A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part I—Theory

1991 ◽  
Vol 58 (2) ◽  
pp. 499-506 ◽  
Author(s):  
M. J. Saran ◽  
R. H. Wagoner
Keyword(s):  
Finite Element ◽  
Nonlinear Problems ◽  
Material Model ◽  
Test Problems ◽  
Large Strains ◽  
Numerical Verification ◽  
Viscoplastic Material ◽  
Highly Nonlinear ◽  
Complex Boundary ◽  
Consistent Tangent Operator

A formulation for finite element simulation of highly nonlinear problems including friction and contact with arbitrarily shaped rigid surfaces is proposed (CFS approach), prompted by difficulties in robust and accurate simulations of industrial forming processes. Nonlinearities are caused by large strains, plastic flow, and complex boundary conditions with frictional contact. In Part I the theoretical basis is described and the appropriate numerical algorithm is derived. The complete set of the governing relations, comprising equilibrium and interfacial equations, is appropriately linearized; resulting in a consistent tangent operator of the Newton-Raphson algorithm. In Part II, as a numerical verification, plane-strain sheet-forming processes are analyzed using a rigid-viscoplastic material model. Results are presented and discussed for test problems and for complex simulation of reverse drawing by concave tools.

Optimization of the Closure-Weld Region of Cylindrical Containers for Long-Term Corrosion Resistance Using the Successive Heuristic Quadratic Approximation Technique*

2003 ◽  
Vol 125 (3) ◽  
pp. 533-539 ◽  
Author(s):  
Zekai Ceylan ◽  
Mohamed B. Trabia
Keyword(s):  
Finite Element ◽  
Random Search ◽  
Nonlinear Problems ◽  
Search Space ◽  
Induction Coil ◽  
Quadratic Approximation ◽  
Approximation Technique ◽  
General Corrosion ◽  
Highly Nonlinear

Welded cylindrical containers are susceptible to stress corrosion cracking (SCC) in the closure-weld area. An induction coil heating technique may be used to relieve the residual stresses in the closure-weld. This technique involves localized heating of the material by the surrounding coils. The material is then cooled to room temperature by quenching. A two-dimensional axisymmetric finite element model is developed to study the effects of induction coil heating and subsequent quenching. The finite element results are validated through an experimental test. The container design is tuned to maximize the compressive stress from the outer surface to a depth that is equal to the long-term general corrosion rate of the container material multiplied by the desired container lifetime. The problem is subject to several geometrical and stress constraints. Two different solution methods are implemented for this purpose. First, an off-the-shelf optimization software is used. The results however were unsatisfactory because of the highly nonlinear nature of the problem. The paper proposes a novel alternative: the Successive Heuristic Quadratic Approximation (SHQA) technique. This algorithm combines successive quadratic approximation with an adaptive random search within varying search space. SHQA promises to be a suitable search method for computationally intensive, highly nonlinear problems.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Finite element simulation of fracture toughness testing of 20MnMoNi55 steel and the effect of loading rate on reference temperature

2020 ◽  
pp. 146442072095667
Author(s):  
Swagatam Paul ◽  
Snehasish Bhattacharjee ◽  
Sanjib Kumar Acharyya ◽  
Prasanta Sahoo
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Loading Rate ◽  
Flow Characteristics ◽  
Material Model ◽  
Compact Tension ◽  
Reference Temperature ◽  
Viscoplastic Material ◽  
Element Simulation

Fracture toughness of ferritic steel in the ductile-to-brittle transition zone is scattered and probabilistic owing to embrittlement. Use of master curve along with the reference temperature ( T0) adopted in ASTM E-1921 is widely accepted for characterization of this embrittlement. Reference temperature is a measure of embrittlement in the temperature scale. Factors affecting fracture toughness like geometry and loading rate are expected to influence the reference temperature. In the present study, the role of the loading rate on the reference temperature for 20MnMoNi55 steel is assessed experimentally using compact tension C(T) and three-point bend (TPB) specimens. Finite element simulation of tests at different loading rates and cryogenic temperature are carried out using a suitable viscoplastic material model that incorporates flow characteristics of the material for varying displacement rates and cryogenic temperatures. Results from simulation studies are compared with experimental ones.

scholarly journals Fracture investigation in starch-based foods

2016 ◽  
Vol 6 (3) ◽  
pp. 20160005 ◽  
Author(s):  
C. G. Skamniotis ◽  
Y. Patel ◽  
M. N. Charalambides ◽  
M. Elliott
Keyword(s):  
Material Model ◽  
Tensile Tests ◽  
Viscoplastic Material ◽  
Rate Dependent ◽  
Highly Nonlinear ◽  
Constitutive Response ◽  
Average Crack ◽  
Damage Law ◽  
Blade Cutting ◽  
Work Of Fracture

The study of oral processing and specifically cutting of the food piece during mastication can lead towards optimization of products for humans or animals. Food materials are complex biocomposites with a highly nonlinear constitutive response. Their fracture properties have not been largely investigated, while the need for models capable of predicting food breakdown increases. In this study, the blade cutting and the essential work of fracture (EWF) methodologies assessed the fracture behaviour of starch-based pet food. Tensile tests revealed rate-dependent stiffness and stress softening effects, attributed to viscoplasticity and micro-cracking, respectively. Cutting data were collected for 5, 10 and 30 mm s −1 sample feed rates, whereas the EWF tests were conducted at 1.7, 3.3 and 8.3 mm s −1 crosshead speeds corresponding to average crack speeds of 4, 7 and 15 mm s −1 , respectively. A reasonable agreement was achieved between cutting and EWF, reporting 1.26, 1.78, 1.76 kJ m −2 and 1.52, 1.37, 1.45 kJ m −2 values, respectively, for the corresponding crack speeds. These toughness data were used in a novel numerical model simulating the ‘first’ bite mastication process. A viscoplastic material model is adopted for the food piece, combined with a damage law that enabled predicting fracture patterns in the product.

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

2015 ◽  
Vol 07 (03) ◽  
pp. 1550047 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Highly Nonlinear ◽  
Lagrangian Finite Element ◽  
Post Buckling

Post-buckling analysis of an axially functionally graded (AFG) cantilever beam subjected to an axial nonfollower compression load is studied in this paper by using the total Lagrangian finite element model of three-dimensional continuum approximations. Material properties of the beam change in the axial direction according to a power-law function. In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of three-dimensional continuum for an eight-node quadratic element. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton–Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations. The obtained results are compared with the published results. In this study, the effects of the material distribution on the post-buckling response of the AFG beam are investigated in detail. The differences between of material distributions are investigated in the post-buckling analysis. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the beam, and it is believed that new results are presented for post-buckling of AFG beams which are of interest to the scientific and engineering community in the area of FGM structures.

Finite Element Analysis of the Rubber of the Prosthetic Knee Joint

2014 ◽  
Vol 607 ◽  
pp. 346-349
Author(s):  
Ying Liu ◽  
Xiu Feng Zhang ◽  
Yan Ma
Keyword(s):  
Finite Element ◽  
Nonlinear Problems ◽  
Element Model ◽  
Element Analysis ◽  
Rubber Material ◽  
Knee Motion ◽  
Prosthetic Knee ◽  
Rubber Bearing ◽  
Highly Nonlinear ◽  
Selection Of

Rubber played a buffer role in prosthetic knee motion. Rubber bearing is a very complicated process, and rubber material itself is nonlinear. ABAQUS software can able to deal with highly nonlinear problems. Input rubber test data in ABAQUS, selection of constitutive model, and then the finite element model is established, which is calculated, finally obtains compression under different loads.

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