We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation

This contribution presents a theoretical and computational framework for two-scale shape optimisation of nonlinear elastic structures. Particularly, minimum compliance optimisation problems with composite (matrix-inclusion) microstructures subjected to static loads and volume-type design constraints are focused. A homogenisation-based FE\(^2\) scheme is extended by an enhanced formulation of variational

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented in a second order topology optimization framework

This work focuses on the development of a super-penalty strategy based on the \(L^2\)-projection of suitable coupling terms to achieve \(C^1\)-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee

Beam-in-beam large sliding contact exists in simulations of drillstring-riser systems, offshore pipe-in-pipe systems, medical catheter-guidewire-stent systems, among others. Large sliding between the pipes may lead to discontinuity of contact force and non-sparsity of system Jacobian in numeric simulations, which then may result in non-physical disturbances and low efficiency. To overcome this phenomenon

Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging to calibrate the model by inferring unknown parameters/fields (e.g., boundary conditions, mechanical properties, and operating parameters) from sparse and noisy

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential

In this work we present a simple and convenient method for handling tensors within computational mechanics frameworks based on the Kelvin decomposition. This methodology was set up within a crystal plasticity framework which permits, using the Kelvin base related to the crystal symmetries, to account for elastic anisotropy. The classical mixed velocity pressure finite element formulation has been modified

This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod’s cross-section, one then obtains discrete points

The contact of nominally flat surfaces can be treated as a bilateral periodic contact problem considering the stochastic surface similarity to the asperity distribution in a representative region. This similarity treatment method can be extended to material inhomogeneities. A novel numerical model for simulating the elastoplastic contact between nominally flat surfaces of materials containing inhomogeneities

We use the algebraic orthogonality of rotation-free and divergence-free fields in the Fourier space to derive the solution of a class of linear homogenization problems as the solution of a large linear system. The effective constitutive tensor constitutes only a small part of the solution vector. Therefore, we propose to use a synchronous and local iterative method that is capable to efficiently compute

A mesh size objective multiscale modeling is developed for fatigue failure prediction of long fiber-reinforced composites based on the multiscale discrete damage theory (MDDT). MDDT tracks the failure processes along discrete failure surfaces at the microscale and concurrently bridges it to continuum-based description of damage at the macroscale. The proposed approach achieves mesh-size objectivity

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used

Recurrent neural networks (RNNs) have demonstrated very impressive performances in learning sequential data, such as in language translation and music generation. Here, we show that the intrinsic computational aspect of RNNs is very similar to that of classical stress update algorithms in modeling history-dependent materials with an emphasis on viscoelasticity. Several numerical examples are designed

Phase field models for fracture are energy-based and employ a continuous field variable, the phase field, to indicate cracks. The width of the transition zone of this field variable between damaged and intact regions is controlled by a regularization parameter. Narrow transition zones are required for a good approximation of the fracture energy which involves steep gradients of the phase field. This

This paper studies the evolution of intergranular localization and stress concentration in three dimensional micron sized specimens through the Gurtin grain boundary model (J Mech Phys Solids 56:640–662, 2008) incorporated into a three dimensional higher-order strain gradient crystal plasticity framework (Yalçinkaya et al. in Int J Solids Struct 49:2625–2636, 2012). The study addresses continuum scale

In nonlinear analysis, performing iterative inverse calculation and nonlinear system construction procedures incurs expensive computational costs. This paper presents an element-wise stiffness evaluation procedure combined with hyper-reduction reduced-order modeling (HE-STEP ROM) method. The proposed approach constructs a non-intrusive reduced-order model based on an element-wise stiffness evaluation

With the rapid developments of modern fabrication techniques, architected structures are increasingly used in many application areas, e.g., lightweight structures, heat exchangers, energy absorption components, aircraft engines, etc. To systematically design optimized architected structures with favorable manufacturability in terms of exact sizes and good connectivity, in the present work, an enhanced

This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance

A stabilized finite element framework for high-speed compressible flows is presented. The Streamline-Upwind/Petrov–Galerkin formulation augmented with discontinuity-capturing (DC) are the main constituents of the framework that enable accurate, efficient, and stable simulations in this flow regime. Full- and reduced-energy formulations are employed for this class of flow problems and their relative

We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that demand a careful analysis when discretized: first, the treatment of periodic boundary conditions; second, the formulation of approximations of systems with three-body

Homogenization theory forms the basis for solving the topology optimization problem (TOP) formulated for designing composite materials. Homogenization is proved to be an efficient approach to effectively determine the equivalent macroscopic properties of the composite material. It relies on the assumption that the composite material presents a periodic pattern on a microstructural level; the simplest

