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Two kinds of time integration methods; the dynamic explicit method and the static implicit method, have been compared, especially with emphasis on the shell formulations and the stress integration methods. Two methods have been applied to the benchmark problem named the S‐rail stamping process, provided by NUMISHEET’96 committee, in order to compare their numerical results with each other and with the average values of the experiments as well. Based on the comparisons, it is shown that both time integration methods can be successfully applied to industrial sheet metal stamping simulations. In detail, the static implicit method is advantageous over the dynamic explicit method in terms of accuracy, while the latter is known to be more efficient than the former in terms of computation efficiency.

The purpose of this paper is to investigate the application of the element‐free Galerkin (EFG) method to the simulation of metal forming processes and to propose a strategy to deal with volumetric locking problem in this context.

The J₂ elastoplastic material model, employed in the work, assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and incorporates a non‐linear isotropic hardening response. The constitutive model is written in terms of the rotated Kirchhoff stress and the logarithmic strain measure. A Total Lagrangian formulation of the problem is considered in order to improve the computational performance of the proposed algorithm. The imposition of the essential boundary conditions and also of the unilateral contact with friction condition are made by the application of the Augmented Lagrangian method. Here, aspects related to the volumetric locking are investigated and an F‐bar approach is applied.

The results show that the proposed approach presents no volumetric locking phenomenon when using the mean dilation approach. Moreover, differently from finite element approximations, no hour‐glass instabilities in the deformation pattern are observed, avoiding in this way the need to devise additional stabilization procedures in the proposed procedure.

This paper demonstrates the implementation and validation of the mean dilation approach, in the scope of the EFG, which was successful in coping with the volumetric locking phenomena and presented no hour‐glass instabilities in the problem cases considered in this work.

To present a new constitutive model for capturing inelastic behavior of brittle materials.

The multi‐surface plasticity theory is employed to describe the damage‐induced mechanisms. An original feature in that respect concerns the multi‐surface criterion which limits the principle values of elastic strains, which is equivalent to Saint‐Venant plasticity model. The latter allows to represent the damage both in tension and in compression.

Provides a quite realistic description of cracking phenomena in brittle materials, with a very few parameters, leading to a very useful tool for analyzing practical engineering problems.

The model is recast in terms of stress resultants and employed within a flat shell elements in order to provide a very efficient tool for analysis of cellular structures. Moreover, a detailed description of the numerical implementation is given.

The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.

The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.

In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.

The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.

The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.

The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve.

Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution.

By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method.

The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the derivation of an efficient computational strategy placing emphasis on consistent elasto‐plastic tangent moduli and stress integration with the radial return method under the restriction of ‘zero normal stress condition’ in thickness direction. The advantageous performance of the standard Newton iteration using a consistent tangent stiffness matrix is compared to the classical scheme with an iteration matrix based on the infinitesimal elasto‐plastic constitutive tensor. Several numerical examples also demonstrate the effectiveness of the standard Newton iteration with respect to modified and quasi‐Newton methods like BFGS and others.

In the framework of the finite element method, the problem of elasto‐plastic consolidation gives rise to a system of non‐linear, coupled residual equations which satisfy the conditions of balance of momentum and balance of mass. In determining the roots of these equations it is necessary that the coupled equations be linearized. To this end, the concept of ‘consistent linearization’ proposed by Simo and Taylor for a single‐phase system is applied to the two‐phase soil‐water system. The roots of the coupled residual equations are solved iteratively by employing Newton's method. It is shown that in non‐linear consolidation analyses, the use of a tangent coefficient matrix derived consistently from the integrated constitutive equation defining the characteristics of the solid skeletal phase results in an iterative solution scheme which preserves the asymptotic rate of quadratic convergence of Newton's method. Numerical examples involving combined radial and vertical flows through an elasto‐plastic soil medium are presented to demonstrate the computational superiority of the above technique over the method based on standard ‘elasto‐plastic continuum formulations’ adopted in most finite element codes.

The purpose of this paper is to study a new method to appraise pressure comfort through displacement distribution, and then explore the relationship between pressure and stiffness coefficient, and elastic elongation of the top part of men’s socks using finite element method.

Through 3D body scanning, a biomechanical lower leg cross-section model is constructed for simulating elastic contact between human body and top part of socks. The human body is regarded as an elastomer and the contact between lower leg and top part of socks is elastic contact, displacement distribution tendency under pressure can be obtained using ANSYS, and the elastic elongation of top part of socks after putting on was calculated based on the displacement values. In this research work, the authors discuss in details with the relationship between pressure and stiffness coefficient, and elastic elongation of top part of socks.

In this research work, the mathematical equation of pressure is obtained which describe the relationship between pressure and stiffness coefficient, and elastic elongation of top part of socks. The results indicated that the predictive values of pressure show good agreement with measured ones after χ2 test. All these solutions supply a theory basis for forecasting of the clothing pressure.

This paper is unconcerned with the simulating of pressure distribution and variation trend when dressing during the course of walking and running.

The paper provides a finite element simulation model of lower leg cross-section located at the top part of men’s socks, and study the relationship between pressure and stiffness coefficient, and elastic elongation of top part of socks. It can supply a new method to appraise pressure comfort.

The main aim of this paper is to present a three‐dimensional numerical material model for concrete which combines plasticity with a classical orthotropic smeared crack formulation. A further aim is to raise a discussion leading to the creation of a comprehensive computer programme for the analyses of reinforced and prestressed concrete structures.

A new numerical material model for concrete is developed and main theoretical explanations are given to aid in understanding the algorithm. The model is based on Mohr‐Coulomb criterion for dominant compression and Rankine criterion for dominant tension influences. A multi‐surface presentation of the model is implemented which permits the rapid convergence of the mathematical procedure. The model includes associated and non‐associated flow rules, strain hardening and softening where the development of the plastic strain was described by the function of cohesion.

Provides information about developing a new numerical material model for concrete.

The model is implemented into the computer programme PRECON3D for the three‐dimensional nonlinear analysis of the reinforced and prestressed concrete structures.

In this model, the very complex behaviour of concrete is defined by elementary material parameters which can be obtained by a standard uniaxial test. The presented model enables a very detailed and precise analysis of reinforced and prestressed concrete structures until crushing with a high accuracy, so that the expensive experimental tests can be reduced. The paper could be very valuable to researchers in this field as a benchmark for their analyses.

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well‐known limitations. In this context, an isochoric‐volumetric decoupled material behavior is assumed and thus the additive deviatoric‐volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so‐called solid‐shell elements for thin‐walled structures is also discussed.