This paper presents an extension of the variational interface fracture model proposed in Khisamitov and Meschke (2018) to model fluid driven fracture in porous materials. The fluid saturated material is described by the theory of poroelasticity and the effective stress concept, while the coupling between fluid flow and fracture initiation and propagation is accomplished via a variational interface

In this paper, a three-dimensional (3D) isogeometric finite element (FE) and boundary element (BE) coupling approach based on non-uniform rational B-splines (NURBS) is developed to simulate the deformed body. Based on the geometric exactness and higher smoothness of isogeometric analysis (IGA), NURBS discretization is applied to the approximation of geometric representation, displacement field and

In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems.We stabilize the method via residual minimization. We discretize the problem using B-spline basis functions. We then seek to minimize the isogeometric residual over a spline space built on a tensor product mesh. We construct the solution over a smooth

The simulation of enhanced geothermal systems (EGS) requires finding the solution to a highly coupled nonlinear set of partial differential equations. Verification of EGS modelling has been difficult due to a lack of analytical or semi-analytical solutions and is typically limited to a subset of processes. A comparison of alternative solution schemes is one method to numerically verify the coupling

This work extends isogeometric thin shell formulations to incorporate constitutive laws generated by stochastic multiscale analyses. The integration of the constitutive law is performed through the thickness of the shell, in order to account for material heterogeneity. At each thickness integration point, a corresponding representative volume element is assigned, defining the microstructural topology

In this paper an Isogeometric Boundary Element Method for three-dimensional lifting flows based on Morino’s (Morino and Kuo, 1974) formulation is presented. Analysis-suitable T-splines are used for the representation of all boundary surfaces and the unknown perturbation potential is approximated by the same T-spline basis used for the geometry. A novel numerical application of the so-called Kutta condition

To date, both the stress-related and multi-material topology optimization problems have been extensively studied. However, there are few works addressing the stress-constrained multi-material topology optimization (SMMTO) problem. Hence, a novel solution to the SMMTO problem is proposed in this paper based on the ordered SIMP method. To be specific, description of the multi-material elastic model is

We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco- elastic/plastic parts. The constitutive equations are obtained through Helmholtz free-energy potentials for Scott-Blair elements, together with a memory-dependent fractional yield function and dissipation inequalities

The Discontinuous Petrov–Galerkin (DPG) method is a widely employed discretization method for Partial Differential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time integration of transient parabolic PDEs. We showed that the resulting DPG-based time-marching scheme is equivalent to exponential integrators for the trace variables. In this work, we

One major merit of phase-field models for fracture is that cracks nucleation, propagation, branching, merging, coalescence and even fragmentation, etc., can be accounted for seamlessly within a standalone regularized variational framework. This fascinating feature overcomes the cumbersomeness in the characterization of non-smooth crack surfaces and the tracking of complex crack paths. However, the

Energy conserving and dissipative algorithm designs in Hamilton’s canonical equations via Petrov–Galerkin time finite element methodology are proposed in this paper that provide new avenues with high-order convergence rate, improved solution accuracy, and controllable numerical dissipation. Lagrange quadratic shape function in time with flexible interpolation points are considered to approximate the

In this paper, based on the Kriging, an efficient minimum limit-state-surface search strategy is proposed for hybrid reliability analysis with both random and multi-super-ellipsoidal variables. The super-ellipsoidal model can represent the commonly used convex model (like ellipsoidal and interval models) in uncertainty analysis, which is a wise choice to represent the uncertainty for the available

The integration of numerical simulation and experimental measurements in cellular materials at the sub-cellular scale is a real challenge. On the experimental side, the almost absence of texture makes displacement fields measurement tricky. On the simulation side, it requires the construction of reliable and specimen-specific geometric and mechanical models from digital images. For this purpose, high

Recycling of Krylov subspaces is often used to obtain an augmentation subspace in the context of iterative algorithms for the solution of sequences of linear systems. However, it still remains difficult to quantify the effect of subspaces recycling and thus to determine the dimension of the subspaces to be recycled targeting a specific accuracy. In that context, this work proposes the Automatic Krylov

