Stress-point Integration Research Articles

Enhanced particle method with stress point integration for simulation of incompressible fluid-nonlinear elastic structure interaction

A fully-Lagrangian particle-based computational method is developed for simulation of incompressible Fluid, non-linear Structure Interaction (FSI) with incorporation of stress point integration (Randles and Libersky, 2005) to resolve instabilities related to zero-energy modes. Structural dynamics is founded on discretization of the divergence of stress according to Moving Least Squares (MLS) method. The stress point integration is incorporated in calculation of structural dynamics, resulting in a Dual Particle Dynamics (DPD) structure model (Randles and Libersky, 2005). A structure model based on nodal integration is also considered for comparison and simply referred to as MLS. The DPD and MLS structure models are coupled with an enhanced projection-based Moving Particle Semi-implicit (MPS) method as the fluid model, resulting in DPD–MPS and MLS–MPS FSI solvers, respectively. The enhanced performance of DPD with respect to MLS is first shown through a set of tests for structure model. Then the superior performance of DPD–MPS FSI solver with respect to MLS–MPS one is demonstrated through a set of FSI benchmark tests. The present study also presents a new algorithm for fluid–structure coupling via components of stress tensors in surface boundary stress points.

Smoothed Particle Hydrodynamics with Stress Points and Centroid Voronoi Tessellation (CVT) Topology Optimization

Various formulations of smoothed particle hydrodynamics (SPH) have been presented by scientists to overcome inherent numerical difficulties including instabilities and inconsistencies. Low approximation accuracy could cause a result of particle inconsistency in SPH and other meshfree methods. In this study, centroid Voronoi tessellation (CVT) topology optimization is used for rearrangement of particles so that the inconsistency due to irregular particle arrangement can be corrected. Using CVT topology optimization method, the SPH particles, which are generated randomly inside a predetermined domain, are moved to the centroids, i.e., the center of mass of the corresponding Voronoi cells based on Lloyd’s algorithm. The volume associated with each particle is determined by its Voronoi cell. On the other hand, it has been shown that particle methods with stress point integration are more stable than the ones using nodal integration. Conventional SPH approximations only use SPH particles, and it results in the so-called tensile instability. In this paper, a new approach of using stress points is introduced to assist SPH approximations and stabilize the SPH methods.

On the numerical implementation of the Closest Point Projection algorithm in anisotropic elasto-plasticity with nonlinear mixed hardening

In finite element analysis, among the possible frameworks for stress-point integration algorithms in computational elastoplasticity, the implicit Closest Point Projection (CPP) algorithm is probably the most used one. The idea behind this algorithm is that all necessary variables, including the flow and hardening directions, are iteratively updated and enforced at the final solution. Therefore the algorithm is fully implicit and the final solution is independent of previous iterations. However, there are several possible implementations of the ideas behind the CPP algorithm. Even though asymptotic quadratic convergence may be obtained in all implementations if the algorithm is properly linearized, these different possibilities result in a different number of local iterations and in a different computational effort. Small stress-integration algorithms are frequently the only iterative core of large strain elastoplastic formulations. At the same time they are responsible for a large share of the overall computational time in finite element simulations and key in the overall robustness. In this work we present a new algorithm based on the ideas of the Closest Point Projection algorithm for anisotropic elastoplasticity with mixed hardening. We also compare our proposal with other possible implementations of the CPP algorithm for the same problem, namely the General CPP implementation and the Governing Parameter Method. We show that our proposal is in general more efficient.

Discrete micromechanics of elastoplastic crystals in the finite deformation range

We present a rate-independent crystal plasticity theory in the finite deformation range. The formulation revolves around theory of distribution and strong discontinuity concepts applied to the slip systems. Uniform and conforming deformation fields are introduced, from which deformation gradients for the crystal lattice and the crystal itself are derived. For a crystal deforming in single slip, we show that the crystal rotates the active slip system the same way as the lattice does, leading to an elegant and exact stress-point integration algorithm for the overall crystal stresses. For a crystal deforming in multiple slips the crystal no longer rotates the slip systems exactly as the lattice does. For this case, we present a stress-point integration algorithm accounting for the exact push-forward operation induced by the lattice on the active systems. We also consider a simplified stress-point integration algorithm for multislip systems that remains highly accurate for a wide range of stress paths considered. The framework for system activation and the selection of linearly independent slip systems follows a well-established ‘ultimate algorithm’ for rate-independent crystal plasticity developed for infinitesimal deformation.

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.

510 浮動応力点積分メッシュフリー法を用いた大変形弾塑性解析(OS5.メッシュフリー/粒子法とその関連技術(3),OS・一般セッション講演)

510 浮動応力点積分メッシュフリー法を用いた大変形弾塑性解析(OS5.メッシュフリー/粒子法とその関連技術(3),OS・一般セッション講演)

Meshfree Large Deformation Analysis Based on Formulation of Floating Stress-Point Integration with Incremental Internal Force

A modified formulation of floating stress-point integration with the updated Lagrangian procedure for large deformation analysis is presented. The modified formulation introduces an incremental internal force to the equilibrium equation instead of the virtual external force introduced in the previous formulation. With this modification, the temporal continuity of the mechanical equilibrium can be kept without introducing the virtual external force, and thus the accumulating error due to time advancing becomes small compared to our previous formulation. Several examples of large deformation analysis including large deformation patch tests are also presented to show the validity and accuracy of the proposing method in comparison with the finite element method.

