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Showing papers in "Computational Mechanics in 2014"


Journal ArticleDOI
TL;DR: PerMIX is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH for multiscale modeling and simulation of fracture in solids.
Abstract: We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation.

430 citations


Journal ArticleDOI
TL;DR: The present work describes continuum modeling of SLM as envisioned for eventual support of part-scale modeling of this fabrication process to determine end-state information such as residual stresses and distortion.
Abstract: Selective laser melting (SLM) is an additive manufacturing process in which multiple, successive layers of metal powders are heated via laser in order to build a part. Modeling of SLM requires consideration of both heat transfer and solid mechanics. The present work describes continuum modeling of SLM as envisioned for eventual support of part-scale modeling of this fabrication process to determine end-state information such as residual stresses and distortion. The determination of the evolving temperatures is dependent on the material, the state of the material (powder or solid), the specified heating, and the configuration. Similarly, the current configuration is dependent on the temperatures, the powder-solid state, and the constitutive models. A multi-physics numerical formulation is required to solve such problems. This article describes the problem formulation, numerical method, and constitutive parameters necessary to solve such a problem. Additionally, various verification and example problems are simulated in the parallel, multi-physics finite element code Diablo, and the results presented herein.

262 citations


Journal ArticleDOI
TL;DR: It is found that the variational immersed-boundary method for FSI remains robust and effective for heart valve analysis when the background fluid mesh undergoes deformations corresponding to the expansion and contraction of the elastic artery.
Abstract: We propose a framework that combines variational immersed-boundary and arbitrary Lagrangian---Eulerian 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 undergoes deformations corresponding to the expansion and contraction of the elastic artery Furthermore, the computations presented in this work show that the arterial wall deformation contributes significantly to the realism of the simulation results, leading to flow rates and valve motions that more closely resemble those observed in practice

250 citations


Journal ArticleDOI
TL;DR: In this article, an adaptive atomistic-continuum numerical method for quasi-static crack growth is proposed, where the phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip.
Abstract: This paper proposes an adaptive atomistic- continuum numerical method for quasi-static crack growth. The phantom node method is used to model the crack in the continuum region and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, a virtual atom cluster is used to model the material of the coarse scale. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip location. The triangular lattice in the fine scale region corresponds to the lattice structure of the (111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom---atom interactions. The method is implemented in two dimensions. The results are compared to pure atomistic simulations; they show excellent agreement.

207 citations


Journal ArticleDOI
TL;DR: In this paper, an extension of the quasi-static phase field model for fracture from Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) to the dynamic case is presented.
Abstract: Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented in Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) to the dynamic case. First of all Hamilton's principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.

202 citations


Journal ArticleDOI
TL;DR: In this paper, a Nitche's method is used to couple non-conforming two and three-dimensional non-uniform rational b-splines (NURBS) patches in the context of isogeometric analysis.
Abstract: We present a Nitche's method to couple non-conforming two and three-dimensional non uniform rational b-splines (NURBS) patches in the context of isogeometric analysis. We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications.

193 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics and obtained improved accuracy relative to the standard extended finite element method at a comparable computational cost.
Abstract: In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting.

181 citations


Journal ArticleDOI
TL;DR: In this article, the FFT-based homogenization for elastic problems at large deformations, with a focus on the following improvements, has been discussed, and an analytical solution for the micromechanical solution field of a two-phase isotropic St.Venant---Kirchhoff laminate is given.
Abstract: In recent years the FFT-based homogenization method of Moulinec and Suquet has been established as a fast, accurate and robust tool for obtaining effective properties in linear elasticity and conductivity problems. In this work we discuss FFT-based homogenization for elastic problems at large deformations, with a focus on the following improvements. Firstly, we exhibit the fixed point method introduced by Moulinec and Suquet for small deformations as a gradient descent method. Secondly, we propose a Newton---Krylov method for large deformations. We give an example for which this methods needs approximately 20 times less iterations than Newton's method using linear fixed point solvers and roughly $$100$$100 times less iterations than the nonlinear fixed point method. However, the Newton---Krylov method requires 4 times more storage than the nonlinear fixed point scheme. Exploiting the special structure we introduce a memory-efficient version with 40 % memory saving. Thirdly, we give an analytical solution for the micromechanical solution field of a two-phase isotropic St.Venant---Kirchhoff laminate. We use this solution for comparison and validation, but it is of independent interest. As an example for a microstructure relevant in engineering we discuss finally the application of the FFT-based method to glass fiber reinforced polymer structures.

