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The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

In the first part of this series of papers on the combined finite/discrete element simulation of shot peening processes, different contact interaction laws for 2D cases are extensively studied with special attention given to the proper selection of the parameter values involved, which is one of the key issues for successful direct simulation. In addition, computational issues including contact forces, partial contact, energy dissipation, and rheological representation are addressed. Numerical examples for a single shot impact system simulated by the coupled finite/discrete element method using different interaction laws are provided to verify the proposed approaches. The results are also compared with those obtained by using only finite element methods. Findings obtained by performing 2D simulations will, in the subsequent article, be used in realistic computational simulations of 3D shot peening processes.

Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.

Inside the finite element framework of LAGAMINE code, the contact conditions are introduced with specific two‐node interface elements and four‐node quadrangular elements or four‐node one point quadrature elements. A non‐associated flow rule is involved for sliding unilateral contact modelling. Two methods of penalty factor computations in the penalty contact algorithms are presented. These methods are then used for contact modelling of two isothermal examples: axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto‐plastic.

Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy.

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration.

The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths.

Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells.

Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures.

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned.

The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established.

Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined.

This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed.

The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.

Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.

The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms.

Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures.

To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments.

To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate.

Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures.

It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.

Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage combined finite/discrete element and explicit/implicit solution strategy is proposed in this paper. The procedure involves, at the first stage, the identification of the residual stress/strain profile under particular peening conditions by employing the combined finite/discrete approach on a small scale sample problem, and then at the second stage, the application of this profile to the entire workpiece to obtain the final deformation and stress distribution using an implicit static analysis. The motivation behind the simulation strategy and the relevant computational and implementation issues are discussed. The numerical example demonstrates the ability of the proposed scheme to simulate a peen forming process.

In this paper, a 3D DEM program TRUBAL, which is capable of calculating the contact between particles considering friction and local plastic deformation, is employed to study the evolution of internal structure of particle assemblies during the consolidation process. Uniaxial powder compaction process is simulated in a cubic periodic unit cell by applying the strain rate to the individual particles. The selection of the proper time steps in DEM for quasi‐static case is discussed. Results in particle scale (microscopic) are obtained and correlated to the statistical bulk response of the assembly. The effects of the microscopic properties of particles (such as friction, plastic contact) on the bulk mechanical response are examined by numerical tests. Correlations between the microscopic properties of particles and the macroscopic continuum behaviours of compacts are discussed. These discussions make it possible to fit DEM results at a macroscopic scale to the experimental measurements by adjusting the particle properties in DEM calculation. An example test is carried out to demonstrate that DEM results could be fitted properly to the experimental results, in the mean time, also provide some microscopic results which are hard to be measured. DEM has the potential to incorporate the microscopic properties of particles into a proper continuum model to perform combined macro and micro study of the powder compaction process.