Showing papers in "Computer Methods in Applied Mechanics and Engineering in 2019"
TL;DR: In this article, the role of magnetic forces on ferrofluid second law treatment via innovative computational method has been reported, and the non-Darcy model has been involved to estimate behavior of porous media.
Abstract: In current simulation, role of magnetic forces on ferrofluid second law treatment via innovative computational method has been reported. To estimate behavior of porous media, Non-Darcy model has been involved. Contours display the impact of magnetic force, Rayleigh and Darcy numbers. Iron oxide is considered as nanoparticles which are dispersed in to water. Results exhibit that exergy drop detracts with reduce of magnetic force. Bejan number detracts with decrease of permeability. As buoyancy forces improve, S gen,th enhances.
TL;DR: In this article, a numerical approach was employed to demonstrate nanofluid MHD flow through a porous enclosure, where Darcy law has been employed to model porous medium, radiation impact was included in energy equation.
Abstract: Innovative numerical approach was employed to demonstrate nanofluid MHD flow through a porous enclosure. To model porous medium, Darcy law has been employed. Radiation impact was included in energy equation. The new method (CVFEM) has been employed due to complex shape of porous cavity. Aluminium oxide with different shapes was dispersed in to water. Viscosity of nanofluid changes with Brownian motion impacts. Roles of radiation, buoyancy and Hartmann number on treatment of alumina were displayed. Results prove that convection detracts with augment of magnetic forces. Radiation can reduce the temperature gradient.
TL;DR: In this article, a numerical approach is applied to analyze the thermal behavior of alumina nanofluid in a duct, and neural network is employed to estimate the heat transfer rate.
Abstract: Heat transfer studying in channels is crucial for transport of the fluids in the oil and gas industry . In this study, numerical approach is applied to analyze the thermal behavior of alumina nanofluid in a duct. Brownian motion impact has been included for predicting nanofluid properties. Neural Network was employed to estimate the heat transfer rate . Numerical data has been obtained via Runge–Kutta method. Our outputs display that GMDH achieved an operative method for an efficient recognition of trends in data. Impact of expansion ratio, nanoparticle concentration, power law index and Reynolds number on Nu was also studied. Our findings reveal that heat transfer intensifies by rise of nanoparticle concentration while it has a reducing trend with rise of expansion ratio.
TL;DR: By discovering a proper topological representation of RVE with fewer degrees of freedom, this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure.
Abstract: In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning techniques . We propose to use a collection of connected mechanistic building blocks with analytical homogenization solutions to describe complex overall material responses which avoids the loss of essential physics in generic neural network . This concept is demonstrated for 2-dimensional RVE problems and network depth up to 7. Based on linear elastic RVE data from offline direct numerical simulations , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm , further enhanced by model compression methods . Importantly, the trained network is valid for any local material laws without the need for additional calibration or micromechanics assumption. Its extrapolations to unknown material and loading spaces for a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations . By discovering a proper topological representation of RVE with fewer degrees of freedom , this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure. It also provides a mechanistic understanding of structure–property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing.
TL;DR: In this paper, a novel methodology is proposed to design a lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structures with predictable yield performance.
Abstract: Advances in additive manufacturing (AM) have drawn considerable interest due to its ability to produce geometrically complex structure, such as lattice materials. In this work, a novel methodology is proposed to design graded lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structure design with predictable yield performance. Instead of using the power law of material interpolation in the SIMP method, asymptotic homogenization method is employed to compute the effective elastic properties of lattice material in terms of design variable, i.e. relative density. For yield strength, a multiscale failure model is proposed to capture yield strength of microstructure with macroscopic stress. At macroscale, a modified Hill’s yield criterion is employed to describe anisotropic yield strength of lattice material. The material constants in Hill’s model are assumed to be a function of relative density, and thus a model is built up to formulate yield strength of lattice structure with macroscopic stress. The experimental verification on the printed samples demonstrates that both the homogenized elastic model and yield model can accurately describe the elasticity and plasticity of the lattice structure. Based on the proposed material interpolation for lattice structure, a lattice structure topology optimization framework is proposed for minimizing total weight of the structure under stress constraint. The sensitivity analysis is performed for the implementation of the optimization algorithm. Two three-dimensionally numerical examples are performed to demonstrate the effectiveness of the proposed optimization method, as well as accuracy of the proposed homogenization technique for graded lattice structure design. Experiment is conducted to systematically examine yielding of the optimally graded lattice structure design and compare its performance with a uniform structure. It is found that the proposed optimization framework is valid for the design examples examined and can significantly enhance mechanical performance of the structure (i.e. yield loading, stiffness, energy absorption, etc.)
