Method For Large Deformation Analysis Research Articles

Weighted radial basis collocation method for large deformation analysis of rubber-like materials

A nonlinear formulation, based on the total Lagrange description of the weighted radial basis collocation method (WRBCM), is proposed for the large deformation analysis of rubber-like materials where the materials are hyperelastic and nearly incompressible. The WRBCM based on the strong form collocation is a genuinely meshfree method that eliminates the need for meshing. As a result, it effectively circumvents challenges associated with mesh distortion during large deformation analysis. The proper weights that should be imposed on the boundary collocation equations are first derived to achieve the optimal convergence in hyperelasticity. In the WRBCM, the support of the shape function remains unchanged throughout material deformation, thereby guaranteeing the absence of tension instability during large deformation analysis. Additionally, by combining WRBCM with a least-squares solution, volumetric locking in nearly incompressible hyperelastic problems can be suppressed. This is due to the infinite continuity possessed by the radial basis approximation, which ensures the divergence-free condition. Several numerical examples are examined, demonstrating the high accuracy and exponential convergence of WRBCM in hyperelastic large deformation analysis. Moreover, no volumetric locking can be observed which further substantiates the effectiveness of applying nonlinear WRBCM to nearly incompressible hyperelastic problems.

Arbitrary mesh‐moving velocity‐based space‐time finite element method for large deformation analysis of solids

SummaryThis paper presents a new velocity‐based space‐time finite element method for computing the large deformation of solids over arbitrary Lagrange/Eulerian moving meshes. The proposed method is oriented toward quasi‐static deformation problems with hypoelastic and neo‐Hookean hyperelastic constitutive models. The Cauchy stress in the weak form of the linear momentum equation is explicitly described in terms of deformation velocity through consistent time integration of objective stress rates transferred in the arbitrary moving mesh. Consequently, the resultant system equation only contains the space‐time nodal velocity as the primary unknown. An iterative algorithm for solving the discretized system equation is implemented, whereby the nonlinearities induced by geometrical change in the computational domain as well as nonlinear constitutive equations are computed in an iterative manner updating the stress and the strain over the moving mesh of the deforming domain. Three benchmark problems, such as uniform beam compression, thick‐cylinder compression with superimposed rigid body rotation and extrusion of a column involving material loss, have been solved in order to examine the accuracy of the proposed numerical scheme. The numerical results have revealed the proper computation of the stress and the displacement of the solids undergoing the large deformation and rotation over the arbitrary Lagrange/Eulerian moving meshes, and have shown the validity and applicability of the proposed method with linear convergence of the iterative algorithm.

A compatible mixed finite element method for large deformation analysis of two‐dimensional compressible solids in spatial configuration

AbstractIn this article, a new mixed finite element formulation is presented for the analysis of two‐dimensional compressible solids in finite strain regime. A three‐field Hu–Washizu functional, with displacement, displacement gradient and stress tensor considered as independent fields, is utilized to develop the formulation in spatial configuration. Certain constraints are imposed on displacement gradient and stress tensor so that they satisfy the required continuity conditions across the boundary of elements. From theoretical standpoint, simplex elements are best suited for the application of continuity constraints. The techniques that are proposed to implement the constraints facilitate their automatic imposition and, hence, they can be regarded as an important feature of the work. Since the exterior calculus provides the basis for the developments presented herein, the relevant topics are discussed within the context of the work. Various technical aspects of the formulation are described in detail. These aspects help to illuminate the mathematical formulation that might seem vague in the first place and, more importantly, they help to provide an efficient implementation for ensuing developments. The performance of the mixed finite element method is studied through benchmark numerical examples and it is compared with other similar elements. It is shown that the element has excellent convergence properties and it is numerically stable, especially for problems where classical first order elements demonstrate stiff or unstable behavior.

A decoupled Arbitrary Lagrangian-Eulerian method for large deformation analysis of saturated sand

In the finite element analysis, large deformation caused by saturated sand liquefaction may lead to numerical problems owing to mesh distortion. Based on the soil–water two-phase mixing theory, the governing equations of the two-phase mixture are derived in the study. Using the operator splitting technique and the decoupled Arbitrary Lagrangian-Eulerian (ALE) frame, a decoupled ALE Finite Element Method is developed to solve the numerical problems caused by the possible mesh distortion in the liquefaction large deformation analysis. The method is applied to one-dimensional consolidation analysis and dynamic liquefaction large deformation analysis of an embankment. The results show that the method can keep the deformed mesh in a healthy state and ensure the accuracy of the numerical solutions in large deformation analysis.