In this study a modeling approach for short fiber-reinforced composites is presented which allows one to consider information from the microstructure of the compound while modeling on the component level. The proposed technique is based on the determination of correlation functions by the moving window method. Using these correlation functions random fields are generated by the Karhunen–Loève expansion

We propose a set of numerical methods for the computation of the frequency-dependent effective primary wave velocity of heterogeneous rocks. We assume the rocks’ internal microstructure is given by micro-computed tomography images. In the low/medium frequency regime, we propose to solve the acoustic equation in the frequency domain by a finite element method (FEM). We employ a perfectly matched layer

This work addresses simultaneous use of geometrically exact shear-rigid rod and shell finite elements and describes both models within the same framework. Parameterization of the rotation field is performed by Rodrigues rotation vector, which makes the incremental updating of the rotational variables remarkably simple. For the rod element, cubic Hermitian interpolation for the displacements together

In this paper, a phase field model of ductile fracture is described within the framework of large plastic strains. Most results dealing with phase field modeling of ductile fracture are carried out on a fixed mesh, which requires a fine mesh throughout all the computation. The aim of this paper is to introduce an adaptive isotropic remeshing strategy coupled with a phase field model of ductile fracture

A multiphase microstructural system of two types of hydrides; f.c.c. δ and b.c.c.. ε hydride precipitates within a parent h.c.p. zircaloy-4 parent matrix were modelled by a crystalline dislocation-density and a finite-element (FE) method that is specialized for large inelastic strains and nonlinear behavior. The different crystalline structure of the hydrides, the parent matrix, and the orientation

Based on the complementary potential energy variational principle, in this work, we proposed a stress-driven homogenization procedure to compute overall effective material properties for elastic composites with locally heterogenous micro-structures. We have developed a novel incremental variational formulation for homogenization problems of both infinitesimal and finite deformations where the macro-stress-based

Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers

The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great potential in the breakthrough of metal additive manufacturing (AM) process modeling, which is an indispensable step to derive the process-structure-property relationship. However, the success of conventional machine learning tools in data science is primarily attributed to the unprecedented large amount of labeled

Multi-dimensional advection diffusion equations involving fractional diffusion flux are studied with finite element formulation. It has been demonstrated that the Galerkin finite element formulation may suffer spatial instability and nodal oscillations due to the fractional diffusion flux in addition to the advection term. To resolve this issue, a fractional streamline upwind Petrov-Galerkin finite

Micromechanics of strain rate dependent elastic response, within the proportionality limit in metals is investigated, on the basis of dislocation kinetics. It is postulated that, the strain rate dependence of proportionality limit stress is dominated by inertia of dislocations, over drag controlled mechanisms. Subsequently, kinetic energy of accelerating edge dislocation at its incipient motion, is

The Periodontal Ligament (PDL) plays a very important role in load transmission between the teeth and alveolar bone. To capture biomechanical responses of Orthodontics, numerical analysis need to consider multiple types of materials: incompressible visco-hyperelastic for the PDL and compressible elastic for teeth. This article proposes a unified-implementation of smoothed finite element methods (UI-SFEM)

In this paper, we outline a constitutive model capable of describing anisotropy and many other features of the behaviour of multiphase granular soils, together with the computational framework that enables its numerical implementation. The constitutive model is formulated within the framework of bounding surface plasticity. It can simulate monotonic and cyclic loading for a wide range of stress and

This study proposes a new elastic–plastic deformation decomposition algorithm for metal clusters to calculate micro-nanoscale elastic and plastic deformation gradients. In the macroscopic plasticity theory, the intermediate configuration is usually constructed by the dissection–unloading method. Because an atomic cluster is equivalent to a small element on a macroscopic object, our decomposition algorithm

In the presented work, a nonlocal gradient enhanced damage model for concrete is proposed with a stress decomposition, to account for shear induced damage. The nonlocal model is an extension of the recently proposed local plasticity damage model by the authors, which can handle directional dependency of damage, pure shear and biaxial damage, damage activation/deactivation and microcracks opening/closure

We present a novel approach to topology optimization based on thermodynamic extremal principles. This approach comprises three advantages: (1) it is valid for arbitrary hyperelastic material formulations while avoiding artificial procedures that were necessary in our previous approaches for topology optimization based on thermodynamic principles; (2) the important constraints of bounded relative density

A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The

An earlier version of this article included a number of typesetting mistakes. These were corrected on October 16, 2020. The publisher apologizes for the errors made during production. The symbol “Λn” was incorrectly published as “Γn” in equations 46 and 47. The correct equations are provided in this correction.

