An explicit integration scheme for finite-deformation plasticity in finite-element methods

A finite element-peridynamic combined multiscale analysis strategy based on implicit integration scheme

We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case, a corotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.

SummaryAn adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ–Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ–Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ–Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ–Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ–Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

The aim of the study is to identify the relevant aspects of numerical analysis of impact of projectiles with soft cores into a package composed of thin flexible plies located on the plastic backing. In order to illustrate the problem, normal impact of 7.62 mm TT projectile into an unclamped package comprising 36 plies of Dyneema SB71 supported on the plastic backing was selected. The problem was solved with the use of the finite element method (FEM) with the explicit integration scheme (central difference method) of motion equations in the matrix form. Based on the conducted numerical computations, it was revealed that obtaining the extreme deformations of a projectile soft core and the backing material in Lagrangian description requires employment of adaptive methods. The proposed R-adaptive method performs its role but must be used carefully due to the mass loss which may appear during calculations.

An adaptive substepping explicit integration scheme with a novel loading-unloading decision method is developed here for the non-isothermal unified hardening (UH) model. The non-isothermal UH model includes a convex subloading surface in the $$p$$p---$$q$$q plane and a nonconvex subloading surface in the $$p$$p---$$T$$T plane. Because of the convex/nonconvex subloading surfaces, the conventional loading-unloading decision method used in stress integration schemes may lead to incorrect elasticity/elastoplasticity judgements. In addition, the conventional loading-unloading decision method is unable to determine the division point that separates the elastic segment from the elastoplastic segment. A simple but robust method, the double cosine (DC) method, is proposed in this paper to solve loading-unloading decision problems. The proposed DC method is then embedded into an adaptive substepping explicit integration scheme to implement the non-isothermal UH model. The accuracy and efficiency of the DC method are discussed by comparing the method with the conventional loading-unloading decision method (the CV method) and the root-finding loading-unloading decision method (the RF method). The performance of the proposed scheme with the DC method is also discussed.

Comparative studies on the performances of implicit and explicit integration schemes are conducted for a double structure hydro-mechanical coupling model of unsaturated expansive clays at an integration point level. The published constitutive model is built on the basis of two pore levels in expansive clay. In this paper, firstly, the implicit and explicit schemes based on the Euler backward and forward integration algorithms are proposed. These schemes can deal with multi-plastic mechanisms defined in the model and distinguish various cases in relation to the number of plastic mechanism active. Secondly, the performances of the integration schemes are demonstrated by comparisons of calculation results of a control-strain test with different strain increment sizes.

Unconditionally stable meshless integration of time-domain Maxwell’s curl equations

Stress integration schemes for elastoplastic constitutive relations for homogeneous materials have been extensively proposed by several researchers during the last two decades. In this paper, a set of micromechanics equations are formulated based on the Transformation Field Analysis (TFA) method. When integrating the constitutive relation of fibrous composites, an implicit integration scheme, namely the Governing Parameter Method (GPM) is employed to provide the overall elastoplastic stress-strain relations for n-phase fiber-reinforced composites using the J 2-plasticity with strain hardening. This integration scheme is employed instead of the conventional explicit stress integration scheme because it only needs to solve a nonlinear algebraic equation instead of a 6 × (n + 1) system of differential-algebraic equations. The proposed integration scheme can accommodate other complex plasticity models as well. More importantly, the combined TFA and GPM approach can also be used as a constitutive model for use in nonlinear finite element method to analyze structural response.

Explicit integration of a thermo-mechanical model for clays

A GPU-based numerical manifold method for modeling the formation of the excavation damaged zone in deep rock tunnels

A tendon-driven robot inspired from the bird neck is studied in this paper. The objective is to propose numerical integrations for this robot. The classical explicit and implicit Euler integration schemes can be used on this robot. When the elasticity in the tendons is not considered, these schemes are stable and give similar numerical integration results but the explicit implementation is faster. By considering the dynamics of the robot joints on one hand and the dynamics of the motors on the other hand, we propose two Euler integration schemes, explicit and implicit, that take into account the elasticity in the tendons. These schemes rely on the dynamics of the robot joints on the one hand, and on the dynamics of the motors on the other hand and it links them by the tendon elastic model. We observe that with the tendon elasticity model, the explicit integration becomes unstable, depending on the time step, while the implicit one stays stable. The numerical integration that uses this implicit scheme with tendon elasticity allows one to obtain more precise results, while the model of the system is more realistic. Moreover, the evolution of the tendon elongation during a desired motion can be obtained while they are computed in the integration scheme.