504 浮動応力点積分によるメッシュフリー大変形解析(OS5. メッシュフリー/粒子法とその関連技術(1),オーガナイズドセッション講演)

504 浮動応力点積分によるメッシュフリー大変形解析(OS5. メッシュフリー/粒子法とその関連技術(1),オーガナイズドセッション講演)

Explicit Runge–Kutta methods for the integration of rate-type constitutive equations

Modern constitutive models have the potential to improve the quality of engineering calculations involving non-linear anisotropic materials. The adoption of complex models in practice, however, depends on the availability of reliable and accurate solution methods for the stress point integration problem. This paper presents a modular implementation of explicit Runge–Kutta methods with error control, that is suitable for use, without change, with any rate-type constitutive model. The paper also shows how the complications caused by the algebraic constraint of conventional plasticity are resolved through a simple subloading modification. With this modification any rate-independent model can be implemented without difficulty, using the integration module as an accurate and robust standard procedure. The effectiveness and efficiency of the method are demonstrated through a comparative evaluation of second and fifth-order formulas, applied to a complex constitutive model for natural clay, full details of which are given.

A meshfree particle method with stress points and its applications at the nanoscale

In this paper, a meshfree particle method with the stress point integration scheme is studied. It has been shown that this meshfree particle method with Lagrangian kernel can provide a stable metho...

A meshfree particle method with stress points and its applications at the nanoscale

In this paper, a meshfree particle method with the stress point integration scheme is studied. It has been shown that this meshfree particle method with Lagrangian kernel can provide a stable method. A finite element mapping technique is introduced to insert stress points and to calculate volumes associated with particles/stress points so that the triangulation and the Voronoi diagram can be avoided. This meshfree particle method can be used for nanoscale simulations via the implementation of the Cauchy-Born rule. It can also be coupled with molecular dynamics based on the bridging domain coupling technique.

Study of the creep characterictics and long-term stability of rock masses in the high slopes of the three gorges ship lock, China

We present a rate-independent crystal plasticity theory in the finite deformation range. The formulation revolves around theory of distribution and strong discontinuity concepts applied to the slip systems. Uniform and conforming deformation fields are introduced, from which deformation gradients for the crystal lattice and the crystal itself are derived. For a crystal deforming in single slip, we show that the crystal rotates the active slip system the same way as the lattice does, leading to an elegant and exact stress-point integration algorithm for the overall crystal stresses. For a crystal deforming in multiple slips the crystal no longer rotates the slip systems exactly as the lattice does. For this case, we present a stress-point integration algorithm accounting for the exact push-forward operation induced by the lattice on the active systems. We also consider a simplified stress-point integration algorithm for multislip systems that remains highly accurate for a wide range of stress paths considered. The framework for system activation and the selection of linearly independent slip systems follows a well-established ‘ultimate algorithm’ for rate-independent crystal plasticity developed for infinitesimal deformation.

Cam-Clay plasticity, Part IV: Implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function

This paper describes a fully implicit stress-point integration algorithm for a class of anisotropic bounding surface plasticity models with ellipsoidal loading function. The plasticity model is coupled with a nonlinear hyperelastic model to ensure that the elastic component of the combined model is energy-conserving. A key feature of the integration algorithm for the combined model is a return mapping in strain space, which allows fully implicit integration and consistent linearization of the constitutive equations. For this class of bounding surface models the consistency condition on the bounding surface is shown to be mathematically equivalent to the consistency condition on the loading surface, thus allowing practically all attributes of the standard return mapping algorithm of classical plasticity theory to be carried over to the bounding surface theory with little modification. As a specific example, the infinitesimal version of modified Cam-Clay theory is used to represent the bounding surface model, and an exponential function is used to interpolate the plastic modulus on the loading surface. Isoerror maps are generated describing the accuracy of the integration algorithm on the stress-point level. Finally, a boundary-value problem involving a strip footing on lightly overconsolidated clay is analyzed to demonstrate the robustness of the algorithm in a finite element setting.

A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation

This paper presents a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard Galerkin approximation. Strain enhancements via jumps in the displacement field are captured and condensed on the material level, leading to a formulation that does not require static condensation to be performed on the element level. The mathematical formulation revolves around the dual response of a macroscopic point cut by a shear band, which requires the satisfaction of the yield condition on the band as the same stress point unloads elastically just outside the band. Precise conditions for the appearance of slip lines, including their initiation and evolution, are outlined for a rate-independent, strain-softening Drucker–Prager model, and explicit analytical expressions are used to describe the orientation of the slip line in a plane strain setting. At post-localization the stress-point integration algorithm along the band is exact and amenable to consistent linearization. Numerical examples involving simple shearing of elastoplastic solids with deviatoric plastic flow, as well as plane strain compression of dilatant cohesive/frictional materials, are presented to demonstrate absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions.

Finite-Element Simulation of Deformation and Breakage in Sheet Metal Forming : 1st Report, Basic Theory

In the analysis of sheet metal forming, the constitutive equations are examined with respect to prediction of breakage strains. Breakage initiation is numerically evaluated by the method proposed previously by one of the authors (Gotoh) in which the onset of localized necking is adopted as the breakage condition. Numerical results of limiting strains evaluated by the use of the J 2-Gotoh's corner (J2G) theory and biquadratic anisotropic yield function are in good agreement with experimental results. Next, the commercial FEM code 'JNIKE3D' is improved by introducing them. The evaluation function for breakage is also introduced into the code. A modified radial return method is proposed and adopted as the stress-point integration algorithm for this anisotropic case. As an example, a necking in tensile test is simulated to verify the effectiveness of the improved JNIKE3D.