TL;DR: In this article, a phase field model for fluid-driven dynamic crack propagation in poroelastic media is proposed and verified through three classical benchmark problems which are compared to analytical solutions for dynamic consolidation and pressure distribution in a single crack and in a specimen with two sets of joints.
Abstract: A phase field model for fluid-driven dynamic crack propagation in poroelastic media is proposed. Therefore, classical Biot poroelasticity theory is applied in the porous medium while arbitrary crack growth is naturally captured by the phase field model. We also account for the transition of the fluid property from the intact medium to the fully broken one by employing indicator functions. We employ a staggered scheme and implement our approach into the software package COMSOL Multiphysics. Our approach is first verified through three classical benchmark problems which are compared to analytical solutions for dynamic consolidation and pressure distribution in a single crack and in a specimen with two sets of joints. Subsequently, we present several 2D and 3D examples of dynamic crack branching and their interaction with pre-existing natural fractures . All presented examples demonstrate the capability of the proposed approach of handling dynamic crack propagation, branching and coalescence of fluid-driven fracture.
TL;DR: The proposed approach provides a reliable and efficient tool for approximating parametrized time-dependent problems, and its effectiveness is illustrated by non-trivial numerical examples.
Abstract: A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order data, a reduced basis is constructed by the proper orthogonal decomposition (POD), and the maps between the time/parameter values and the projection coefficients onto the RB are approximated as a regression model. With a natural tensor grid between the time and the parameters in the database, a singular-value decomposition (SVD) is used to extract the principal components in the data of projection coefficients. The regression functions are represented as the linear combinations of several tensor products of two Gaussian processes, one of time and the other of parameters. During the online stage, the solutions at new time/parameter locations in the domain of interest can be recovered rapidly as outputs from the regression models. Featuring a non-intrusive nature and the complete decoupling of the offline and online stages, the proposed approach provides a reliable and efficient tool for approximating parametrized time-dependent problems, and its effectiveness is illustrated by non-trivial numerical examples.
TL;DR: The Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity is extended and combinations of the three representational paradigms thereof are considered to represent the evolving data sets of different classes of inElastic materials.
Abstract: We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: (i) materials with memory, i. e., conditioning the material data set to the past history of deformation; (ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain; and (iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.
TL;DR: In this article, a new phase field model that can simulate well compressive-shear fractures in rock-like materials was proposed, where only the compressive part of the strain is used in the new driving force with consideration of the influence of cohesion and internal friction angle.
Abstract: Compressive-shear fracture is commonly observed in rock-like materials. However, this fracture type cannot be captured by current phase field models (PFMs), which have been proven an effective tool for modeling fracture initiation , propagation, coalescence , and branching in solids. The existing PFMs also cannot describe the influence of cohesion and internal friction angle on load–displacement curve during compression tests. Therefore, to develop a new phase field model that can simulate well compressive-shear fractures in rock-like materials, we construct a new driving force in the evolution equation of phase field. Strain spectral decomposition is applied and only the compressive part of the strain is used in the new driving force with consideration of the influence of cohesion and internal friction angle. For ease of implementation, a hybrid formulation is established for the phase field modeling. Then, we test the brittle compressive-shear fractures in uniaxial compression tests on intact rock-like specimens as well as those with a single or two parallel inclined flaws. All numerical results are in good agreement with the experimental observation, validating the feasibility and practicability of the proposed PFM for simulating brittle compressive-shear fractures.
