSTRACT FROM AUTHOR]

• The prostate tumor growth model. • An asymptotic analysis. • A generalized moving least squares technique. • Experimental data. This paper focuses on presenting an asymptotic analysis and employing simulations of a model describing the growth of local prostate tumor (known as a moving interface problem) in two-dimensional spaces. We first demonstrate that the proposed mathematical model produces the diffuse interfaces with the hyperbolic tangent profile using an asymptotic analysis. Next, we apply a meshless method, namely the generalized moving least squares approximation for discretizing the model in the space variables. The main benefits of the developed meshless method are: First, it does not need a background mesh (or triangulation) for constructing the approximation. Second, the obtained numerical results suggest that the proposed meshless method does not need to be combined with any adaptive technique for capturing the evolving interface between the tumor and the neighboring healthy tissue with proper accuracy. A semi-implicit backward differentiation formula of order 1 is used to deal with the time variable. The resulting fully discrete scheme obtained here is a linear system of algebraic equations per time step solved by an iterative scheme based on a Krylov subspace, namely the generalized minimal residual method with zero–fill incomplete lower–upper preconditioner. Finally, some simulation results based on estimated and experimental data taken from the literature are presented to show the process of prostate tumor growth in two-dimensional tissues, i.e., a square, a circle and non-convex domains using both uniform and quasi-uniform points. [ABSTRACT FROM AUTHOR]

This paper focuses on predicting the severity of freeway traffic accidents by employing twelve accident-related parameters in a genetic algorithm (GA), pattern search and artificial neural network (ANN) modelling methods. The models were developed using the input parameters of driver's age and gender, the use of a seat belt, the type and safety of a vehicle, weather conditions, road surface, speed ratio, crash time, crash type, collision type and traffic flow. The models were constructed based on 1000 of crashes in total that occurred during 2007 on the Tehran–Ghom Freeway due to the fact that the remaining records were not suitable for this study. The GA evaluated eleven equations to obtain the best one. Then, GA and PS methods were combined using the best GA equation. The neural network used multi-layer perceptron (MLP) architecture that consisted of a multi-layer feed-forward network with hidden sigmoid and linear output neurons that could also fit multi-dimensional mapping problems arbitrarily well. The ANN was applied during training, testing and validation and had 12 inputs, 25 neurons in the hidden layers and 3 neurons in the output layer. The best-fit model was selected according to the R-value, root mean square errors (RMSE), mean absolute errors (MAE) and the sum of square error (SSE). The highest R-value was obtained for the ANN around 0.87, demonstrating that the ANN provided the best prediction. The combination of GA and PS methods allowed for various prediction rankings ranging from linear relationships to complex equations. The advantage of these models is improving themselves adding new data. [ABSTRACT FROM PUBLISHER]

The influence of a wet environment on the fatigue behaviour of high-strength concrete has become more important in recent years with the expansion of offshore wind energy systems. According to the few investigations documented in the literature, the fatigue resistance of specimens submerged in water is significantly lower compared to that of specimens in dry conditions. However, it is still not clear how the wet environment and the moisture content in concrete influence its fatigue behaviour and which damage mechanisms are involved in the deterioration process. Here the results of a joint project are reported, in which the impact of moisture content in concrete on fatigue deterioration are investigated experimentally and numerically. Aside from the number of cycles to failure, the development of stiffness and acoustic emission (AE) hits are analysed as damage inductors and discussed along with results of microstructural investigations to provide insights into the degradation mechanisms. Subsequently, an efficient numeric modelling approach to water-induced fatigue damage is presented. The results of the fatigue tests show an accelerated degradation behaviour with increasing moisture content of the concrete. Further, it was found that the AE hits of specimens submerged in water occur exclusively close to the minimum stress level in contrast to specimens subjected to dry conditions, which means that additional damage mechanisms are acting with increasing moisture content in the concrete. [ABSTRACT FROM AUTHOR]

• A new meshless method is developed for nonstationary Boussinesq (NB) equations. • The proposed idea is based on the variational multiscale interpolating EFG method. • The proper orthogonal decomposition method is used to generate a reduced order model. • The POD-VMIEFG method gives acceptable results for simulating the NB equations. In the recent decade, meshless methods have been handled for solving some PDEs due to their easiness. One of the most efficient meshless methods is the element free Galerkin (EFG) method. The test and trial functions of the EFG are based upon the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG (VMEFG) procedure. In the current article, the shape functions of interpolating moving least squares (IMLS) approximation are applied to the variational multiscale EFG technique to numerical study the Navier–Stokes equations coupled with a heat transfer equation such that this model is well-known as two-dimensional nonstationary Boussinesq equations. In order to reduce the computational time of simulation, we employ a reduced order model (ROM) based on the proper orthogonal decomposition (POD) technique. In the current paper, we developed a new reduced order model based on the meshless numerical procedure for solving an important model in fluid mechanics. To illustrate the reduction in CPU time as well as the efficiency of the proposed method, we investigate two-dimensional cases. [ABSTRACT FROM AUTHOR]