# Improved boundary-integral equation method for time-dependent inelastic deformation in metals

## Abstract

Efficient solution of boundary-value problems for time-dependent inelastic deformation in metallic structures are generally solved by finite element methods and separate descriptions for time-independent plasticity and time-dependent creep are normally used. The boundary-integral equation method was recently applied for the first time to such problems. A very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler type time-integration scheme with automatic time-step control for time integration is presented. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor--corrector scheme for time-integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time-histories of loadings. The numerical results presented in the paper are for certain illustrative problems.

- Authors:

- Publication Date:

- Research Org.:
- Cornell Univ., Ithaca, NY (USA). Dept. of Theoretical and Applied Mechanics

- OSTI Identifier:
- 5940965

- Report Number(s):
- COO-2733-20

- DOE Contract Number:
- EY-76-S-02-2733

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; BOUNDARY-VALUE PROBLEMS; MATHEMATICAL MODELS; METALS; PLATES; STAINLESS STEEL-304; BOUNDARY CONDITIONS; CREEP; DEFORMATION; ELASTICITY; PLASTICITY; STRESSES; TIME DEPENDENCE; ALLOYS; CHROMIUM ALLOYS; CHROMIUM STEELS; CHROMIUM-NICKEL STEELS; CORROSION RESISTANT ALLOYS; ELEMENTS; HEAT RESISTANT MATERIALS; HEAT RESISTING ALLOYS; IRON ALLOYS; IRON BASE ALLOYS; MATERIALS; MECHANICAL PROPERTIES; NICKEL ALLOYS; STAINLESS STEELS; STEELS; TENSILE PROPERTIES; 360103* - Metals & Alloys- Mechanical Properties

### Citation Formats

```
Morjaria, M., and Mukherjee, S.
```*Improved boundary-integral equation method for time-dependent inelastic deformation in metals*. United States: N. p., 1979.
Web. doi:10.2172/5940965.

```
Morjaria, M., & Mukherjee, S.
```*Improved boundary-integral equation method for time-dependent inelastic deformation in metals*. United States. doi:10.2172/5940965.

```
Morjaria, M., and Mukherjee, S. Thu .
"Improved boundary-integral equation method for time-dependent inelastic deformation in metals". United States. doi:10.2172/5940965. https://www.osti.gov/servlets/purl/5940965.
```

```
@article{osti_5940965,
```

title = {Improved boundary-integral equation method for time-dependent inelastic deformation in metals},

author = {Morjaria, M. and Mukherjee, S.},

abstractNote = {Efficient solution of boundary-value problems for time-dependent inelastic deformation in metallic structures are generally solved by finite element methods and separate descriptions for time-independent plasticity and time-dependent creep are normally used. The boundary-integral equation method was recently applied for the first time to such problems. A very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler type time-integration scheme with automatic time-step control for time integration is presented. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor--corrector scheme for time-integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time-histories of loadings. The numerical results presented in the paper are for certain illustrative problems.},

doi = {10.2172/5940965},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1979},

month = {2}

}