TL;DR: A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials.
Abstract: In contrast to the composition uniformity of homogeneous materials, heterogeneous materials are normally composed of two or more distinctive constituents. It is usually recognized that the effective material property of a heterogeneous material is related to the mechanical property and the distribution pattern of each forming constituent. However, to establish an explicit relationship between the macroscale mechanical property and the microstructure appears to be complicated. On the other hand, machine learning methods are broadly employed to excavate inherent rules and correlations based on a significant amount of data samples. Specifically, deep neural networks are established to deal with situations where input–output mappings are extensively complex. In this paper, a method is proposed to establish the implicit mapping between the effective mechanical property and the mesoscale structure of heterogeneous materials. Shale is employed in this paper as an example to illustrate the method. At the mesoscale, a shale sample is a complex heterogeneous composite that consists of multiple mineral constituents. The mechanical properties of each mineral constituent vary significantly, and mineral constituents are distributed in an utterly random manner within shale samples. Large quantities of shale samples are generated based on mesoscale scanning electron microscopy images using a stochastic reconstruction algorithm. Image processing techniques are employed to transform the shale sample images to finite element models. Finite element analysis is utilized to evaluate the effective mechanical properties of the shale samples. A convolutional neural network is trained based on the images of stochastic shale samples and their effective moduli. The trained network is validated to be able to predict the effective moduli of real shale samples accurately and efficiently. Not limited to shale, the proposed method can be further extended to predict effective mechanical properties of other heterogeneous materials.
TL;DR: Because the derivative of the surrogate model is important for sensitivity analysis of the macroscale topology optimization, a neural network training procedure based on the Sobolev norm is described, and an alternative method is developed to enable creation of void regions.
Abstract: We are concerned with optimization of macroscale elastic structures that are designed utilizing spatially varying microscale metamaterials. The macroscale optimization is accomplished using gradient-based nonlinear topological optimization. But instead of using density as the optimization decision variable, the decision variables are the multiple parameters that define the local microscale metamaterial. This is accomplished using single layer feedforward Gaussian basis function networks as a surrogate models of the elastic response of the microscale metamaterial. The surrogate models are trained using highly resolved continuum finite element simulations of the microscale metamaterials and hence are significantly more accurate than analytical models e.g. classical beam theory . Because the derivative of the surrogate model is important for sensitivity analysis of the macroscale topology optimization , a neural network training procedure based on the Sobolev norm is described. Since the SIMP method is not appropriate for spatially varying lattices , an alternative method is developed to enable creation of void regions. The efficacy of this approach is demonstrated via several examples in which the optimal graded metamaterial outperforms a traditional solid structure.
TL;DR: In this article, a concise overview on numerical schemes for the sub-diffusion model with nonsmooth problem data is given, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis.
Abstract: Over the past few decades, there has been substantial interest in evolution equations that involve a fractional-order derivative of order in time, commonly known as subdiffusion, due to their many successful applications in engineering, physics, biology and finance. Thus, it is of paramount importance to develop and to analyze efficient and accurate numerical methods for reliably simulating such models, and the literature on the topic is vast and fast growing. The present paper gives a concise overview on numerical schemes for the subdiffusion model with nonsmooth problem data, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis. We focus on the following topics of the subdiffusion model: regularity theory, Galerkin finite element discretization in space, time-stepping schemes (including convolution quadrature and L1 type schemes), and space–time variational formulations, and compare the results with that for standard parabolic problems. Further, these aspects are showcased with illustrative numerical experiments and complemented with perspectives and pointers to relevant literature.
TL;DR: In this paper, a phase-field/gradient damage formulation for cohesive fracture is extended to the dynamic case, and the model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.
Abstract: We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress–strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro- and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation , with particular emphasis on dynamic fracture .
TL;DR: It is demonstrated that a consistent introduction of the PST inside the SPH model leads to a new set of equations where some additional terms containing the particle shifting velocity δ u have to be taken into account.