155 citations


Journal ArticleDOI
TL;DR: This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM).
Abstract: This paper is the first investigation establishing the link between the meshfree state-based peridynamics method and other meshfree methods, in particular with the moving least squares reproducing kernel particle method (RKPM). It is concluded that the discretization of state-based peridynamics leads directly to an approximation of the derivatives that can be obtained from RKPM. However, state-based peridynamics obtains the same result at a significantly lower computational cost which motivates its use in large-scale computations. In light of the findings of this study, an update to the method is proposed such that the limitations regarding application of boundary conditions and the use of non-uniform grids are corrected by using the reproducing kernel approximation.

135 citations


Journal ArticleDOI
TL;DR: In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths.
Abstract: We present the space---time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

127 citations


Journal ArticleDOI
TL;DR: A space–time (ST) interface-tracking method that can deal with topology change (TC) and is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation ofThe interface motion.
Abstract: To address the computational challenges associated with contact between moving interfaces, such as those in cardiovascular fluid–structure interaction (FSI), parachute FSI, and flapping-wing aerodynamics, we introduce a space–time (ST) interface-tracking method that can deal with topology change (TC). In cardiovascular FSI, our primary target is heart valves. The method is a new version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method, and we call it ST-TC. It includes a master–slave system that maintains the connectivity of the “parent” mesh when there is contact between the moving interfaces. It is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation of the interface motion. We explain the method with conceptual examples and present 2D test computations with models representative of the classes of problems we are targeting.

Journal ArticleDOI
TL;DR: The shape optimization study is designed to reduce thrombotic risk, a major clinical problem in PVADs, and uses the surrogate management framework, a derivative-free pattern search optimization method that relies on surrogates for increased efficiency.
Abstract: In this paper we perform shape optimization of a pediatric pulsatile ventricular assist device (PVAD). The device simulation is carried out using fluid---structure interaction (FSI) modeling techniques within a computational framework that combines FEM for fluid mechanics and isogeometric analysis for structural mechanics modeling. The PVAD FSI simulations are performed under realistic conditions (i.e., flow speeds, pressure levels, boundary conditions, etc.), and account for the interaction of air, blood, and a thin structural membrane separating the two fluid subdomains. The shape optimization study is designed to reduce thrombotic risk, a major clinical problem in PVADs. Thrombotic risk is quantified in terms of particle residence time in the device blood chamber. Methods to compute particle residence time in the context of moving spatial domains are presented in a companion paper published in the same issue (Comput Mech, doi: 10.1007/s00466-013-0931-y , 2013). The surrogate management framework, a derivative-free pattern search optimization method that relies on surrogates for increased efficiency, is employed in this work. For the optimization study shown here, particle residence time is used to define a suitable cost or objective function, while four adjustable design optimization parameters are used to define the device geometry. The FSI-based optimization framework is implemented in a parallel computing environment, and deployed with minimal user intervention. Using five SEARCH/POLL steps the optimization scheme identifies a PVAD design with significantly better throughput efficiency than the original device.

Journal ArticleDOI
TL;DR: These computations demonstrate that the ST-TC method can bring interface-tracking accuracy to fluid mechanics of heart valves, and can do that with computational practicality.
Abstract: Fluid mechanics computation of heart valves with an interface-tracking (moving-mesh) method was one of the classes of computations targeted in introducing the space---time (ST) interface tracking method with topology change (ST-TC). The ST-TC method is a new version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It can deal with an actual contact between solid surfaces in flow problems with moving interfaces, while still possessing the desirable features of interface-tracking methods, such as better resolution of the boundary layers. The DSD/SST method with effective mesh update can already handle moving-interface problems when the solid surfaces are in near contact or create near TC, if the "nearness" is sufficiently "near" for the purpose of solving the problem. That, however, is not the case in fluid mechanics of heart valves, as the solid surfaces need to be brought into an actual contact when the flow has to be completely blocked. Here we extend the ST-TC method to 3D fluid mechanics computation of heart valve models. We present computations for two models: an aortic valve with coronary arteries and a mechanical aortic valve. These computations demonstrate that the ST-TC method can bring interface-tracking accuracy to fluid mechanics of heart valves, and can do that with computational practicality.

