Boundary element formulations for large strain-large deformation problems of viscoplasticity

doi:10.1016/0020-7683(84)90074-X

International Journal of Solids and Structures

Volume 20, Issue 1, 1984, Pages 41-53

https://doi.org/10.1016/0020-7683(84)90074-X Get rights and content

Abstract

Boundary element formulations with numerical solution strategies, for viscoplasticity problems in the presence of large strains and large deformations, are presented in this paper.

References (11)

R.M. McMeeking et al.
Finite element formulations for problems of large elastic-plastic deformation
Int. J. Solids Structures
(1975)
E.H. Lee et al.
Stress and deformation analysis of the metal extrusion process
Comput. Meth. Appl. Mech. Engng
(1977)
E.H. Lee et al.
Stress and deformation analysis of metal forming processes
A. Chandra et al.
A Anite element formulation for large strain-large deformation problems in plasticity and viscoplasticity

There are more references available in the full text version of this article.

Cited by (25)

A hybrid micro-macro BEM with micro-scale inclusion-crack interactions
1996, International Journal of Solids and Structures
Local analysis schemes capable of detailed representations of micro-features of a problem are integrated with a macro-scale BEM technique capable of handling finite geometries and realistic boundary conditions. This paper focuses on micro-scale interactions among cracks and inclusions as well as their ramifications on macro-scale damage evaluations. The micro-scale effects are introduced into the macro-scale BEM computations through an augmented fundamental solution obtained from an integral equation representation of the micro-scale features. The proposed hybrid micro-macro BEM formulation allows complete decomposition of the real problem into two sub-problems, one residing entirely at the micro-level while the other resides at the macro-level. This allows for investigations of the micro-structural attributes while retaining the macro-scale geometric features and actual boundary conditions for the structural component under consideration. As a first attempt, dilute inclusion densities with strong inclusion-crack and crack-crack interactions are considered. The numerical results obtained from the hybrid BEM analysis establish the accuracy and effectiveness of the proposed micro-macro computational scheme for this class of problems. The proposed micro-macro BEM formulation can be easily extended to investigate the effects of other micro-features (e.g., interfaces, short or continuous fibers, in the context of linear elasticity) on macro-scale failure modes observed in structural components.
A hybrid BEM formulation for multiple cracks in orthotropic elastic components
1995, Computers and Structures
Local analysis schemes capable of detailed representations of micro-features (e.g. micro-crack interactions) of a problem are integrated with a macro-scale BEM technique capable of handling orthotropic elastic components with complex finite geometries and realistic boundary conditions. The micro-scale effects are introduced into the macro-scale BEM analysis through an augmented fundamental solution obtained from an integral equation representation of the micro-scale features. The proposed hybrid micro-macro BEM formulation allows decomposition of the complete problem into two sub-problems, one residing entirely at the micro-level and the other at the macro-level. This allows for investigations of the effects of the micro-structural attributes while retaining the macro-scale geometric features and actual boundary conditions for the component or structure under consideration. As a first attempt, elastic fracture mechanics problems with interacting cracks at close spacings are considered. The proposed micro-macro BEM formulation can easily be extended to investigate the effects of other micro-features (e.g. interfaces, short or continuous fiber reinforcements, voids, and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.
Design sensitivities in problems involving material and geometric nonlinearities
1994, International Journal of Solids and Structures
The subject of this paper is the determination of design sensitivity coefficients (DSCs) for linear (elasticity) and nonlinear (both material and geometric) problems in solid mechanics. DSCs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body, with respect to parameters (called design variables) that control the initial, undeformed shape of the body. In nonlinear problems, these DSCs are history dependent.
The direct differentiation approach (DDA) of the relevant derivative boundary element method (DBEM) formulation is employed here to obtain the DSCs. Modelling of sharp corners on the boundary of a body is given special attention here. Numerical results are presented for illustrative examples. The numerically obtained sensitivities, even for stresses on the boundary of a body, are shown, in general, to be very accurate. Typically, it is difficult to obtain DSCs for boundary stresses accurately by other methods—yet they are very useful for optimal shape design of bodies.
Ongoing research is currently focused on numerical calculation of DSCs for large deformation problems and use of these DSCs in process optimization. An important future application area of this work is optimal design of manufacturing processes such as extrusion or forging.
Analyses of metal forming problems by the boundary element method
1994, International Journal of Solids and Structures
Forming is one of the most common manufacturing processes. This paper reviews the applications of the boundary element method (BEM) to analyses of various forming processes, e.g. extrusion, rolling, profile rolling, etc.
The boundary element formulations for elastic-plastic and elastic-viscoplastic problems involving large strains and rotations are considered first. The elastic strains are assumed to remain small. The rotations and nonelastic strains, however, are allowed to be large. Bulk compressibility effects, which are often ignored for finite strain problems of metallic solids, are explicitly included here.
An updated Lagrangian approach is adopted for the BEM analyses of forming processes. The frictional conditions at the tool-workpiece interface are introduced through a smeared interface element. For several forming problems, the frictional stresses change direction at the neutral region, and the location of this region is not known a priori. It is demonstrated here that the BEM can be used to efficiently and accurately analyse this class of planar and axisymmetric forming problems involving both material and geometric nonlinearities, along with complicated interface conditions. The numerical results obtained from the FEM analyses are also compared to those obtained from FEM with regard to efficiency and accuracy.
A boundary element analysis of the axisymmetric extrusion processes
1991, International Journal of Non-Linear Mechanics
The subject of this paper is a boundary element method (BEM) analysis of the axisymmetric extrusion processes. It is demonstrated that BEM may be used to analyse, efficiently and accurately, this complicated class of metal forming problems involving both geometric and material non-linearities. An updated Lagrangian approach is adopted in this analysis. The frictional conditions at the die-workpiece interface are introduced through a smeared interface element. Numerical results for sample problems of axisymmetric extrusion of Fe-0.05 carbon steel at a temperature of 1173 K, obtained by the BEM, are presented and discussed in this paper. A state variable elastic-viscoplastic model is used for material description. The BEM results are compared against those obtained by FEM for the same sample problems.
A boundary element formulation for design sensitivities in problems involving both geometric and material nonlinearities
1991, Mathematical and Computer Modelling
A BEM formulation for the determination of design sensitivities for shape optimization in problems involving both geometric and material nonlinearities is presented in this paper. This approach in based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantage of the BEM regarding accuracy, while avoiding strongly singular kernels. This approach provides a new avenue toward efficient shape optimization of elastic-viscoplastic or elastic-plastic problems involving large strains and rotations.

View all citing articles on Scopus

View full text

Boundary element formulations for large strain-large deformation problems of viscoplasticity

Abstract

Int. J. Solids Structures

Comput. Meth. Appl. Mech. Engng

Stress and deformation analysis of metal forming processes

A Anite element formulation for large strain-large deformation problems in plasticity and viscoplasticity