Abstract: In the present work a consistent inclusion of a particle shifting technique (PST) in the weakly compressible Smoothed Particle Hydrodynamic (SPH) models is discussed. Recently, it has been shown that the use of PST can largely improve both the accuracy and the robustness of SPH models. In particular, the δ + -SPH model is a weakly-compressible SPH model where a PST is adopted along with a diffusive term in the continuity equation that helps removing the high-frequency noise on the pressure field. This specific SPH model is able to overcome the main drawbacks that afflict the standard weakly-compressible SPH model. In this work we demonstrate that a consistent introduction of the PST inside the SPH model leads to a new set of equations where some additional terms containing the particle shifting velocity δ u have to be taken into account. The effects of these δ u -terms become crucial for problems in confined or periodic domains, as well as for long-time simulations of free-surface flows. The proposed scheme is tested against challenging benchmark cases, highlighting when the δ u -terms play an important role or not. Further improvements of the PST algorithms for the numerical treatment of the scheme close to the free surface and along the solid boundaries are also discussed.
TL;DR: A simple strategy to efficiently collect stress–strain data from the micro model is proposed, and the RNN model is modified such that it resembles a nonlinear finite element analysis procedure during training.
Abstract: FE 2 multiscale simulations of history-dependent materials are accelerated by means of a recurrent neural network (RNN) surrogate for the history-dependent micro level response. We propose a simple strategy to efficiently collect stress–strain data from the micro model, and we modify the RNN model such that it resembles a nonlinear finite element analysis procedure during training. We then implement the trained RNN model in the FE 2 scheme and employ automatic differentiation to compute the consistent tangent. The exceptional performance of the proposed model is demonstrated through a number of academic examples using strain-softening Perzyna viscoplasticity as the nonlinear material model at the micro level.
TL;DR: Two new implicit static solution procedures to study crack propagation problems by adopting a Peridynamic-based numerical tool, and compares them with the Sequentially Linear Analysis are introduced.
Abstract: The static solution of crack propagation problems can be an efficient way to find both the failure load of a structure and the shape of the crack pattern. The paper introduces two new implicit static solution procedures to study crack propagation problems by adopting a Peridynamic-based numerical tool, and compares them with the Sequentially Linear Analysis. We discretize the structures in space by adopting a coupled FEM–PD approach, which exploits the flexibility of FEM to reduce the overall computational cost of the simulation. The results of several numerical examples indicate the main novel conclusions of the paper: when using a PD-based software, controlling the maximum number of bonds broken in each iteration may increase significantly the accuracy of the solution and keep the computational cost to an acceptable level.
TL;DR: In this article, a modified couple stress theory and isogeometric analysis (IGA) was used to simulate the small-scale effects on bending and buckling on composite laminate microplate under complex boundary conditions in thermal environment.
Abstract: The use of modified couple stress theory to simulate the size-dependent phenomenon of composite laminate microplate is commonly limited to simple boundary conditions and mechanical bending load. The small-scale effects on bending and buckling on composite laminate microplate under complex boundary conditions in thermal environment have not been understood fully in the literature. Hence, this research develops, for the first time, a model to overcome the above limitation through the combination of a new modified couple stress theory and isogeometric analysis (IGA). By solving the governing equation using IGA, the thermal displacement, stress and thermal buckling load for various material length scale parameters are obtained. To satisfy the continuous shear stress condition at the layer interfaces, the equilibrium equations as integrated in-plane stress derivatives over the thickness are imposed. In addition, the non-uniform rational B-splines (NURBS) satisfy the higher-order derivative of shape function using the equilibrium equation. Furthermore, to show the effectiveness of presented model for capturing the size effect on thermal bending and thermal buckling of multi-ply laminate microplate, the influences of fiber orientation, thickness ratio, boundary condition and the variation in material length scale parameter are investigated.
TL;DR: In this article, the authors investigated the postbuckling and geometrically nonlinear behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells.
