Numerical Analysis of Time-Dependent Inelastic Deformation in Metallic Media Using the Boundary-Integral Equation Method

Abstract

A numerical analysis procedure using the boundary-integral equation method is presented for the solution of problems of time-dependent inelastic deformation in planar metallic bodies. The formulation allows the use of both classical creep theories as well as newer theories of inelastic deformation using state variables. Numerical results are presented for plane stress problems using either the power law equations of creep or the state variable theory due to Hart. Comparison of BIE and analytical methods for simple problems shows good agreement. Other features of the numerical solutions of more complicated problems are discussed in the paper.

Boundary element analysis of time-dependent inelastic deformation of cracked plates loaded in anti-plane shear

“…For a,body with an elliptic cutout- (Fig. 3), the equations for the rates of The'fkrst rwo terms in equation (14) are analogous to equation (6) and the last term, which represents a ldyer of concenrration n-~(") on the cutout boun-. .…”

“…Thus, if a kernel defined as the real part of 4 is used in a folsaulatfon analogous to equation (6) for a body with a circular cutout, the cutout will be , ' crack. Now The l a s t term i n equation (9) has s i n g u l a r i t i e s a t ' 5 = 0 and 6 = r ini'…”

A boundary element formulation for planar time-dependent inelastic deformation of plates with cutouts

“…[1,2]), but applications to nonlinear inelasticity problems have been relatively few. The authors of this paper together with others, have been interested in the application of the BEM to problems of time-dependent inelastic deformation [3][4][5][6][7]. Planar problems are considered in refs.…”

“…The kernels used in the integral equations in refs. [3][4][5][6] are the usual Kelvin traction and displacement functions for unit point loads in an infinite region. In the numerical procedure, boundary conditions along outsids as well as inslue boundaries {in multiply connected bodies) are satisfied at discrete points.…”

Finite element analysis of time‐dependent inelastic deformation in the presence of transient thermal stresses

“…Spatial integration of the relevant equations have been carried out by the finite element or boundary element method [8][9][10][11] and time-integration by a march forward time-integration scheme with automatic time step control [12]. In these papers, two-dimensional isothermal inelastic daformation problems have been solved and the constitutive model due to Hart [1,2] has been used.…”