Large deformation finite element analyses in TBM tunnel excavation: CEL and auto-remeshing approach

Analyzing tunnel excavation behavior involves large deformation issues. For this reason, large deformation analysis method is required to rigorously investigate the actual effect of excavation on surrounding ground. Two major numerical approaches capable of considering large deformations are applied to investigating the effect of tunnel boring machine excavation: coupled Eulerian-Lagrangian (CEL) and the automatic remeshing after small strain approach. The theoretical basis and application of the methods will be discussed before their relative performance is evaluated through the ground response due to TBM excavation. The ground response will be quantified by estimating the range of the excavation damaged zone (EDZ). By comparing the results, the range of the size of the EDZ will be suggested along the vertical and horizontal direction along the TBM advancement. Based on the computed results, it was found that the size of EDZ around the excavation surface and the tendencies was in good agreement among the two methods. Numerical results clearly show that the size of the EDZ around the tunnel tends to be bigger for harder rocks. The size of the EDZ is found to be direct proportional to the tunnel diameter, whereas the depth of the tunnel is inversely proportional due to higher confinement stress around the excavation surface.

GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics

Particle finite element method (PFEM) is an effective numerical tool for solving large-deformation problems in geomechanics. By incorporating the node integration technique with strain smoothing into the PFEM, we proposed the smoothed particle finite element method (SPFEM). This paper extends the SPFEM to three-dimensional cases and presents a SPFEM executed on graphics processing units (GPUs) to boost the computational efficiency. The detailed parallel computing strategy on GPU is introduced. New computation formulations related to the strain smoothing technique are proposed to save memory space in the GPU parallel computing. Several benchmark problems are solved to validate the proposed approach and to evaluate the GPU acceleration performance. Numerical examples show that with the new formulations not only the memory space can be saved but also the computational efficiency is improved. The computational cost is reduced by ~70% for the double-precision GPU parallel computing with the new formulations. Compared with the sequential CPU simulation, the GPU-accelerated simulation results in a significant speedup. The overall speedup ranges from 8.21 to 11.17 for double-precision simulations. Furthermore, the capability of the GPU-accelerated SPFEM in solving large-scale complicated problems is demonstrated by modelling the progressive failure of a long slope with strain-softening soil.

Computational efficient discrete time transfer matrix method for large deformation analysis of flexible manipulators

In this article, a large deformation analysis of a flexible manipulator is examined by using the discrete time transfer matrix method. Since this robotic analysis is very demanding in terms of both computation time and memory usage, the main goal is to reduce the computational complexity compared to the conventional algorithm. In this study, the proposed model is validated with Euler–Bernoulli beam and a corresponding ADAMS model. A planar robotic arm in the presence of links and joints flexibility is studied. It concludes that the theoretical formulation attributes for large flexible multibody systems and practical robotic application.

Strong-Form Formulated Generalized Displacement Control Method for Large Deformation Analysis

The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocation methods computationally efficient. In the incremental–iterative process, how to accurately reflect the change in the slope of the load–deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.

On large deformation analysis method using mesh-independent data points to store the strain history dependent quantities

On large deformation analysis method using mesh-independent data points to store the strain history dependent quantities

On Application of the Maximum Entropy Meshless Method for Large Deformation Analysis of Geotechnical Problems

Traditional grid-based numerical techniques such as the Finite Element Method (FEM) are known to suffer when large deformations of the continuum are encountered. As such, there has been limited success using this class of methods to solve many of the complex problems encountered in computational geomechanics. The potential of Meshfree techniques for addressing this perceived deficiency has been recognised. This study presents a robust Maximum Entropy Meshless (MEM) method for the analysis of problems involving geometrical nonlinearity in computational geomechanics. The method is validated via simulation of an undrained layer of soil under a rigid and rough strip footing undergoing large deformations and its merit is demonstrated through a comparison of the results with those obtained via the FEM.

Spatiotemporal evolution rule of rocks fracture surrounding gob-side roadway with model experiments

A series of plane-strain physical model experiments are carried out to study the spatiotemporal evolution rule of rocks fracture surrounding gob-side roadway, which is subjected to the pressure induced by the mining process. The digital photogrammetry technology and large deformation analysis method are applied to measure the deformation and fracture of surrounding rocks. The experimental results indicate that the deformation and fracture of coal pillars are the cause to the instability and failure of the surrounding rocks. The spatiotemporal evolution rule of the rock deformation and fracture surrounding gob-side roadway is obtained. The coal pillar and the roof near coal pillar should be strengthened in support design. The engineering application results also can provide a useful guide that the combined support with wire meshes, beam, anchor bolt and cable is an effective method.

