Finite Element Modeling of the Punch Stretching of Square Plates

1988 ◽  
Vol 55 (3) ◽  
pp. 667-671 ◽  
Author(s):  
E. Nakamachi ◽  
R. Sowerby
Keyword(s):  
Finite Element ◽  
Strain Distribution ◽  
Pure Aluminum ◽  
Strain Tensor ◽  
Deformation Mode ◽  
Cauchy Stress ◽  
Normal Anisotropy ◽  
Stick Model ◽  
Punch Geometry ◽  
Updated Lagrangian

The paper presents an updated Lagrangian-type finite element procedure, formulated with reference to a surface embedded coordinated system. Membrane shell theory is employed, and an attempt is made to calculate the strain distribution incurred by a peripherally clamped square plate, when impressed by a rigid punch. Three different punch geometries were considered. The material is treated as a rate insentive, elastic work-hardening solid, which obeys the J2 flow theory; both finite deformation and normal anisotropy can be considered. A linear relationship between the Jaumann rate of Cauchy stress and the Eulerian rate of Green’s strain tensor is derived. A slip-stick model was adopted for the interfacial frictional conditions. This was achieved by considering the equilibrium of a constant strain-element node in contact with the tools, and deciding whether such a node would stick or slip under Coulomb friction conditions. It is demonstrated that the punch geometry and frictional conditions exert a strong influence on the deformation mode, and hence, upon the overall strain distribution. The predictions were checked against experimental observations when stretch-forming square plates of pure aluminum, 0.5-mm thick. Contours of equal height on the deforming blanks were determined using a Moir´e fringe technique. The agreement between theory and experiment was favorable.

scholarly journals Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it

2012 ◽  
Vol 468 (2146) ◽  
pp. 3047-3058 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Mahendra Gattu ◽  
Jan Vorel
Keyword(s):  
Finite Element ◽  
Finite Strain ◽  
Strain Tensor ◽  
Biological Tissues ◽  
Organic Soils ◽  
Osteoporotic Bone ◽  
Cauchy Stress ◽  
Ceramic Foams ◽  
Commercial Program ◽  
Updated Lagrangian

Most commercial finite-element programs use the Jaumann (or co-rotational) rate of Cauchy stress in their incremental (Riks) updated Lagrangian loading procedure. This rate was shown long ago not to be work-conjugate with the Hencky (logarithmic) finite strain tensor used in these programs, nor with any other finite strain tensor. The lack of work-conjugacy has been either overlooked or believed to cause only negligible errors. Presented are examples of indentation of a naval-type sandwich plate with a polymeric foam core, in which the error can reach 28.8 per cent in the load and 15.3 per cent in the work of load (relative to uncorrected results). Generally, similar errors must be expected for all highly compressible materials, such as metallic and ceramic foams, honeycomb, loess, silt, organic soils, pumice, tuff, osteoporotic bone, light wood, carton and various biological tissues. It is shown that a previously derived equation relating the tangential moduli tensors associated with the Jaumann rates of Cauchy and Kirchhoff stresses can be used in the user’s material subroutine of a black-box commercial program to cancel the error due to the lack of work-conjugacy and make the program perform exactly as if the Jaumann rate of Kirchhoff stress, which is work-conjugate, were used.

FINITE ELEMENT ANALYSIS OF CONSTRAINED GROOVE PRESSING OF PURE ALUMINUM SHEETS

2013 ◽  
Vol 02 (01) ◽  
pp. 1350001 ◽  
Author(s):  
S. S. SATHEESH KUMAR ◽  
I. BALASUNDAR ◽  
T. RAGHU
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Plastic Strain ◽  
Deformation Behavior ◽  
Strain Distribution ◽  
Pure Aluminum ◽  
Detailed Examination ◽  
Deformation Characteristics ◽  
Element Analysis ◽  
Aluminum Sheets

Constrained groove pressing (CGP) is an attractive severe plastic deformation technique capable of processing ultrafine grained/nanostructured sheet materials. The deformation behavior of pure aluminum during constrained groove pressing is investigated by carrying out a two-dimensional finite element analysis (FEA). FEA predicted deformation behavior observed during each stages of pressing indicated almost negligible deformation in flat regions, whereas the inclined shear regions revealed diverse deformation characteristics. The plastic strain distributions unveiled inhomogeneous strain distribution at the end of one pass. Detailed examination of plastic strain evolution during CGP along various sections divulged superior strain distribution along middle surfaces when compared to top and bottom surfaces. The degree of strain homogeneity is evaluated quantitatively along different regions of the sheet and is correlated to the deformation characteristics. Load–stroke characteristics obtained during corrugating and flattening of sheets exhibited three stages and two stages behavior, respectively. The results obtained from the analysis are experimentally validated by processing pure aluminum sheets by CGP and the measured deformation homogeneity is benchmarked with FEA results.

