Abstract A novel technique to formulate arbritrary faceted polyhedral elements in three-dimensions is presented. The formulation is applicable for arbitrary faceted polyhedra, provided that a scaling requirement is satisfied and the polyhedron facets are planar. A triangulation process can be applied to non-planar facets to generate an admissible geometry. The formulation adopts two separate scaled

Abstract The moving particle simulation (MPS) method has proved to be an effective technique to model fluid flows with free surfaces. However, it still remains a challenging task to treat the wall boundary problem with complicated geometries accurately and robustly. The purpose of this work is to propose a two-dimensional ghost cell boundary model for the explicit MPS method to achieve this end. The

Abstract Computational analysis of particle-laden-airflow erosion can help engineers have a better understanding of the erosion process, maintenance and protection of turbomachinery components. We present an integrated method for this class of computational analysis. The main components of the method are the residual-based Variational Multiscale (VMS) method, a finite element particle-cloud tracking

Abstract We present a phase field based MITC4+ shell element formulation to simulate fracture propagation in thin shell structures. The employed MITC4+ approach renders the element shear- and membrane- locking free, hence providing high-fidelity fracture simulations in planar and curved topologies. To capture the mechanical response under bending-dominated fracture, a crack-driving force description

Abstract We describe a strategy for implicit a posteriori error estimation in cut finite elements. Our approach is based on the definition of local residual-driven corrector problems that use a local order elevation of the finite element space to construct a correction of the current approximation. The recovered higher-order accurate approximation is then used to construct error estimation in energy

Abstract Numerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for

Abstract An isotropic gradient-enhanced damage model is applied to shape optimisation in order to establish a computational optimal design framework in view of optimal damage distributions. The model is derived from a free Helmholtz energy density enriched by the damage gradient contribution. The Karush–Kuhn–Tucker conditions are solved on a global finite element level by means of a Fischer–Burmeister

Abstract Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome

Abstract This work presents a fast Fourier transform (FFT) based method that can be used to model interface decohesion. The inability of an FFT solver to deal with sharp interfaces discards the use of conventional cohesive zones to model the interfacial mechanical behaviour within this framework. This limitation is overcome by approximating sharp interfaces (e.g. grain/phase boundaries) with an interphase

Abstract This paper presents an analysis of the vibrational behavior of a rotating viscoelastic sandwich pre-twisted beams with a setting angle and with various viscoelastic stiffness laws. The governing equations of motion are derived using the Lagrange formulation and the assumed modes method. The obtained nonlinear eigenvalue problems are solved by using an iterative nonlinear eigensolver leading

Abstract This study proposes new models for thermodynamic properties and thermoelastic constitutive relation of materials with cubic crystal structures. The motion equation of atoms in cubic crystal structures is decomposed into structural deformation and thermal vibration at first. Then based on the thermo-mechanical coupling mechanism, both the thermal and mechanical aspects of structural deformation

Abstract Variational multiscale methods, and their precursors, stabilized methods, have been playing a core-method role in semi-discrete and space–time (ST) flow computations for decades. These methods are sometimes supplemented with discontinuity-capturing (DC) methods. The stabilization and DC parameters embedded in most of these methods play a significant role. Various well-performing stabilization

Abstract This paper describes a new surface-to-surface contact search method for contact problems between curved surfaces defined by the non-uniform rational B-spline basis functions. The method consists of a global search method based on the hierarchical virtual axis aligned bounding boxes and a local contact search method enhanced by the deep learning. The artificial neural network is employed to

Abstract A new numerical approach for the time independent Helmholtz equation on irregular domains has been developed. Trivial Cartesian meshes and simple 9-point stencil equations with unknown coefficients are used for 2-D irregular domains. The calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the

Abstract Industrial forming processes depend on several physical effects, including large deformation thermomechanical damage, localized near the contact zone of the forming tools. The main challenge in this process relies on the detailed knowledge of the desired thermoplastic effects at finite strains and the undesired initiation of macro-cracks. For the numerical solution of this problem, a regularized

Abstract We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s

Abstract This paper is concerned with the energy-dissipation Brezis–Ekeland–Nayroles variational principle (BEN principle) for the numerical study of quasi-static elastoplastic and viscoplastic problems in small strains. This principle is based on the dissipation potential and its Fenchel transform and allows to have a consistent view of the whole evolution by computing the nonlinear response along

Abstract This study presents a crack phase-field approach for anisotropic continua to model, in particular, fracture of fiber-reinforced matrix composites. Starting with the variational formulation of the multi-field problem of fracture in terms of the deformation and the crack phase fields, the governing equations feature the evolution of the anisotropic crack phase-field and the balance of linear

Abstract This work develops a simple finite element for the geometrically exact analysis of Bernoulli–Euler rods. Transversal shear deformation is not accounted for. Energetically conjugated cross-sectional stresses and strains are defined. A straight reference configuration is assumed for the rod. The cross-section undergoes a rigid body motion. A rotation tensor with the Rodrigues formula is used

