We present a gradient enhanced damage model for ductile fracture modeling, describing the degraded material response coupled to temperature. Continuum thermodynamics is used to represent components of the energy dissipation as induced by the effective material response, thermal effects and damage evolution. As prototype for the effective material serves the viscoplastic Johnson-Cook constitutive model

In this paper, we investigate the use of a consecutive-interpolation for polyhedral finite element method (CIPFEM) in the analysis of three-dimensional solid mechanics problems. A displacement-based Galerkin weak form is used, in which the nodal degrees of freedom and their derivatives are both considered for the approximation scheme. Based on arbitrary star-convex polyhedral elements using piecewise

This paper demonstrates gradient driven density-based topology optimization of transient impact problems with friction. The sensitivities are obtained using the semi-discrete adjoint approach in which the temporal components are obtained by the "differentiate then discretize" whereas the spatial part is determined discretely. In this work, the sensitivity analysis method is extended to a mixed formulation

In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero-energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two-phase stabilization scheme is formulated based on an energy method that

The current study investigates the stability and failure analysis of thin-walled composite columns with a top-hat and channel cross section, subjected to axial compression. The analyzed structures were made of composite material (carbon fiber reinforced polymer) by autoclave technique. The study included experimental tests on actual specimens and numerical simulations on numerical models using finite

Uncertainties associated with spatially varying parameters are modeled through random fields discretized into a finite number of random variables. Standard discretization methods, such as the Karhunen–Loève expansion, use series representations for which the truncation order is specified a priori. However, when data is used to update random fields through Bayesian inference, a different truncation

In this study, we evaluate the performance of feedback control-based time step adaptivity schemes for the nonlocal Cahn–Hilliard equation derived from the Ohta–Kawasaki free energy functional. The temporal adaptivity scheme is recast under the linear feedback control theory equipped with an error estimation that extrapolates the solution obtained from an energy-stable, fully implicit time marching

An 8-node quadrilateral plane element US-QUAD8 is developed for linear isotropic hardening material in the framework of updated Lagrangian unsymmetric finite formulation where B L matrix is constructed by classical shape function, and B R matrix by the higher-order Lagrangian basis function in global coordinate system. The present element eliminates the influence of Jacobian in the elemental stiffness

Phase field models have a very good capability in predicting the crack path, but most of them represent the dependence of the regularization parameter on the load-carrying capacity of structures. In this paper, a phase field model is coupled with isotropic damage model aiming to resolve this issue in the fracture simulations of quasi-brittle materials. Damage variables are calculated by a continuum

Different from previous discrete element methods (DEM) where irregular 3D particle shapes are approximated by subspheres, vertices or voxels, this study aims to develop an innovative and computationally effective DEM method directly employing spherical harmonic functions for simulations of 3D irregular-shaped particles. First, the discrete surface points of a 3D irregular-shaped particle are represented

In this article, the 3D viscoelastic computational grains (CGs) with spherical inclusions, with and without interphases/coatings are developed to study the viscoelastic behavior of polymer-based heterogeneous materials. Papkovich–Neuber solutions and spherical harmonics are adopted to develop the independent displacement fields inside the grains, and Wachspress coordinate is used to interpolate compatible

While deriving the theoretical part of paper [1] again for chapter 5 in the book “Computational Geomechanics: Theory and Applications”, Second Edition, with authors A. Chan, M. Pastor, B. Schrefler, T. Shiomi, O. C. Zienkiewicz, ISBN9781118350478, in print at Wiley, the senior author discovered errors in some equations of this paper. The errors occurred during the transcription of the mass balance

In this article, we develop an extension of the Fourier transform solution method in order to solve conduction equation with nonperiodic boundary conditions (BC). The periodic Lippmann–Schwinger equation for porous materials is extended to the case of non-periodicity with relevant source terms on the boundary. The method is formulated in Fourier space based on the temperature as unknown, using the

The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems. Some important issues attract much attention, such as the computation of infinite domains, the treatment of softening of boundaries due to an incomplete horizon

The Material Point Method (MPM) can be regarded as a meshfree extension of the Finite Element Method (FEM). This fact has two interesting consequences. On the one hand, this puts a vast literature at our disposal, and much of the techniques originally engineered for the FEM can be adapted for the MPM framework with some modifications. On the other hand, many of this inheritance has been adopted without

Modeling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach toward constructing the governing equations of bending of an elastic-plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for

Based on the local frame approach, a new geometrically exact shell with drilling rotations is proposed in the SE(3) framework when dealing with the finite deformation and rotation issues. To eliminate the geometric nonlinearity of rigid-body motion, a drilling rotation formulation is applied to the 5-DoF shell presented in advance. As expected, the shell with drilling rotations completely eliminates

We introduce in this article a unified algorithm which allows the selection of collocation stencils, based on the visibility criterion, for convex, concave, and singular problems solved using a collocation method. The algorithm can be applied to any 2D or 3D problem. We show the importance of using a threshold angle, in conjunction with the visibility criterion, to assess of the inclusion of a node