Abstract: An investigation into the postbuckling and geometrically nonlinear behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells is carried out in this study. The discrete nonlinear equation system is established based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT). The nonlinearity of shells is formed in the Total Lagrangian approach considering the von Karman assumption. The incremental solutions are obtained by using a modified Riks method. In the present formulation, the rule of mixture is used to estimate the effective material properties of FG-CNTRC shells. Effects of CNTs distribution, volume fraction and CNTs orientation on the postbuckling behavior of FG-CNTRC shells are particularly investigated. Exact geometries of shells are modeled by using NURBS interpolation. Several verifications are given to show the high reliability of the proposed formulation. Especially, some complex postbuckling curves of FG-CNTRC panels and cylinders are first provided that could be useful for future references.
TL;DR: The numerical experiments demonstrate that the convergence capability of the proposed adaptive conjugate single-loop approach (AC-SLA) is significantly superior to the PMA, RIA, and SORA.
Abstract: The single-loop approach (SLA) for reliability-based design optimization (RBDO) is one of the most efficient schemes for optimization problems with linear and weak nonlinear probabilistic constraints. However, it may produce unstable results or increase computational efforts when using the ordinary search direction to determine the optimum design in RBDO problems with highly nonlinear probabilistic constraints. The conjugate gradient (CG) is a promising sensitivity vector for locating the most probable point (MPP) of highly nonlinear concave performance functions. However, the MPP computation using the CG may require a high computational burden for convex constraints To overcome the drawbacks of the SLA the adaptive conjugate single-loop approach (AC-SLA) is proposed for RBDO problems with a large variety of nonlinear constraints. The sensitivity vector of the probabilistic constraints is adaptively computed using the CG vector with a dynamical conjugate scalar factor (DCF). The DCF is adjusted within the range from 0 to 2 using two adaptive coefficients, which are adapted based on the new and previous points. Moreover, the Lyapunov exponents are developed as a general tool for detecting the robustness of different MPP approximation algorithms. The method is also applied to solve a reliability-based topology optimization (RBTO) problem. The ability of the AC-SLA in six RBDO benchmark problems, one applicable to an RBDO aircraft engineering problem and one for RBTO problem, is compared in terms of both robustness and efficiency using the SLA, performance measure approach (PMA), reliability index approach (RIA), and sequential optimization and reliability assessment (SORA). The numerical experiments demonstrate that the convergence capability of the proposed AC-SLA is significantly superior to the PMA, RIA, and SORA. The computational effort of the AC-SLA is significantly reduced, with stable results.
TL;DR: Numerical examples show that both the size and the lattice pattern of substructure have essential influences on the design, indicating the necessity of performing connected hierarchical modeling and design.
Abstract: This work presents a generalized topology optimization approach for the design of hierarchical lattice structures with the development of an Approximation of Reduced Substructure with Penalization (ARSP) model. The structure is assumed to be composed of substructures with a common lattice geometry pattern. Unlike conventional homogenization-based designs assuming the separation of scales, this work considers two different yet connected scales. Each substructure is condensed first into a super-element with a reduced degrees of freedom and is associated with a density design variable indicating the material volume fraction. The density design variable is linked to a lattice geometry feature parameter. A surrogate model is particularly built with the aid of proper orthogonal decomposition and diffuse approximation, mapping the density to super-element stiffness matrix. The derivative of super-element matrix with respect to the associated density can therefore be evaluated efficiently and explicitly. The super-element matrix is further augmented with a penalized density to control the structural complexity. The optimality criteria method is used for the update of design variables. Numerical examples show that both the size and the lattice pattern of substructure have essential influences on the design, indicating the necessity of performing connected hierarchical modeling and design.
TL;DR: A combination method of projection-outline-based active learning Kriging and AIS, termed as POALK-AIS, to improve the computational efficiency of AIS in cases with time-consuming performance functions is proposed.