Energy-Conservation Error Due to Use of Green–Naghdi Objective Stress Rate in Commercial Finite-Element Codes and Its Compensation

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Zdeňek P. Bažant ◽  
Jan Vorel
Keyword(s):  
Finite Element ◽  
Energy Conservation ◽  
Strain Tensor ◽  
High Volume ◽  
Cauchy Stress ◽  
Commercial Software ◽  
Steel Cylinder ◽  
Kirchhoff Stress ◽  
Jaumann Rate ◽  
Objective Stress

The objective stress rates used in most commercial finite element programs are the Jaumann rate of Kirchhoff stress, Jaumann rates of Cauchy stress, or Green–Naghdi rate. The last two were long ago shown not to be associated by work with any finite strain tensor, and the first has often been combined with tangential moduli not associated by work. The error in energy conservation was thought to be negligible, but recently, several papers presented examples of structures with high volume compressibility or a high degree of orthotropy in which the use of commercial software with the Jaumann rate of Cauchy or Kirchhoff stress leads to major errors in energy conservation, on the order of 25–100%. The present paper focuses on the Green–Naghdi rate, which is used in the explicit nonlinear algorithms of commercial software, e.g., in subroutine VUMAT of ABAQUS. This rate can also lead to major violations of energy conservation (or work conjugacy)—not only because of high compressibility or pronounced orthotropy but also because of large material rotations. This fact is first demonstrated analytically. Then an example of a notched steel cylinder made of steel and undergoing compression with the formation of a plastic shear band is simulated numerically by subroutine VUMAT in ABAQUS. It is found that the energy conservation error of the Green–Naghdi rate exceeds 5% or 30% when the specimen shortens by 26% or 38%, respectively. Revisions in commercial software are needed but, even in their absence, correct results can be obtained with the existing software. To this end, the appropriate transformation of tangential moduli, to be implemented in the user's material subroutine, is derived.

The Comparison between Continuous Confined Strip Shearing (C2S2) and ECAP Conform in Regard to Equivalent Plastic Strain Distribution for Al 1100

2012 ◽  
Vol 05 ◽  
pp. 400-409 ◽  
Author(s):  
A. R. Shahab ◽  
S. A. A. Akbari Mousavi ◽  
Sh. Ranjbar Bahadori ◽  
S. M. Ebrahimi
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Strain Distribution ◽  
Pure Aluminum ◽  
Continuous Process ◽  
Processing Condition ◽  
Equivalent Plastic Strain ◽  
Finite Element Software ◽  
Angular Pressing ◽  
Commercially Pure

During the last years lots of efforts have been done to industrialize equal channel angular pressing (ECAP) technique. Both Continuous Confined Strip Shearing (C2S2) and ECAP-Conform methods are rather recent techniques, making a continuous process from ECAP method. In present study both mentioned processes were simulated with ABAQUS Finite Element software for commercially pure aluminum. During C2S2 process the sample gradually experienced equivalent plastic strain (PEEQ) of 0.13 at initial stages of bending, while during ECAP-Conform the sample underwent rather sudden magnitude of strain of about 0.52 at primary stages, and it remained constant during the rest of the process. The final magnitude of the PEEQ differed significantly between two processes, as it was 0.86 and 1.36 in C2S2 and ECAP-Conform, respectively. Therefore, in the same processing condition employing the ECAP-Conform method led to a finer microstructure in comparison with C2S2 technique.

Nonlinear Viscoelastic Finite Element Analysis of Adhesive Joints

1988 ◽  
Vol 16 (3) ◽  
pp. 146-170 ◽  
Author(s):  
S. Roy ◽  
J. N. Reddy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Viscoelastic Behavior ◽  
Bonded Joints ◽  
Adhesively Bonded ◽  
Element Analysis ◽  
Adhesively Bonded Joints ◽  
Nonlinear Viscoelastic ◽  
Structural Failures ◽  
Updated Lagrangian

Abstract A good understanding of the process of adhesion from the mechanics viewpoint and the predictive capability for structural failures associated with adhesively bonded joints require a realistic modeling (both constitutive and kinematic) of the constituent materials. The present investigation deals with the development of an Updated Lagrangian formulation and the associated finite element analysis of adhesively bonded joints. The formulation accounts for the geometric nonlinearity of the adherends and the nonlinear viscoelastic behavior of the adhesive. Sample numerical problems are presented to show the stress and strain distributions in bonded joints.

