Large Deformation Analysis of Hyperelastic Membranes Containing a Hole or Inclusion

2010 ◽  
Vol 146-147 ◽  
pp. 696-700
Author(s):  
Wen Jia Wang ◽  
Bo Liu ◽  
Jian Bing Sang ◽  
Chen Hua Lu
Keyword(s):  
Large Deformation ◽  
Constitutive Relation ◽  
Numerical Solutions ◽  
Constitutive Models ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Incompressible Materials ◽  
Strain Invariant ◽  
Solutions Of Equations ◽  
Constitutive Parameters

A large deformation analysis has been given by using a modified Gao’s second constitutive relation. In certain circumstances, the new constitutive relation may be simplified to the Mooney-Rivlin and Neo-Hookean models. With regard to incompressible materials, when the influence of the second strain invariant is neglected, the modified model brings a unified form of Gao’s two constitutive models. The new constitutive relation has been utilized to resolve a problem of a hyperelastic membrane containing a hole or rigid inclusion. The basic governing equations of incompressible materials have been obtained and numerical solutions of equations illustrate how constitutive parameters affect the result of membranes’ deformation. These conclusions may provide helps to practical problems.

An Incremental Constitutive Relation of Unilateral Contact Friction for Large Deformation Analysis

1985 ◽  
Vol 52 (3) ◽  
pp. 639-648 ◽  
Author(s):  
J.-H. Cheng ◽  
N. Kikuchi
Keyword(s):  
Large Deformation ◽  
Constitutive Relation ◽  
Contact Friction ◽  
Deformation Analysis ◽  
Elastoplastic Material ◽  
Unknown Parameters ◽  
Large Deformation Analysis ◽  
Proposed Model ◽  
Updated Lagrangian Approach ◽  
Updated Lagrangian

An incremental constitutive relation of friction contact is presented for large deformation analysis. After a brief review of published explanations of friction, a model is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and nonlocal effects are discussed. Formulations of a quasistatic boundary value problem based on the updated Lagrangian approach are summarized. The elastoplastic material is assumed to behave according to the generalized Prandtl-Reuss constitutive equation. Finite element methods are employed to solve the problem. Two examples are selected to demonstrate the capability and adequacy of the proposed model.

Large deformation analysis of moderately thick viscoelastic plates

2019 ◽  
Vol 163 ◽  
pp. 146-167 ◽  
Author(s):  
Nasrin Jafari ◽  
Mojtaba Azhari ◽  
Bijan Boroomand
Keyword(s):  
Large Deformation ◽  
Deformation Analysis ◽  
Large Deformation Analysis

Meshless TL and UL Approaches for Large Deformation Analysis

2010 ◽  
Vol 139-141 ◽  
pp. 893-896 ◽  
Author(s):  
Yuan Tong Gu
Keyword(s):  
Large Deformation ◽  
Computational Efficiency ◽  
Metal Forming ◽  
Weak Form ◽  
Superior Performance ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Updated Lagrangian ◽  
Local Weak Form ◽  
Large Deformation Problems

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using in the UL approach than using in the TL approach.

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