Numerical integration of rate constitutive equations in finite deformation analysis

1983 ◽  
Vol 40 (2) ◽  
pp. 137-158 ◽  
Author(s):  
Peter M. Pinsky ◽  
Miguel Ortiz ◽  
Karl S. Pister
Keyword(s):  
Numerical Integration ◽  
Finite Deformation ◽  
Constitutive Equations ◽  
Deformation Analysis

An Orthogonal Cutting Model Based on Finite Deformation Analysis: Part II — Constitutive Equations and Experimental Verification

1999 ◽  
Author(s):  
Y. Zheng ◽  
J. W. Sutherland
Keyword(s):  
Finite Deformation ◽  
Constitutive Equations ◽  
Orthogonal Cutting ◽  
Shear Angle ◽  
Deformation Analysis ◽  
Tool Steels ◽  
Model Based ◽  
Cutting Operation ◽  
Cutting Experiment ◽  
Cutting Model

Abstract In Part I of this paper, a model based on finite deformation analysis was developed to predict the forces in an orthogonal cutting operation. In the second part of the paper, the constitutive equations for O1 and L6 tool steels are developed using Hopkinson bar tests. A total of 90 statistically designed orthogonal cutting tests are conducted to investigate the cutting mechanics of O1 and L6 tool steels. Then the cutting model developed in Part I of this paper is applied to simulate all the 90 cutting tests using the measured material constitutive equations. All the measurable model outputs are calculated and compared with the corresponding cutting experiment results. The comparisons show that the cutting model based on finite deformation analysis can be successfully applied to predict the cutting forces, shear angle, and various relationships in machining (orthogonal cutting) tests.

scholarly journals An improved meshless method for finite deformation problem in compressible hyperelastic media

2021 ◽  
Author(s):  
Nha Thanh Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong ◽  
Tinh Quoc Bui
Keyword(s):  
Numerical Integration ◽  
Large Deformation ◽  
Finite Deformation ◽  
Interpolation Method ◽  
Large Strain ◽  
Elastic Solid ◽  
Meshfree Method ◽  
Deformation Analysis ◽  
Deformation Problem ◽  
Deformation State

Hyperelastic materials are considered as special category of elastic solid materials because of their nonlinear complicated constitutive laws. Due to large strain state, the behaviour of such materials is often considered in finite deformation analysis. The nonlinear large deformation behavior of such materials is important. In this study, a novel meshless radial point interpolation method (RPIM) enhanced by Cartesian transformation method (CTM), an effective numerical integration, is presented for nonlinear behavior of hyperelastic media under finite deformation state with total Lagrange formulation. Unlike the mesh-based approaches, the meshless methods have shown their advantages in analysis of large deformation problems. The developed CTM-based RPIM is thus free from the need for background cells, which are often used for numerical integration in many conventional meshfree approaches. The developed meshfree method owns some desirable features of an effective technique in solving large deformation, which will be illustrated through the numerical experiments in which our computed results are validated against reference solutions derived from other approaches. 

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Nonlinear Finite Deformation Analysis of Beams and Columns

1994 ◽  
Vol 120 (10) ◽  
pp. 2136-2153 ◽  
Author(s):  
Ronald Y. S. Pak ◽  
Eric J. Stauffer
Keyword(s):  
Finite Deformation ◽  
Deformation Analysis
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