Representation of Mechanical Behavior in the Presence of Changing Internal Structure

Abstract

The paper is concerned with the representation of the relationship that exists, for a given material and temperature and for small deformations, between histories of applied stress and the observed strain and the accompanying changes in internal structure of the material. Emphasis is given to creep damage in metals as a vehicle for illustration of the main ideas introduced in the paper. In particular, the role played by irreducible even rank tensors in the representation of internal structure is discussed and clarified. The restrictions placed by thermodynamics on constitutive equations are considered and the use of potentials in these equations is examined and criticized.

A feasibility study of the Master SN curve approach for short fiber reinforced composites

“…For implementing the MSNC approach, first a realization of the RVE is created from the 2 nd order orientation tensor by the methods proposed by Onat and Leckie [40]. For all the calculations presented in this paper the size of the RVE is 2000 inclusions.…”

An Irreversible Thermodynamics Theory for Damage Mechanics of Solids

“…Cumulative damage analysis plays a key role in life prediction of components and structures subjected to load histories. As a result, many damage models have been proposed in the literature, such as linear damage models, nonlinear damage models, linear elastic fracture mechanics models, continuum damage mechanics models and energy-based damage models (Kachanov, 1958(Kachanov, , 1986Rabotnov, 1969;Valanis, 1971Valanis, , 1977Chaboche, 1988;Murakami, 1988;Murakami and Kamiya, 1997;Onat and Leckie, 1988;Ju, 1989Ju, , 1990Krajcinovic, 1989;Bazant, 1991;Chow and Chen, 1992;Lemaitre, 1996;Voyiadjis and Thiagarajan, 1996;Shi and Voyiadjis, 1997;Bonora and Newaz, 1998). Damage evolution function based on thermodynamics and statistical physics was first introduced by Basaran and Yan (1998) who established a relationship between entropy and damage for solids undergoing plastic deformations.…”

On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

“…Indeed, this is the form that is typically employed in discussing the general structure of the "thermodynamically -based" constitutive equations developed [1---5,8,13]; whereby the mathematical constructs such as the flow or dissipation potential and the attendant normality/generalized normality relations, i.e., the fl -form [6,8,9,[15][16][17]20,22] are introduced solely for conveniencein satisfyingthe aboveconstraints basedon simple properties of non-negativeness In its volumetric differential form, the Gibb's thermodynamic potential G(aij,a/3,W), can be written as follows [2,25]: (2). That is Both of these options are described separately, below.…”

“…These involve energy dissipations and material stiffness variations due to physical changes in the microstructure. Consequently, thermodynamic arguments have often been utilized as a foundation on which phenomenological constitutive laws may be formulated, i.e., the so---called internal variable formalism [1][2][3][4][5][6][7][8]. Material descriptions such as elastoplastic, viscoplastic, continuum-based damage, etc., (all falling into this framework) have been subjects of extensive research over the years [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”