Abstract: In this paper, the adaptive importance sampling (AIS) method is extended for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probabilities. In AIS, the design space is divided into random and interval variable subspaces. In random variable subspace, Markov Chain Monte Carlo (MCMC) is employed to generate samples which populate the failure regions. Then based on these samples, two kernel sampling density functions are established for estimations of the lower and upper bounds of failure probability. To improve the computational efficiency of AIS in cases with time-consuming performance functions, a combination method of projection-outline-based active learning Kriging and AIS, termed as POALK-AIS, is proposed in this paper. In this method, design of experiments is sequentially updated for the construction of Kriging metamodel with focus on the approximation accuracy of the projection outlines on the limit-state surface. During the procedure of POALK-AIS, multiple groups of sample points simulated by AIS are used to calculate the upper and lower bounds of failure probability. The accuracy, efficiency and robustness of POALK-AIS for HRA-RI with small failure probabilities are verified by five test examples.
TL;DR: A new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the topology of the macrostructure, the topologies of multiple materialmicrostructures and their overall distribution in the Macrostructure is proposed.
Abstract: This paper proposes a new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the topology of the macrostructure, the topologies of multiple material microstructures and their overall distribution in the macrostructure. The multiscale design involves two optimization stages: the free material distribution optimization and the concurrent topology optimization. Firstly, the variable thickness sheet (VTS) method with the regularization mechanism is used to generate multiple element density distributions in the macro design domain. Hence, different groups of elements with the identical densities can be uniformly arranged in their corresponding domains, and each domain in the space will be periodically configured by a unique representative microstructure. Secondly, with the discrete material distributions achieved in the macro domain, the topology of the macrostructure and topologies of multiple representative microstructures are concurrently optimized by a parametric level set method combined with the numerical homogenization method. Finally. Several 2D and 3D numerical examples are provided to demonstrate the effectiveness of the proposed multiscale topology optimization method.
TL;DR: The IGAB EM is applied to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis.
Abstract: The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm.
TL;DR: A unified fracture–porous medium hydraulic fracturing model is derived, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths.
Abstract: Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith’s theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method’s capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures.
TL;DR: In this paper, a homogenization-based approach is proposed to perform compliance minimization and projection of coated structures with orthotropic infill material in 2D, where the design space is relaxed to allow for a composite material description, which means that designs with complex microstructures can be obtained on relatively coarse meshes.
Abstract: This paper concerns compliance minimization and projection of coated structures with orthotropic infill material in 2D. The purpose of the work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. The design space is relaxed to allow for a composite material description, which means that designs with complex microstructures can be obtained on relatively coarse meshes. Second, a method is presented to project the homogenization-based designs on a fine but realizable scale. A novel method to adaptively refine the lattice structure is presented to allow for a regular spacing of the infill. Numerical experiments show excellent behavior of the projected designs, with structural performance almost identical to the homogenization-based designs. Furthermore, a reduction in computational cost of at least an order of magnitude is achieved, compared to a related approach in which the infill is optimized using a density-based approach.
TL;DR: A method that utilizes machine learning to generate a direct relationship between the element state and its forces, which avoids the complex task of finding the internal displacement field and eliminates the need for numerical iterations.
Abstract: Many multiscale finite element formulations can become computationally expensive because they rely on detailed models of the element’s internal displacement field. This issue is exacerbated in the presence of nonlinear problems , where numerical iterations are generally needed. We propose a method that utilizes machine learning to generate a direct relationship between the element state and its forces, which avoids the complex task of finding the internal displacement field and eliminates the need for numerical iterations. To generate our model, we choose an existing finite element formulation, extract data from an instance of that element, and feed that data to the machine learning algorithm . The result is an approximated model of the element that can be used in the same context. Unlike most data-driven techniques applied to individual elements, our method is not tied to any particular machine learning algorithm, and it does not impose any restriction on the solver of choice. In addition, we guarantee that our elements are physically accurate by enforcing frame indifference and conservation of linear and angular momentum . Our results indicate that this can considerably reduce the error of the method and the computational cost of producing and solving the model.