This work presents the development of an explicit/implicit particle finite element method (PFEM) for the 2D modeling of metal cutting processes. The purpose is to study the efficiency of implicit and explicit time integration schemes in terms of precision, accuracy and computing time. The formulation for implicit and explicit time marching schemes is developed, and a detailed study on the explicit solution steps is presented. The PFEM remeshing procedures for insertion and removal of particles have been improved to model the multiple scales of time and/or space of the solution. The detection and treatment of the rigid tool contact are presented for both, implicit and explicit schemes. The performance of explicit/implicit integration is studied with a set of different two-dimensional orthogonal cutting tests of AISI 4340 steel at cutting speeds ranging from 1 m/s up to 30 m/s. It was shown that if the correct selection of the time integration scheme is made, the computing time can decrease up to 40 times. It allows us to affirm that the computing time of the PFEM simulations can be excessive due to the used time marching scheme independently of the meshing process. As a practical result, a set of recommendations to select the time integration schemes for a given cutting speed are given. This is intended to minimize one of the negative constraints pointed out by the industry when using metal cutting simulators.

In this work, a 2D pore pressure cohesive zone model is presented to simulate the hydraulic fracture propagation in naturally fractured formation, in which the fracturing process is governed by a bilinear cohesive zone model equipped with Coulomb's friction law and the fluid flow within the hydraulic fracture is described by the lubrication equation. In this model, fluid leak‐off into rock matrix is ignored and a fully explicit temporal integration scheme is adopted to overcome the convergence issue of conventional implicit scheme (eg, Newton‐Raphson method). The advantage of the proposed model is that it does not require any special crossing criterion to determine the interaction behavior when the hydraulic fracture hits the natural fracture. Implementation of the model was described in detail, and then, the model was verified with well‐known analytical solution of KGD problem and criteria of hydraulic fracture crossing natural fracture. The capability of the proposed model to capture the interaction behavior between hydraulic fracture and natural fracture was demonstrated by the good agreement of the modeling result and analytical solution. Several numerical cases were performed to investigate the impact of key factors on fracture network evolution during hydraulic fracturing treatment. Results show that fracture network is not only governed by the spatial distribution of natural fracture, but also greatly affected by the initial hydraulic aperture of natural fracture and in situ stress contrast.

Existing techniques for real-time simulation of object deformation are well suited for animating soft materials like human tissue or two-dimensional systems such as cloth. However. simulation of deformation in malleable materials and fracture in brittle materials has only been done offline because the underlying equations of motion are numerically stiff. requiring many small steps in explicit integration schemes. In contrast. the better-behaved implicit integration techniques are more expensive per time step. particularly for volumetric meshes. We present a stable hybrid method for simulating deformation and fracture of materials in real-time. In our system. the effects of impact forces are computed only at discrete collision events. At these impacts. we treat objects as if they are anchored and compute their static eqUilibrium response using the Finite Element technique. Static analysis is not time-step bound and its stability is independent of the stiffness of the equations. The resulting deformations. or possible fractures. are computed based on internal stress tensors. Between collisions. disconnected objects are treated as rigid bodies. The simulator is demonstrated as part of a system that provides the user with physically-based tools to interactively manipulate 3D models.

This works concerns the development of a virtual prototyping tool dedicated to electro-thermo-mechanical simulation of power converters. The FEM code, written using an object-oriented language, includes a dual Schur Domain Decomposition Method. The solving of problems including floating subdomains can be performed in steady-state cases, whereas one can couple multi-timestep implicit and explicit integration schemes in transient analysis. The last part of this work is about the study of an industrial benchmark concerning the power converters used in railway transport: the electro-thermal simulation of a switch in transient analysis. This example allows to compare different strategies of tearing into subdomains and the use of different timesteps on the same structure.