Abstract In this work, we focus on the family of shell formulations referred to as “solid shells”, where the simulation of shell-type structures is performed by means of a mesh of 3D solid elements, with typically only one element through the thickness. We propose a novel approach for alleviating shear and membrane locking phenomena, which typically appear in thin structures, based on the projection

Abstract A numerical formulation for the modeling of turbulent cavitating flows is presented. The flow field is governed by the 3D, time-dependent Navier–Stokes equations for a compressible isothermal mixture. The Arbitrary Lagrangian–Eulerian Variational Multiscale (ALE-VMS) formulation is adopted to model the turbulent flow on moving domains with no-slip boundary conditions imposed weakly. The formulation

Abstract This paper discusses the finite element modeling of cracking of quasi-brittle materials under cyclic loading. A damage based crack model is proposed, which considers tensile and compressive damage, irreversible strains upon unloading in compression, as well as micro-crack closure-reopening effects with special attention to the sliding of open cracks (MCRS). The model is implemented in conjunction

Abstract A new adaptive refinement strategy for phase-field models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phase-field models. The strategy is based on considering two types of elements: h-refined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest

Abstract Fine scale computations of bolted assemblies are generally too costly and hardly tractable within an optimization process. Thus, finite elements (FE) connectors or user-elements are commonly used in FE commercial codes by engineers as substitutes for bolts. In this paper, a non-linear FE connector with its identification methodology is proposed to model the behaviour of a single-bolt joint

Deformation of soft polymeric materials often involves complex nonlinear or transient mechanical behaviors. This is due to the dynamic behaviors of polymer chains at the molecular level within the polymer network. In this paper, we present a computational formulation to describe the transient behavior (e.g., viscoelasticity) of soft polymer networks with dynamic bonds undergoing large to extreme deformation

Radio-frequency electrosurgical procedures are widely used to simultaneously dissect and coagulate tissue. Experiments suggest that evaporation of cellular and intra-cellular water plays a significant role in the evolution of the temperature field at the tissue level, which is not adequately captured in a single scale energy balance equation. Here, we propose a two-scale model to study the effects

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of

We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem

Micro-structural analyses are an important tool to understand material behavior on a macroscopic scale. The analysis of a microstructure is usually computationally very demanding and there are several reduced order modeling techniques available in literature to limit the computational costs of repetitive analyses of a single representative volume element. These techniques to speed up the integration

When immersed in solution, surface-active particles interact with solute molecules and migrate along gradients of solute concentration. Depending on the conditions, this phenomenon could arise from either diffusiophoresis or the Marangoni effect, both of which involve strong interactions between the fluid and the particle surface. We introduce here a numerical approach that can accurately capture these

Axons are living systems that display highly dynamic changes in stiffness, viscosity, and internal stress. However, the mechanistic origin of these phenomenological properties remains elusive. Here we establish a computational mechanics model that interprets cellular-level characteristics as emergent properties from molecular-level events. We create an axon model of discrete microtubules, which are

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks

A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface

This contribution presents a novel homogenization technique for modeling heterogeneous materials with micro-inertia effects such as locally resonant acoustic metamaterials. Linear elastodynamics is used to model the micro and macro scale problems and an extended first order Computational Homogenization framework is used to establish the coupling. Craig Bampton Mode Synthesis is then applied to solve

This paper builds on a recently developed immersogeometric fluid-structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition

We propose a framework that combines variational immersed-boundary and arbitrary Lagrangian-Eulerian (ALE) methods for fluid-structure interaction (FSI) simulation of a bioprosthetic heart valve implanted in an artery that is allowed to deform in the model. We find that the variational immersed-boundary method for FSI remains robust and effective for heart valve analysis when the background fluid mesh

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally

This work focuses on the identification of heterogeneous linear elastic moduli in the context of frequency-domain, coupled acoustic-structure interaction (ASI), using either solid displacement or fluid pressure measurement data. The approach postulates the inverse problem as an optimization problem where the solution is obtained by minimizing a modified error in constitutive equation (MECE) functional

The complex vascular dynamics and wall deposition of systemically injected nanoparticles is regulated by their geometrical properties (size, shape) and biophysical parameters (ligand-receptor bond type and surface density, local shear rates). Although sophisticated computational models have been developed to capture the vascular behavior of nanoparticles, it is increasingly recognized that purely deterministic

A multi-physics model was developed to study the delivery of magnetic nanoparticles (MNPs) to the stent-implanted region under an external magnetic field. The model is firstly validated by experimental work in literature. Then, effects of external magnetic field strength, magnetic particle size, and flow velocity on MNPs' targeting and binding have been analyzed through a parametric study. Two new

Micron- to nanometer-sized ultrasound agents, like encapsulated microbubbles and echogenic liposomes, are being developed for diagnostic imaging and ultrasound mediated drug/gene delivery. This review provides an overview of the current state of the art of the mathematical models of the acoustic behavior of ultrasound contrast microbubbles. We also present a review of the in vitro experimental characterization

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational efficiency remains to be highly relevant. In this paper, we present two methods to overcome locking phenomena, one based on a displacement-pressure formulation using