Journal ArticleDOI
TL;DR: In this article, the authors presented a sequentially-coupled space-time (ST) computational fluid-structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV).
Abstract: We present a sequentially-coupled space---time (ST) computational fluid---structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The structural mechanics computations are based on the Kirchhoff---Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.

Journal ArticleDOI
TL;DR: In this article, an improved meshless Shepard and least squares (MSLS) interpolation is developed by using dually defined nodal supports such that no singular weight function is required, and the proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain.
Abstract: The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.

Journal ArticleDOI
TL;DR: The results suggest that the proposed preconditioning scheme leads to condition numbers similar to that of a body-fitted mesh using the traditional finite element method without loss of solution accuracy.
Abstract: The extended finite element method (XFEM) is an approach for solving problems with non-smooth solutions, which arise from geometric features such as cracks, holes, and material inclusions. In the XFEM, the approximate solution is locally enriched to capture the discontinuities without requiring a mesh which conforms to the geometric features. One drawback of the XFEM is that an ill-conditioned system of equations results when the ratio of volumes on either side of the interface in an element is small. Such interface configurations are often unavoidable, in particular for moving interface problems on fixed meshes. In general, the ill-conditioning reduces the performance of iterative linear solvers and impedes the convergence of solvers for nonlinear problems. This paper studies the XFEM with a Heaviside enrichment strategy for solving problems with stationary and moving material interfaces. A generalized formulation of the XFEM is combined with the level set method to implicitly define the embedded interface geometry. In order to avoid the ill-conditioning, a simple and efficient scheme based on a geometric preconditioner and constraining degrees of freedom to zero for small intersections is proposed. The geometric preconditioner is computed from the nodal basis functions, and therefore may be constructed prior to building the system of equations. This feature and the low-cost of constructing the preconditioning matrix makes it well suited for nonlinear problems with fixed and moving interfaces. It is shown by numerical examples that the proposed preconditioning scheme performs well for discontinuous problems and $$C^0$$C0-continuous problems with both the stabilized Lagrange and Nitsche methods for enforcing the continuity constraint at the interface. Numerical examples are presented which compare the condition number and solution error with and without the proposed preconditioning scheme. The results suggest that the proposed preconditioning scheme leads to condition numbers similar to that of a body-fitted mesh using the traditional finite element method without loss of solution accuracy.

Journal ArticleDOI
TL;DR: In this paper, a modular computational framework was developed to combine the various steps within the overall additive manufacturing process, including particle deposition, laser heating, and phase transformation, and numerical examples were provided.
Abstract: Many additive manufacturing technologies involve the deposition of particles onto a surface followed by selective, targeted, laser heating. This paper develops a modular computational framework which combines the various steps within this overall process. Specifically, the framework synthesizes the following: Numerical examples are provided and extensions are also addressed for two advanced processing scenarios involving solid-liquid-gas phase transformations.

Journal ArticleDOI
Kenji Takizawa1
TL;DR: The new directions for the ST methods include the variational multiscale version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid meshes, and ST interface-tracking with topology change.
Abstract: This is an overview of the new directions we have taken the space---time (ST) methods in bringing solution and analysis to different classes of computationally challenging engineering problems. The classes of problems we have focused on include bio-inspired flapping-wing aerodynamics, wind-turbine aerodynamics, and cardiovascular fluid mechanics. The new directions for the ST methods include the variational multiscale version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid meshes, ST techniques with continuous representation in time, and ST interface-tracking with topology change. We describe the new directions and present examples of the challenging problems solved.