In this article, the propagating effect of uncertainties in nonlinear structural systems is investigated. Via considering uncertain-but-bounded parameters as interval variables, a Newton iteration-based interval analysis method (NI-IAM) is proposed to quantify the uncertainty of the nonlinear structural response, namely predicting the upper and lower bounds of the response. In the proposed method,

This article proposes a generic approach to obtain semi-analytical mesh sensitivities and shows how to compute mesh updates for any tetrahedral mesher. The proposed strategy allows sensitivities to be computed for a given mesh or first improve an initial mesh and then compute sensitivities. The strategy is based on a modification of Persson and Strang's mesher, Distmesh, analogizing the mesh to a simple

Part consolidation (PC) is becoming a viable cost savings approach due to the increased design freedom associated with industry adoption of additive manufacturing. However, there is little research focused on mathematical approaches for assembly level design generation, with most work aimed at providing best practices for merging several parts into one. This article presents a novel topology optimization

In this work, we have developed a temperature-dependent higher-order Cauchy–Born (THCB) rule for multiscale crystal defect dynamics (MCDD) of crystalline solids based on the harmonic approximation. As a template, we employed the THCB rule to develop an atomistic-informed constitutive model for the body-centered cubic (BCC) single crystal tantalum ( α -Ta). Considering the effect of strain gradients

The peridynamic bond-associated material correspondence model is a reformulation of the conventional correspondence model, in which the concept of bond-associated states were introduced to inherently remove the material instability. Numerical studies, in terms of deformation analysis, have shown the effectiveness of the bond-associated model in removing the material instability. In this study, the

Over recent decades coupled MoM/FEM formulation emerged as dominant method for solving EM scattering problems over inhomogeneous domains. Initial efforts on coupling of edge element BEM with edge element FEM have lost momentum and somehow disappeared from recent literature, possibly because of mathematical and other issues. This article, however, presents correct coupling of edge element BEM with edge

In this paper, we address discrete linear systems in the frequency domain, where both frequency and random parameters are considered. Sampling such a system many times is computationally challenging if the size is too large, which is often the case for a finite element discretization of partial differential equations. We propose an adaptive method, steered by dual error indicators, which combines rational

C. A. Duarte commented on our paper,1 arguing that our work misrepresents and leads to incorrect conclusions about his manuscript.2 The source of the argument is the use of the name “Gupta, Duarte, and Dhankar's displacement correlation method” or “GDD-DCM” to refer to the particular version of the displacement correlation method (DCM) that we implemented in order to have a reference of performance

Error was identified in Reference 1 subsequent to its publication. The citing [12] should read as2: [12] Donea J, Huerta A, Ponthot J-Ph, Rodríguez-Ferran A. Arbitrary Lagrangian–Eulerian Methods, chapter 14. American Cancer Society, Atlanta, Georgia, 2004. The Figure reference “Figure 3A” on page 818 (both) and page 820, “Figure 1A”, should be read as, Figure 2A. We apologize for this error.

This paper considers the problem of determining probabilistic entropy fluctuations, which are important for understanding uncertainty propagation in mechanical systems in the elasto-plastic regime. Probabilistic entropy is conceptualized based on an initial definition by Shannon, which demands discrete representation of the uncertainty source. Numerical analysis is performed using the Response Function

In the present work, we consider the industrial problem of estimating in real-time the mold-steel heat flux in continuous casting mold. We approach this problem by first considering the mold modeling problem (direct problem). Then, we plant the heat flux estimation problem as the inverse problem of estimating a Neumann boundary condition having as data pointwise temperature measurements in the interior

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation

When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures

Soft wetting, that is, the interaction of liquid–fluid interfaces with deformable elastic structures, provides a rich variety of physical phenomena (stick-slip motion, durotaxis, Shuttleworth effect, etc.) which are not yet understood. We propose a novel phase-field approach to study such problems. The method uses two phase-fields to describe the three domains (solid, liquid, ambient fluid) by the

We propose a reformulation for a recent integral equations approach to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation results in additional speed-up and better convergence. We show that the solutions of the reformulated equations are in one-to-one correspondence with those of the original integral equations and derive conditions under which

A corotational flat shell element for the geometrically nonlinear analysis of laminated composite structures is presented. The element is obtained from the Hellinger–Reissner variational principle with assumed stress and displacement fields. The stress interpolation is derived from the linear elastic solution for symmetric composite materials. The element is isostatic, namely the stress interpolation

We present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The method is the automatic variationally stable FE method of Calo et al., in which we consider a Petrov–Galerkin weak formulation where the stress and displacement variables are in the space H(div) and H1, respectively. This allows us to employ a fully conforming FE discretization for

For effective bone healing, the stiffness of the bone plate should be adjusted to different bone-healing processes. Thus, the design of stiffness-changeable structures that take into account the time effect is of importance. To this end, this study introduces a novel topological optimization approach for the composite structural layout design considering material degradation to realize structures with

This article presents a methodology aiming at easing considerably the generation of high-quality meshes for complex three-dimensional (3D) domains. To this end, a mesh size field h(x) is computed, taking surface curvatures and geometric features into account. The size field is tuned by five intuitive parameters and yields quality meshes for arbitrary geometries. Mesh size is initialized on a surface