Study on Stress and Strain of Anchorage Using Finite Element Method

2013 ◽  
Vol 325-326 ◽  
pp. 1314-1317
Author(s):  
Cong Sheng Chen ◽  
Ping He ◽  
Cheng Yong Wang ◽  
Xue Hui Chen ◽  
Lei Huang ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Distribution ◽  
Maximum Stress ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Integrated Modeling ◽  
Stress And Strain ◽  
Steel Strand ◽  
Prestressed State ◽  
Stress And Strain Distribution

Three-dimensional integrated modeling method and the numerical simulation of elastoplastic finite element are adopted in the paper. The mechanical response of the five holes anchorage is analyzed in certain prestressed state. The stress and strain distribution information of the anchor ring, clip and steel strand is obtained respectively, and the structure safety is discussed by investigating on the maximum stress and strain.

Errors Caused by Non-Work-Conjugate Stress and Strain Measures and Necessary Corrections in Finite Element Programs

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Wooseok Ji ◽  
Anthony M. Waas ◽  
Zdeněk P. Bažant
Keyword(s):  
Finite Element ◽  
Fiber Composite ◽  
Strain Tensor ◽  
Stress And Strain ◽  
Hencky Strain ◽  
Tangential Stiffness ◽  
Jaumann Rate ◽  
Lagrangian Strain ◽  
Strain Formulation ◽  
Accurate Expression

Many finite element programs including standard commercial software such as ABAQUS use an incremental finite strain formulation that is not fully work-conjugate, i.e., the work of stress increments on the strain increments does not give a second-order accurate expression for work. In particular, the stress increments based on the Jaumann rate of Kirchhoff stress are work-conjugate with the increments of the Hencky (logarithmic) strain tensor but are paired in many finite element programs with the increments of Green’s Lagrangian strain tensor. Although this problem was pointed out as early 1971, a demonstration of its significance in realistic situations has been lacking. Here it is shown that, in buckling of compressed highly orthotropic columns or sandwich columns that are very “soft” in shear, the use of such nonconjugate stress and strain increments can cause large errors, as high as 100% of the critical load, even if the strains are small. A similar situation may arise when severe damage such as distributed cracking leads to a highly anisotropic tangential stiffness matrix, or when axial cracks between fibers severely weaken a uniaxial fiber composite or wood. A revision of these finite element programs is advisable, and will in fact be easy—it will suffice to replace the Jaumann rate with the Truesdell rate. Alternatively, the Green’s Lagrangian strain could be replaced with the Hencky strain.

scholarly journals Dynamic constitutive relation of 5083P-O aluminium alloy and its influence on energy-absorbing structure

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880733
Author(s):  
Yue Feng ◽  
Shoune Xiao ◽  
Bing Yang ◽  
Tao Zhu ◽  
Guangwu Yang ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Aluminium Alloy ◽  
Constitutive Relation ◽  
High Strain ◽  
Deformation Mode ◽  
Strain Rates ◽  
Strengthening Effect ◽  
Element Simulation ◽  
Energy Absorbing

Dynamic and quasi-static tensile tests of 5083P-O aluminium alloy were carried out using RPL100 electronic creep/fatigue testing machine and the split Hopkinson tension bar, respectively. The dynamic constitutive relation of the material at high strain rates was studied, and the constitutive model in accordance with Cowper–Symonds form was established. At the same time, a method to describe the constitutive relation of material using the strain rate interpolation method which is included in LS-DYNA software was proposed. The advantages and accuracy of this method were verified by comparing the results of the finite element simulation with the fitting results of the Cowper-Symonds model. The influence of material strain rate effect on squeezing force, energy absorption and deformation mode of the squeezing energy-absorbing structure based on the constitutive models of 5083P-O were studied by means of finite element simulation. The results show that when the strain rate of the structure deformation is low, the material strain rate strengthening effect has little influence on the structure. However, with the increase of the strain rate, the strengthening effect of the material will improve the squeezing force and the energy absorption of the structure, and will also influence the deformation mode, that is, the decrease of the deformation with high strain rates while the increase of the deformation with low strain rates.

Does femoral strain distribution coincide with the occurrence of cervical versus trochanteric hip fractures? An experimental finite element study

2010 ◽  
Vol 48 (7) ◽  
pp. 711-717 ◽  
Author(s):  
Janne E. M. Koivumäki ◽  
Jérôme Thevenot ◽  
Pasi Pulkkinen ◽  
Jukka A. Salmi ◽  
Volker Kuhn ◽  
...  
Keyword(s):  
Finite Element ◽  
Hip Fractures ◽  
Strain Distribution ◽  
Finite Element Study ◽  
Element Study
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