An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh moving technique (MMT) used to adapt the computational mesh in the moving fluid domain. An ideal MMT is computationally inexpensive, can handle large mesh motions without inverting mesh elements and can sustain an FSI simulation for extensive periods of time without irreversibly distorting the

This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are considered. A highly flexible analytical approach proposed

Second-order unconditionally stable schemes of linear multi-step methods, and their equivalent single-step methods, are developed in this paper. The parameters of the linear two-, three-, and four-step methods are determined for optimal accuracy, unconditional stability and tunable algorithmic dissipation. The linear three- and four-step schemes are presented for the first time. As an alternative,

An energy–momentum conserving temporal integration scheme is presented for a recently proposed geometrically exact shell formulation with drilling degrees of freedom. The scheme is based on a novel idea of defining mixed discrete derivatives for holonomic constraint functions with displacements and rotations. By defining general discrete derivative expressions with unknown terms, the mixed discrete

Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material originating from unresolved heterogeneities and the

Grain boundary strengthening effect for polycrystalline copper is studied numerically using crystal plasticity in conjunction with cylindrical indentation simulations under the plane strain condition. In order to compare with an isotropic, heterogeneous continuum model a new constitutive relation is developed. This new nonlocal continuum model that encompasses the heterogeneity in yield strength based

In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The classical

This paper investigates the dynamic characteristics of a multilevel structure for the transportation and storage of spent nuclear fuel (SNF) from commercial power plants. The nuclear fuel is stored in slender rods that are grouped together into fuel assemblies (FA). In a sealed cylindrical container called “canister”, the FA are inserted into a honeycomb basket. The objective of this paper is to develop

Light structural metals have been extensively applied throughout the transportation sector in recent years with greater impetus to reduce vehicle weight and enhance energy efficiency. However, their use is restricted by the engineering challenge of fatigue crack growth and the need to understand, simulate, and predict crack propagation mechanisms with respect to materials’ microstructure. To address

A class of isothermal dissipative continua being often referred to as “standard dissipative” is considered. The initial boundary value problem describing the behavior of these continua can be conveniently formulated in terms of a Helmholtz free energy functional, a dissipation functional, a power functional, and, possibly, a Lagrangian multiplier functional. In order to obtain (approximate) solutions

Statistical Volume Elements (SVEs) are employed to evaluate homogenized mesoscopic ductile failure response of a carbon nanofiber reinforced composite under uniaxial tensile and compressive loadings. In the mesoscale analysis, after virtual reconstruction of the material microstructure, 2D finite element models are generated for each SVE using a non-iterative meshing algorithm named CISAMR, which fully

The paper deals with a numerical model to investigate the influence of stress state on damage and failure in the ductile steel X5CrNi18-10. The numerical analysis is based on an anisotropic continuum damage model taking into account yield and damage criteria as well as evolution equations for plastic and damage strain rate tensors. Results of numerical simulations of biaxial experiments with the X0-

The hierarchical deep-learning neural network (HiDeNN) is systematically developed through the construction of structured deep neural networks (DNNs) in a hierarchical manner, and a special case of HiDeNN for representing Finite Element Method (or HiDeNN-FEM in short) is established. In HiDeNN-FEM, weights and biases are functions of the nodal positions, hence the training process in HiDeNN-FEM includes

The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions and the displacement fields. The underlying idea embedded in arbitrary finite polygons

Neural network constitutive models (NNCMs) for crystal structures are proposed based on computationally generated high-fidelity data. Stress, and tangent modulus data are generated under various strain states using empirical potentials and first-principles calculations. Strain–stress artificial neural network and strain-tangent modulus ANN are constructed. The symmetry conditions are considered for

This paper presents an adaptive strategy for phase-field simulations with transition to fracture. The phase-field equations are solved only in small subdomains around crack tips to determine propagation, while an extended finite element method (XFEM) discretization is used in the rest of the domain to represent sharp cracks, enabling to use a coarser discretization and therefore reducing the computational

We demonstrate a Bayesian method for the “real-time” characterization and forecasting of partially observed COVID-19 epidemic. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and

The standard Yee FDTD algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of this classical scheme to 3D unstructured co-volume meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This circumvents the problem of accuracy losses, which are normally associated with the use of a staircased

The original article was published with errors in some sentences. The correct sentences are provided in this correction.

Fully coupled global equations are proposed for enhancing the performance of Finite Element analysis of unsaturated soils. The governing equation describing mechanical equilibrium is formulated in terms of net stress, and in the mass conservation equation the contribution of this net stress in determining the change of degree of saturation is also included. The novelty of this paper is the development

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with