In this paper, we establish a binary fluid surfactant model by coupling two mass-conserved Allen–Cahn equations and the Navier–Stokes equations and consider numerical simulations of the developed model. Due to a large number of nonlinear and nonlocal coupling terms in the model, it is very challenging to design an efficient and accurate numerical scheme, especially the full decoupling scheme with second-order

Sparse Bayesian learning (SBL) has attracted substantial interest in recent years for reliable estimation of sparse parameter vectors of dimension much larger than the number of measurements. However, the theory of online sequential estimation of sparsely changing parameter vectors is much less studied. We present a sequential SBL framework for recursive learning of sparse vectors that also change

The in-depth knowledge of rarefied gas dynamics is crucial to address challenges in a wide range of engineering problems, where gas flows are usually multiscale, i.e., covering a wide range of Knudsen numbers. As the traditional Navier–Stokes equations fail, gas kinetic equations are required to model the flows. So far, very few numerical methods are designed to efficiently solve the multiscale gas

In this work an explicit a posteriori error estimator for the steady incompressible Navier–Stokes equations is investigated. The error estimator is based on the variational multiscale theory, where the numerical solution is decomposed in resolved scales (FEM solution) and unresolved scales (FEM error). The error is estimated locally considering the residuals that emerge from the numerical solution

This paper introduces a novel method to model non-deterministic quantities based on experimental measurement data. The focus of this work is on quantities that vary over a continuous domain, e.g., material properties, time-dependent strain rate effects, or stress–strain curves. These quantities are modelled by means of the recently introduced concept of interval fields. An interval field defines intervals

A two-way coupling method of the three-dimensional (3D) isogeometric approach and the least-square moving particle semi-implicit method (LSMPS) is presented for handling the fluid–structure interaction problems. This method takes advantages of isogeometric analysis (IGA) for structure deformation, e.g. the exact representation of the structure geometry and high accuracy for solution fields with relatively

In the present study, an effective optimization framework of aerodynamic shape design is established based on the multi-fidelity deep neural network (MFDNN) model. The objective of the current work is to construct a high-accuracy multi-fidelity surrogate model correlating the configuration parameters of an aircraft and its aerodynamic performance by blending different fidelity information and adaptively

The design of rotating fluid devices, such as flow machines, mixers, and separators, with a focus on performance improvement is of high interest. They usually operate under high Reynolds numbers featuring turbulent flows. In this research, the topology optimization model of turbulent flows is expanded by adapting the Spalart–Allmaras (SA) model with the Rotation/Curvature Correction to consider a density-based

In this paper, we propose a novel trajectory-approximation technique as a time-integration scheme in a semi-Lagrangian framework, which is generally applicable to solve advectional partial differential equations in engineering and physics. The proposed trajectory-approximation technique resolves strong nonlinearity in the Cauchy problem and saves computational costs in comparison with the existing

This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the construction of a database from which an artificial neural network can be trained to learn the nonlinear relationship between the hyperparameters of a prior stochastic

Thermal multi-phase flow analysis has been proven to be an indispensable tool in metal additive manufacturing (AM) modeling, yet accurate and efficient simulations of metal AM processes remains challenging. This paper presents a flexible and effective thermal multi-phase flow model for directed energy deposition (DED) processes. Departing from the data-fitted or presumed deposit shapes in the literature

The classical boundary element method (BEM) is widely used to obtain detailed information on the acoustic performance of large-scale dynamical systems due to the nature of semi-analytical characteristic. Its use, however, results in asymmetric and dense system matrix, which makes original full-order model evaluation very time consuming and memory demanding. Moreover, the frequency sweep analysis which

Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to

In this paper, a phase-field model is presented for the description of brittle fracture in a Reissner–Mindlin plate and shell formulation. The shell kinematics as well as the phase-field variable are described on the midsurface of the structure. Non-Uniform Rational B-Spline basis functions are used for the discretization of both the displacement/rotations and the phase-field. The spectral decomposition