Large deformation analysis of anisotropic rubber hose along cyclic path by homogenization and path interpolation methods

Automotive braking hose used to deliver the hydraulic braking force to the drake disc is in a lamination composition of rubber and fabric braided layers to prevent the oil leakage and the excessive radial deformation. Currently, the configuration and durability become a hot issue in the design of braking hose, because both substantially affect the oil leakage caused by the micro cracks and the interference with other adjacent parts. The design of braking hose including its configuration has been relied on the trial-and-error experiment because there is no reliable numerical analysis technique. A main obstacle in developing the numerical analysis technique is the geometry modeling of braided layer which is woven with fabric cords of small diameter. The microstructure of braided layer has been simplified as an isotropic layer because of its painstaking modeling job and the necessity of huge number of finite elements. However, such a simple model could not successfully reproduce the out-of-deformation of braking hose which is produced by the orthotropic braided layers. Meanwhile, the braking hose undergoes cyclic large deformation during the steering motion and bump/rebound motions of vehicle. In this context, the goal of this study is to introduce a modeling-effective but reliable large deformation analysis method for braking hose along the specified cyclic path making use of the homogenization and path interpolation methods. The numerical results are also presented to illustrate the proposed numerical analysis method.

Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations

A displacement-based Galerkin meshfree method for large deformation analysis of nearly-incompressible elastic solids is presented. Nodal discretization of the domain is defined by a Delaunay tessellation (three-node triangles and four-node tetrahedra), which is used to form the meshfree basis functions and to numerically integrate the weak form integrals. In the proposed approach for nearly-incompressible solids, a volume-averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes. The nodal dilatational constraint is then projected onto the linear approximation space. The displacement field is constructed on the linear space and enriched with bubble-like meshfree basis functions for stability. The new procedure leads to a displacement-based formulation that is similar to F -bar methodologies in finite elements and isogeometric analysis. We adopt maximum-entropy meshfree basis functions, and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions. The nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly-incompressible large deformation analysis on Delaunay meshes.

Floating stress-point integration meshfree method for large deformation analysis of elastic and elastoplastic materials

SUMMARY A new meshfree formulation of stress-point integration, called the floating stress-point integration meshfree method, is proposed for the large deformation analysis of elastic and elastoplastic materials. This method is a Galerkin meshfree method with an updated Lagrangian procedure and a quasi-implicit time-advancing scheme without any background cell for domain integration. Its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation, which is not generally used in meshfree formulations. Hence, this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved. The details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method. Copyright © 2012 John Wiley & Sons, Ltd.

The Finite Cell Method for large deformation analysis

AbstractThe Finite Cell Method (FCM) combines the fictitious domain approach with high‐order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation‐free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Novel Meshfree Method for Large Deformation Analysis of Elastic and Viscoelastic Bodies without Using Background Cells

A Galerkin-type new meshfree formulation for large deformation analysis of elastic and viscoelastic bodies with a quasi-implicit time advancing scheme was proposed. The proposed method uses floating stress-points for the domain integration instead of background cell integration or nodal integration. The nodes and stress-points are initially arranged in the domain in a similar way of finite elements with coarseness and fineness. The number of stress-points is set greater than that of the nodes so that zero-energy modes don't arise unlike nodal integration methods without stabilization. Shape functions and their derivatives at each stress-points are defined by moving least squares (MLS) approximation with variable support radii and are updated in every time steps. A scaling-typed integration correction was introduced for the satisfaction of integration constraints. A patch test and beam bending analyses were performed to verify and evaluate the accuracy of the proposed method. Additionally, a press forming-like analysis that is difficult to be analysed with finite element methods without adaptive meshing technique was performed and successfully converged.

Meshfree method for large deformation analysis–a reproducing kernel particle approach

This work concerns the analysis of large displacement problems using the meshfree approach. Meshless algorithms based on the reproducing kernel particle estimate are proposed and applied to the analysis of typical two-dimensional large displacement problems. Due to the lack of Kronecker delta properties in meshless shape functions, the penalty method is explored and employed to enforce the essential boundary conditions. Results of numerical examples involving both geometrical and material nonlinearities show that the meshless model has at least similar effectiveness and accuracy as compared to the finite element method.

Optimum design of geometrically nonlinear elastic-plastic steel frames with tapered members

Steel frames having members with nonuniform cross-sections are preferred in design cases where the architectural constraints are flexible. In such cases they produce economical solutions. In this study an algorithm is presented for the optimum design of such frames in which linear variation of cross-sections is considered. Each member introduces two variables into the design problem provided that they are not linked together. The first is the cross-sectional area at one end and the other is the ratio of areas at both ends. The design algorithm is obtained by coupling the optimality criteria approach with large deformation analysis method of elastic-plastic frames. The optimality criteria method is used to develop a recursive relationship for design variables considering displacement constraints. This relationship requires nonlinear response of the frame at every design cycle which is computed by an algorithm based on Euclerian formulation including elastic-plastic effects. The design algorithm is outlined in steps and number of design examples are presented to demonstrate its application.

Coupled distinct element-finite element method for large deformation analysis of rock masses. Technical note : Pan, X D; Reed, M B Int J Rock Mech Min SciV28, N1, Jan 1991, P93–99

Coupled distinct element-finite element method for large deformation analysis of rock masses. Technical note : Pan, X D; Reed, M B Int J Rock Mech Min SciV28, N1, Jan 1991, P93–99

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids

Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.