Journal ArticleDOI
TL;DR: A continuum-based model of particle residence time for moving-domain fluid mechanics and fluid–structure interaction (FSI) computations is proposed, analyzed, and applied to the simulation of an adult pulsatile ventricular assist device (PVAD).
Abstract: A continuum-based model of particle residence time for moving-domain fluid mechanics and fluid---structure interaction (FSI) computations is proposed, analyzed, and applied to the simulation of an adult pulsatile ventricular assist device (PVAD). Residence time is a quantity of clinical interest for blood pumps because it correlates with thrombotic risk. The proposed technique may be easily implemented in any flow or FSI solver. In the context of PVADs the results of the model may be used to assess how efficiently the pump moves the blood through its interior. Three scalar measures of particle residence time are also proposed. These scalar quantities may be used in the PVAD design with the goal of reducing thrombotic risk.

Journal ArticleDOI
TL;DR: In this paper, a fluid-structure interaction (FSI) analysis of the thoracic aorta was performed using the ST-VMS method, which is the variational multiscale version of the deforming-spatial-domain/stabilized space-time (DSD/SST) method.
Abstract: We present a fluid---structure interaction (FSI) analysis of the blood flow and geometrical characteristics in the thoracic aorta. The FSI is handled with the sequentially-coupled arterial FSI technique. The fluid mechanics equations are solved with the ST-VMS method, which is the variational multiscale version of the deforming-spatial-domain/stabilized space---time (DSD/SST) method. We focus on the relationship between the centerline geometry of the aorta and the flow field, which influences the wall shear stress distribution. The centerlines of the aorta models we use in our analysis are extracted from the CT scans, and we assume a constant diameter. Torsion-free model geometries are generated by projecting the original centerline to its averaged plane of curvature. The flow fields for the original and projected geometries are compared to examine the influence of the torsion.

Journal ArticleDOI
TL;DR: In this paper, the interface is discretized with generalized contact elements which account for both contact and cohesive debonding within a unified framework, which is suitable for non-matching discretizations of the interacting surfaces in presence of large deformations and large relative displacements.
Abstract: Cohesive zone (CZ) models have long been used by the scientific community to analyze the progressive damage of materials and interfaces. In these models, non-linear relationships between tractions and relative displacements are assumed, which dictate both the work of separation per unit fracture surface and the peak stress that has to be reached for the crack formation. This contribution deals with isogeometric CZ modeling of interface debonding. The interface is discretized with generalized contact elements which account for both contact and cohesive debonding within a unified framework. The formulation is suitable for non-matching discretizations of the interacting surfaces in presence of large deformations and large relative displacements. The isogeometric discretizations are based on non uniform rational B-splines as well as analysis-suitable T-splines enabling local refinement. Conventional Lagrange polynomial discretizations are also used for comparison purposes. Some numerical examples demonstrate that the proposed formulation based on isogeometric analysis is a computationally accurate and efficient technology to solve challenging interface debonding problems in 2D and 3D.

Journal ArticleDOI
TL;DR: This work introduces space–time computation techniques with continuous representation in time (ST-C), using temporal NURBS basis functions, and proposes two versions of ST-C, where the smooth solution is extracted by projection from a solution computed with a different temporal representation, typically a discontinuous one.
Abstract: We introduce space---time computation techniques with continuous representation in time (ST-C), using temporal NURBS basis functions. This gives us a temporally smooth, NURBS-based solution, which is desirable in some cases, and a more efficient way of dealing with the computed data. We propose two versions of ST-C. In the first version, the smooth solution is extracted by projection from a solution computed with a different temporal representation, typically a discontinuous one. We use a successive projection technique with a small number of temporal NURBS basis functions at each projection, and therefore the extraction can take place as the solution with discontinuous temporal representation is being computed, without storing a large amount of time-history data. This version is not limited to solutions computed with ST techniques. In the second version, the solution with continuous temporal representation is computed directly by using a small number of temporal NURBS basis functions in the variational formulation associated with each time step.