The total Lagrangian Material Point Method (TLMPM) is an efficient formulation of the well known Material Point Method (MPM). Unlike the MPM, it is not subject to cell-crossing instabilities or numerical failure, and features better quadrature. However, the TLMPM is unable to model (no-slip) contacts seamlessly as the standard updated Lagrangian MPM. This paper presents a contact algorithm for the

Direct numerical simulation based on experimental stress–strain data without explicit constitutive models is an active research topic. In this paper, a mechanistic-based, data-driven computational framework is proposed for elastoplastic materials undergoing finite strain. Harnessing the physical insights from the existing model-based plasticity theory, multiplicative decomposition of deformation gradient

We present an approach to build a reduced-order model for nonlinear, time-dependent, parametrized partial differential equations in a nonintrusive manner. The approach is based on combining proper orthogonal decomposition (POD) with a Smolyak hierarchical interpolation model for the POD coefficients. The sampling of the high-fidelity model to generate the snapshots is based on a locally adaptive sparse

We propose a framework to improve one-point quadrature and, more generally, reduced integration for finite element methods (FEM), Isogeometric Analysis (IGA), and immersed methods. The framework makes use of first- and higher-order Taylor expansion of the integrands involved in the principle of virtual work, and the analytical integration of the resulting correction terms. Explicit forms of the correction

In this paper we present a method to overcome membrane locking of thin shells. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel constraints. The number of constraints is decreased on triangular meshes compared to reduced integration techniques, in the lowest order case asymptotically by a factor two

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a

Subsurface flow problems usually involve some degree of uncertainty. Consequently, uncertainty quantification is commonly necessary for subsurface flow prediction. In this work, we propose a methodology for efficient uncertainty quantification for dynamic subsurface flow with a surrogate constructed by the Theory-guided Neural Network (TgNN). The TgNN here is specially designed for problems with stochastic

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy densities. We consider both the assumption of a constant fracture energy and the case of a fracture energy dependent on the martensitic volume fraction. The framework

An extended immersed boundary methodology utilizing a semi-implicit direct forcing approach was formulated for the simulation of incompressible flows in the presence of periodically moving immersed bodies. The methodology utilizes a Schur complement approach to enforce no-slip kinematic constraints for immersed surfaces. The methodology is split into an “embarrassingly” parallel pre-computing stage

Among the proposed formulations for rigid multibody dynamics, the minimal coordinates approach permits to parametrize the system motion with the minimal amount of degrees of freedom without the need of additional constraints equations. This leads to a system of ordinary differential equations to describe the motion which enables a straightforward combination of the model with control or estimation

The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual, and often biased nature of the commonly adopted calibration

In Parts I (Bonet et al., 2015) and II (Gil et al., 2016) of this series, a novel computational framework was presented for the numerical analysis of large strain fast solid dynamics in compressible and nearly/truly incompressible isothermal hyperelasticity. The methodology exploited the use of a system of first order Total Lagrangian conservation laws formulated in terms of the linear momentum and

The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave)

The initiation and propagation of aortic dissection have not yet been fully elucidated. An essential role is attributed to the degradation of inter-lamellar elastic fibers in the aortic media which causes a significant lowering of the radial strength. Inter-lamellar elastic fibers are aligned radially and contribute mainly to the cohesion of the lamellar units in the aortic media. Computational studies

This work focuses on the characterization of narrow vertical cracks of finite size using optically excited lock-in thermography (OLT). To characterize these cracks, we need to solve an ill-posed inverse problem. As a previous step to the solution of this inverse problem, we propose a sensitivity analysis to quantify the influence that the parameters involved in the model have on the surface temperature

This paper presents an interface stabilized method for moving and deforming interface problems in immiscible, discrete, multi-phase flows. The evolution of the interface is represented in the momentum balance equations written in an Eulerian frame via the dependence of the local value of density and viscosity of the fluids on the spatial location of the interphase boundary. The motion of the interface