TL;DR: In this paper, the Scalar Auxiliary Variable (SAV) approach was combined with the stabilization technique to arrive at a novel Stabilized-SAV approach, where three linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficient, are added to enhance the stability while keeping the required accuracy.
Abstract: In this paper, we consider numerical approximations for solving the anisotropic Cahn–Hilliard model. We combine the Scalar Auxiliary Variable (SAV) approach with the stabilization technique to arrive at a novel Stabilized-SAV approach, where three linear stabilization terms, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficient, are added to enhance the stability while keeping the required accuracy. The schemes are very easy-to-implement and fast in the sense that all nonlinear terms are treated in a semi-explicit way, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously and present numerous 2D and 3D numerical simulations to demonstrate the stability and accuracy.
TL;DR: In this article, a meta-modeling framework that employs deep reinforcement learning (DRL) to generate mechanical constitutive models for interfaces is presented, where the constitutive model is conceptualized as information flow in directed graphs.
Abstract: This paper presents a new meta-modeling framework that employs deep reinforcement learning (DRL) to generate mechanical constitutive models for interfaces. The constitutive models are conceptualized as information flow in directed graphs. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). Thus meta-modeling can be formulated as a Markov decision process with well-defined states, actions, rules, objective functions and rewards. By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive model it generated through self-playing, in the same way AlphaGo Zero (the algorithm that outplayed the world champion in the game of Go) improves its gameplay. Our numerical examples show that this automated meta-modeling framework does not only produces models which outperform existing cohesive models on benchmark traction–separation data, but is also capable of detecting hidden mechanisms among micro-structural features and incorporating them in constitutive models to improve the forward prediction accuracy, both of which are difficult tasks to do manually.
TL;DR: An effective and efficient topology optimization method, termed as Isogeometric Topology Optimization (ITO), is proposed for systematic design of both 2D and 3D auxetic metamaterials based on isogeometric analysis (IGA).
Abstract: In this paper, an effective and efficient topology optimization method, termed as Isogeometric Topology Optimization (ITO), is proposed for systematic design of both 2D and 3D auxetic metamaterials based on isogeometric analysis (IGA). Firstly, a density distribution function (DDF) with the desired smoothness and continuity, to represent the topological changes of structures, is constructed using the Shepard function and non-uniform rational B-splines (NURBS) basis functions. Secondly, an energy-based homogenization method (EBHM) to evaluate material effective properties is numerically implemented by IGA, with the imposing of the periodic boundary formulation on material microstructure. Thirdly, a topology optimization formulation for 2D and 3D auxetic metamaterials is developed based on the DDF, where the objective function is defined as a combination of the homogenized elastic tensor and the IGA is applied to solve the structural responses. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. Finally, several numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method. A series of auxetic microstructures with different deformation mechanisms (e.g. the re-entrant and chiral) can be obtained. The auxetic behavior of material microstructures are numerically validated using ANSYS, and the optimized designs are prototyped using the Selective Laser Sintering (SLS) technique.
TL;DR: A robust design approach, based on eroded, intermediate and dilated projections, to handle uniform manufacturing uncertainties in stress-constrained topology optimization and a simple scheme to increase accuracy of stress evaluation at jagged edges is proposed.
Abstract: This paper proposes a robust design approach, based on eroded, intermediate and dilated projections, to handle uniform manufacturing uncertainties in stress-constrained topology optimization. In addition, a simple scheme is proposed to increase accuracy of stress evaluation at jagged edges, based on limiting sharpness of the projections to intentionally allow a thin layer of intermediate material between solid and void phases. A reference problem is analyzed through voxel-based finite element models, demonstrating that, in association with a proper choice of stiffness and stress interpolation functions, the proposed scheme can ensure consistent stress magnitude and smooth stress behavior for uniform boundary variation. Optimization problems are solved and post-processing with body-fitted meshes is performed over optimized solutions, demonstrating that: (1) stresses evaluated with voxel-based meshes containing thin soft transition boundaries are consistent with stresses evaluated with body-fitted meshes; and (2) optimized structures are robust with respect to uniform boundary variations.