Journal ArticleDOI
TL;DR: In this article, a volume-compensated particle model (VCPM) is proposed for the study of fracture phenomena of homogeneous isotropic solids in a 2D non-local lattice spring model.
Abstract: A generalized 2D non-local lattice spring model, the Volume-Compensated Particle Model (VCPM), is proposed for the study of fracture phenomena of homogeneous isotropic solids in this paper. In the proposed VCPM, both the pairwise local and the multi-body non-local interaction forces among particles are considered. Special focus is on the investigation of the failure anisotropy or directional preference of the crack path while modeling fracture phenomena within the framework of regular lattice spring models. Different from random network models, a generalized regular lattice framework to include multiple non-local forces from neighboring particles is proposed to eliminate/reduce this well-known failure anisotropy issue. Several benchmarks are tested to assess the performance of the proposed methodology. Discussions and conclusions are drawn based on the current study.

Journal ArticleDOI
TL;DR: This work presents the special modeling techniques and strategies devised to address the computational challenges encountered in FSI modeling of the reefed stages and disreefing of the main and drogue parachutes and demonstrates that it has to a great extent overcome one of the most formidable challenges in F SI modeling of spacecraft parachutes.
Abstract: Orion spacecraft main and drogue parachutes are used in multiple stages, starting with a "reefed" stage where a cable along the parachute skirt constrains the diameter to be less than the diameter in the subsequent stage. After a period of time during the descent, the cable is cut and the parachute "disreefs" (i.e. expands) to the next stage. Fluid---structure interaction (FSI) modeling of the reefed stages and disreefing involve computational challenges beyond those in FSI modeling of fully-open spacecraft parachutes. These additional challenges are created by the increased geometric complexities and by the rapid changes in the parachute geometry during disreefing. The computational challenges are further increased because of the added geometric porosity of the latest design of the Orion spacecraft main parachutes. The "windows" created by the removal of panels compound the geometric and flow complexity. That is because the Homogenized Modeling of Geometric Porosity, introduced to deal with the flow through the hundreds of gaps and slits involved in the construction of spacecraft parachutes, cannot accurately model the flow through the windows, which needs to be actually resolved during the FSI computation. In parachute FSI computations, the resolved geometric porosity is significantly more challenging than the modeled geometric porosity, especially in computing the reefed stages and disreefing. Orion spacecraft main and drogue parachutes will both have three stages, with computation of the Stage 1 shape and disreefing from Stage 1 to Stage 2 for the main parachute being the most challenging because of the lowest "reefing ratio" (the ratio of the reefed skirt diameter to the nominal diameter). We present the special modeling techniques and strategies we devised to address the computational challenges encountered in FSI modeling of the reefed stages and disreefing of the main and drogue parachutes. We report, for a single parachute, FSI computation of both reefed stages and both disreefing events for both the main and drogue parachutes. In the case of the main parachute, we also report, for a 2-parachute cluster, FSI computation of the disreefing from Stage 2 to Stage 3. With results from these computations, we demonstrate that we have to a great extent overcome one of the most formidable challenges in FSI modeling of spacecraft parachutes.

Journal ArticleDOI
TL;DR: The present work proposes a consistent derivation of a new interface element for large deformation analyses that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface.
Abstract: Decohesion undergoing large displacements takes place in a wide range of applications. In these problems, interface element formulations for large displacements should be used to accurately deal with coupled material and geometrical nonlinearities. The present work proposes a consistent derivation of a new interface element for large deformation analyses. The resulting compact derivation leads to an operational formulation that enables the accommodation of any order of kinematic interpolation and constitutive behavior of the interface. The derived interface element has been implemented into the finite element codes FEAP and ABAQUS by means of user-defined routines. The interplay between geometrical and material nonlinearities is investigated by considering two different constitutive models for the interface (tension cut-off and polynomial cohesive zone models) and small or finite deformation for the continuum. Numerical examples are proposed to assess the mesh independency of the new interface element and to demonstrate the robustness of the formulation. A comparison with experimental results for peeling confirms the predictive capabilities of the formulation.