The base force element method (BFEM), formulated according the principle of complementary energy, is a new finite element method (FEM) that deals with nonlinear problems. Using the BFEM, the linear elastic model and large elastic deformation model of the plane truss element are derived, and the large elastic deformation model is expanded into a three-dimensional setting in this study. The rotating

This article presents a topology optimization method for structures consisting of multiple lattice components under a certain size, which can be manufactured with an additive manufacturing machine with a size limit and assembled via conventional joining processes, such as welding, gluing, riveting, and bolting. The proposed method can simultaneously optimize overall structural topology, partitioning

This article introduces the R2 Fill method, which is an algorithm for filling a region with particles isotropically. The method's isotropy is tested geometrically and then mechanically with the Discrete Element Method (DEM). It applies to planar and three-dimensional problems and is simpler to implement and has competitive metrics compared to other Advancing Front packing algorithms. The DEM formulation

In this article, a computational model is presented for the analysis of coupled thermo‐hydro‐mechanical process with phase change (evaporation/condensation) in fractured porous media in order to model multiphase fluid flows, heat transfer, and discontinuous deformation by employing the extended finite element method. The ideal gas law and Dalton's law are employed to consider vapor and dry air as miscible

This work presents an efficient and accuracy‐improved time explicit solution methodology for the simulation of contact‐impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bipenalty contact‐impact formulation that incorporates stiffness and mass penalties preserving the stability limit of contact‐free

This article presents two extensions of the empirical interpolation method (EIM) designed to deal with vector interpolation problems. These reduced‐order modeling techniques are aimed at exploiting pointwise (vector) measurements to obtain the unknown field reconstruction and they are preferred to other, more efficient, techniques as the proper orthogonal decomposition (POD) because of their intrinsic

An elastoplastic topology optimization framework for limiting plastic work generation while maximizing stiffness is presented. The kinematics and constitutive model are based on finite strain linear isotropic hardening plasticity, and the balance laws are solved using a total Lagrangian finite element formulation. Aggregation of the specific plastic work combined with an adaptive normalization scheme

We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve

The time‐discontinuous Galerkin finite element method (TDGFEM) has advantages in reducing spurious numerical oscillations and capturing discontinuities of solutions in space for high‐frequency dynamical problems. This article extends TDGFEM into Cosserat media to focus on impulse wave propagations, involving rotational wave and effects of microstructures. The Cosserat continuum theory contains additional

Model order reduction (MOR) has become one of the most widely used tools to create efficient surrogate models for time‐critical applications. For nonlinear models, however, linear MOR approaches are only practicable to a limited extent. Nonlinear approaches, on the contrary, often require intrusive manipulations of the used simulation code. Hence, nonintrusive MOR approaches using classic model order

A high‐performance shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell finite element method is proposed for linear and geometrically nonlinear analyses of shells. First, an arbitrary polygonal Mindlin–Reissner plate element and an arbitrary polygonal membrane element with drilling degrees of freedom are constructed based on hybrid displacement‐function and hybrid stress‐function

This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set‐valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method

The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the

This study proposes a topology optimization method for dynamic problems based on the finite deformation theory to derive a structure that can reduce deformations for arbitrary dynamic loads that have large deformations. To obtain a structure that can minimize deformations due to dynamic loading for the isotropic hyperelastic model, the square norm of dynamic compliance is set as the objective function

In the literature, blood flow study in an arterial segment/arterial network, using one‐dimensional wave propagation model, has been carried out considering flat/parabolic/logarithmic/different degree polynomial velocity profile functions. However, such assumptions are not capable of capturing actual blood and arterial wall interaction occurring while the blood flows through the arteries. In this study

In this article, a fully aggregation‐based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point systems can already be found, for example, in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development

Using an autoencoder for dimensionality reduction, this article presents a novel projection‐based reduced‐order model for eigenvalue problems. Reduced‐order modeling relies on finding suitable basis functions which define a low‐dimensional space in which a high‐dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose

The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite

In materials, the evolution of crack surfaces is intimately linked with the self‐contact occurring between them. The developed contact forces not only mitigate the effect of stress concentration at crack tip but also contribute significantly to the transfer of shear and normal stresses. In this article, we present a numerical framework to study the simultaneous process of fracture and self‐contact

Despite the potential and the increasing popularity of the boundary element method (BEM), modal analyses based on BEM are not yet put into engineering practice, mainly due to the lack of efficient solvers for the underlying nonlinear eigenvalue problem (EVP). In this article, we review a subspace iteration method based on FEAST for the solution of vibroacoustic EVPs involving the finite element method

In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise

The application of the submodeling technique to finite element (FE) wear analyses has been recently proposed as an efficient solution to reduce the computational cost of the simulations and provide accurate numerical results. However, the method was validated only on single point contact cases. The present study proposes a generalization of the wear submodeling procedure that can be used to speed up

Three kinds of fragile points methods based on Petrov‐Galerkin weak‐forms (PG‐FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow‐up of the previous study on the original FPM based on a symmetric Galerkin weak‐form. The trial function is piecewise‐continuous, written as local Taylor expansions at the fragile points. A modified radial basis