In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized Level-Set method (PLSM) is conducted, in which the unknown-but-bounded (UBB) uncertainties of material and external loads are taken into account simultaneously. By interpolating the level set function (LSF) with the compactly supported radial basis functions

To achieve real-time simulations for flexible multibody dynamics (FMBD) systems, we suggest data-driven modeling based on deep neural networks (DNNs). While a DNN can represent system dynamics accurately, two main factors of FMBD systems require demanding computational costs for training a DNN. One is a fine discretization of flexible bodies, which produces a large number of training data. The other

Homogenizing the constitutive response of materials with nonlinear and history-dependent behavior at the microscale is particularly challenging. In this case, the only option is generally to homogenize numerically via concurrent multiscale models (CMMs). Unfortunately, these methods are not practical as their computational cost becomes prohibitive for engineering-scale applications. In this work, we

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares interpolation. It combines several attributes that are not simultaneously satisfied in the existing model order reduction methods for dynamical systems with moving boundaries

Optimal design of electronic devices such as sensors is essential since it results in more accurate output at the shortest possible time. In this work, we develop optimal Bayesian inversion for electrical impedance tomography (EIT) technology in order to improve the quality of medical images generated by EIT and to put this promising imaging technology into practice. We optimize Bayesian experimental

In this paper, we present a 3D Smoothed Particle Hydrodynamics (SPH) model with powder resolved to simulate complex Laser Assisted Additive Manufacturing (LAAM) processes. To the best knowledge of the authors, this is the most comprehensive and complete SPH model for LAAM simulations to date. Major and important underlying physical processes are considered in the model. These include the transient

This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the

In this work, a unified AI-framework named Hierarchical Deep Learning Neural Network (HiDeNN) is proposed to solve challenging computational science and engineering problems with little or no available physics as well as with extreme computational demand. The detailed construction and mathematical elements of HiDeNN are introduced and discussed to show the flexibility of the framework for diverse problems

This paper presents an ellipsoidal Newton’s iteration method for predicting the response of nonlinear structural systems with uncertain-but-bounded parameters. In the study, the uncertainty in parameters is expressed in terms of an ellipsoid set in an appropriate vector space and the bounds for the solution set of the nonlinear equations are aiming to be calculated effectively. In the framework of

Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. In particular, the use of linear finite elements to discretize both stress equilibrium and phase-field equations is widespread in the literature. However, the use of P1 Lagrange shape functions

Javili et al. recently reported a continuum-kinematics-inspired peridynamic model, in which theoretical aspects regarding the balance of linear and angular momentum and other conservation principles are considered. However, the analytical formulation of the model constants and the microelastic potential energy functions and numerical implementation were not defined. In this paper, a novel linear elastic

A new formulation is proposed for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design in the context of extreme loading. Many strides have been made in recent years regarding continuum topology optimization with elastoplasticity and buckling separately, but these phenomena are typically not considered together. The formulation we propose is computationally

A quadrilateral bi-cubic G1-conforming finite element for the analysis of Kirchhoff–Love shell assemblies based on the rational Gregory interpolation is presented. The Gregory interpolation removes the symmetry of the second cross derivative at the corners of the element that allows an independent control of the side rotations of the boundaries of the element. In this way G1-conformity of the deformation

In this paper we address an unresolved problem in the numerical modeling of cardiac electromechanics, that is the onset of numerical oscillations due to the dependence of force generation models on the fibers shortening velocity. A way to avoid numerical oscillations is to use monolithic schemes for the solution of the coupled problem of active–passive mechanics. However, staggered strategies, which

In this paper, we present high order accurate positivity-preserving conservative remapping algorithm which is based on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. We use a third-order method on 2D quadrilateral meshes as an example to present the algorithm. The method can effectively remap the physical variables after mesh rezoning in the ALE algorithm. By calculating