Journal ArticleDOI
TL;DR: The spectral cell method as mentioned in this paper is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure, taking advantage of explicit timeintegration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system.
Abstract: In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1---3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

Journal ArticleDOI
TL;DR: In this article, the Assumed Natural Strain (ANS) method proposed for Lagrangian formulations is extended to NURBS-based elements in the context of solid-shell formulations.
Abstract: In isogeometric analysis (IGA), the functions used to describe the CAD geometry (such as NURBS) are also employed, in an isoparametric fashion, for the approximation of the unknown fields, leading to an exact geometry representation. Since the introduction of IGA, it has been shown that the high regularity properties of the employed functions lead in many cases to superior accuracy per degree of freedom with respect to standard FEM. However, as in Lagrangian elements, NURBS-based formulations can be negatively affected by the appearance of non-physical phenomena that "lock" the solution when constrained problems are considered. In order to alleviate such locking behaviors, the Assumed Natural Strain (ANS) method proposed for Lagrangian formulations is extended to NURBS-based elements in the present work, within the context of solid-shell formulations. The performance of the proposed methodology is assessed by means of a set of numerical examples. The results allow to conclude that the employment of the ANS method to quadratic NURBS-based elements successfully alleviates non-physical phenomena such as shear and membrane locking, significantly improving the element performance.

Journal ArticleDOI
TL;DR: In this article, the conventional extended finite element method (XFEM) is enhanced to simulate dynamic crack branching, which is a top challenge issue in fracture mechanics and finite element methods.
Abstract: The conventional extended finite element method (XFEM) is enhanced in this paper to simulate dynamic crack branching, which is a top challenge issue in fracture mechanics and finite element method. XFEM uses the enriched shape functions with special characteristics to represent the discontinuity in computation field. In order to describe branched cracks, it is necessary to set up the additional enrichment. Here we have developed two kinds of branched elements, namely the "element crossed by two separated cracks" and "element embedded by a junction". Another series of enriched degrees of freedom are introduced to seize the additional discontinuity in the elements. A shifted enrichment scheme is used to avoid the treatment of blending element. Correspondingly a new mass lumping method is developed for the branched elements based on the kinetic conservation. The derivation of the mass matrix of a four-node quadrilateral element which contains two strong discontinuities is specially presented. Then by choosing crack speed as the branching criterion, the branching process of a single mode I crack is simulated. The results including the branching angle and propagation routes are compared with that obtained by the conventionally used element deletion method.

Journal ArticleDOI
TL;DR: In this paper, the authors present a model for incompressible finite strain orthotropic hyperelasticity using logarithmic strains, where the energy function shape and the material data of the model are obtained solving the equilibrium equations of the different experiments.
Abstract: We present a model for incompressible finite strain orthotropic hyperelasticity using logarithmic strains. The model does not have a prescribed shape. Instead, the energy function shape and the material data of the model are obtained solving the equilibrium equations of the different experiments. As a result the model almost exactly replicates the given experimental data for all six tests needed to completely define our nonlinear orthotropic material. We derive the constitutive tensor and demonstrate the efficiency of the finite element implementation for complex loading situations.

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TL;DR: The multiscale methods the authors devised for gore curvature calculation from FSI modeling of spacecraft parachutes are presented, including those based on the multiscales sequentially-coupled FSI technique and using NURBS meshes.
Abstract: There are now some sophisticated and powerful methods for computer modeling of parachutes. These methods are capable of addressing some of the most formidable computational challenges encountered in parachute modeling, including fluid---structure interaction (FSI) between the parachute and air flow, design complexities such as those seen in spacecraft parachutes, and operational complexities such as use in clusters and disreefing. One should be able to extract from a reliable full-scale parachute modeling any data or analysis needed. In some cases, however, the parachute engineers may want to perform quickly an extended or repetitive analysis with methods based on simplified models. Some of the data needed by a simplified model can very effectively be extracted from a full-scale computer modeling that serves as a pilot. A good example of such data is the circumferential curvature of a parachute gore, where a gore is the slice of the parachute canopy between two radial reinforcement cables running from the parachute vent to the skirt. We present the multiscale methods we devised for gore curvature calculation from FSI modeling of spacecraft parachutes. The methods include those based on the multiscale sequentially-coupled FSI technique and using NURBS meshes. We show how the methods work for the fully-open and two reefed stages of the Orion spacecraft main and drogue parachutes.