Search results

This paper aims to develop a simple and efficient shell element for large strains hyper‐elastic analyses.

Based on the classical MITC4 shell element formulation a 3D shell element with finite strain kinematics is developed. The new quadrilateral shell element has five dof per node and two global dof to model the thickness stretching. The shell element is implemented for hyperelastic material models and the application of different hyperelastic constitutive relations is discussed.

The results obtained considering three of the hyperelastic material models available in the literature are quite different when the developed strains are relatively high; this indicates that, for analyzing actual engineering examples, experimental data should be used to decide on the most suitable constitutive relation.

The 3D version of the MITC4 element was developed.

The numerical simulation of metal forming processes follows a highly non‐linear analysis where general aspects such as elastoplasticity, finite deformation and contact mechanics are combined. Approximated solutions obtained by finite element techniques require strong computational effort, that contradicts the need of interactive industrial applications. The first part of the work deals with the description of the main elements of the formulation, with attention to mathematical modelling and the approximating algorithms in the incremental iterative frame of non‐linear analysis, ending with the results obtained in hot rolling simulation. The second part is dedicated to computational efficiency analysis and the presentation of the related methods and results obtained in this work.

The kinematics of small and large deformations (displacements, rotations and strains) is described by use of the engineering strain, the logarithmic strain, the Seth‐Hill class of strains and the rate‐type strains derived using the Lagrangian and the ‘Relative’ descriptions. The displacement gradient is computed for two and three dimensions and the error associated with use of the small rotation approximation is plotted. The components of the rotation tensor are derived for a four‐noded isoparametric quadrilateral finite element for determining the error due to small displacement and rotation approximations. Finally, the various strain measures are computed and plotted for representative problems.

The purpose of this study is to quantify the impact of the variation of microstructural features on macroscopic and microscopic fields. The application of multi-scale methods in the context of constitutive modeling of microheterogeneous materials requires the choice of a representative volume element (RVE) of the considered microstructure, which may be based on some idealized assumptions and/or on experimental observations. In any case, a realistic microstructure within the RVE is either computationally too expensive or not fully accessible by experimental measurement techniques, which introduces some uncertainty regarding the microstructural features.

In this paper, a systematical variation of microstructural parameters controlling the morphology of an RVE with an idealized microstructure is conducted and the impact on macroscopic quantities of interest as well as microstructural fields and their statistics is investigated. The study is carried out under macroscopically homogeneous deformation states using the direct micro-macro scale transition approach.

The variation of microstructural parameters, such as inclusion volume fraction, aspect ratio and orientation of the inclusion with respect to the overall loading, influences the macroscopic behavior, especially the micromechanical fields significantly.

The systematic assessment of the impact of microstructural parameters on both macroscopic quantities and statistics of the micromechanical fields allows for a quantitative comparison of different microstructure morphologies and a reliable identification of microstructural parameters that promote failure initialization in microheterogeneous materials.

This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.

The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.

The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.

This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

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.

In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of Cauchy stress is suggested based on the general form of spin tensors, defining objective stress rates. The endochronic constitutive equations are extended using the concept of corotational stress rates and additive decomposition of deformation rate. The constitutive relations are specialized for thin‐walled tubes under torsion and a procedure for solving the ordinary differential equations for cases of simple and pure torsion is developed. The axial effects for various materials, subjected to simple and pure torsion, are simulated and compared with experimental data. The results clearly indicate that the new combined rate endochronic model can be effectively used to describe the behavior of material in the finite strain range.

The purpose of this work is to apply a recently proposed constitutive model for mechanically induced martensitic transformations to the prediction of transformation loci. Additionally, this study aims to elucidate if a stress-assisted criterion can account for transformations in the so-called strain-induced regime.

The model is derived by generalising the stress-based criterion of Patel and Cohen (1953), relying on lattice information obtained using the Phenomenological Theory of Martensite Crystallography. Transformation multipliers (cf. plastic multipliers) are introduced, from which the martensite volume fraction evolution ensues. The associated transformation functions provide a variant selection mechanism. Austenite plasticity follows a classical single crystal formulation, to account for transformations in the strain-induced regime. The resulting model is incorporated into a fully implicit RVE-based computational homogenisation finite element code.

Results show good agreement with experimental data for a meta-stable austenitic stainless steel. In particular, the transformation locus is well reproduced, even in a material with considerable slip plasticity at the martensite onset, corroborating the hypothesis that an energy-based criterion can account for transformations in both stress-assisted and strain-induced regimes.

A recently developed constitutive model for mechanically induced martensitic transformations is further assessed and validated. Its formulation is fundamentally based on a physical metallurgical mechanism and derived in a thermodynamically consistent way, inheriting a consistent mechanical dissipation. This model draws on a reduced number of phenomenological elements and is a step towards the fully predictive modelling of materials that exhibit such phenomena.

The purpose of equal channel angular pressing (ECAP) is producing ultra-fine grain materials. In practical applications, it is important to understand and predict effect of different process parameters on deformed parts. One of the most important process parameters is friction coefficient. Behavior evaluation of different lubricants in the ECAP process is the aim of this research.

The present study concerns the experimental measurements of the effective strain by means of gridded parts for three different lubricants, graphite, molybdenum disulfide and zinc stearate, to evaluate friction coefficient in ECAP process. Mesh size was 2 × 2 mm² and embedded in parts made of AL2024; process was done in ambient temperature, and parts were in annealed situation. After the process, strain measured by optical and analytical methods for evaluation of lubricants’ behavior with different friction coefficients.

This study shows that zinc stearate has better effects rather than other lubricants in ECAP process and ECAPed parts.

The fatal challenge for researchers and industrial applications of ECAP process is lubrication. This research is a guide for scientists and engineers (in the future applications) to reduce and control bad frictional effects, produce better parts (more strain homogenous parts), prevent die failures and decrease press tonnage in ECAP process.

Discusses an alternative formulation for the incremental determination of stresses in strain measures that can be used to replace the stress rates currently employed. The formulation is based on Doyle‐Hill generalized definition of strain, the corresponding conjugate stresses and an isotropic hyperelastic constitutive equation. When used to analyze the simple shear deformation, the proposed formulation avoids the pathologies usually observed (oscillations, pressure build up, path dependence). The origin and importance of these pathologies is then discussed in relation to different materials behavior. It is shown that the incremental procedure used together with the logarithmic definition of strain is the most convenient, but that other approximations may be used in well defined particular situations. The numerical algorithms proposed are detailed in an Appendix.