Oriented Damage in Ductile Sheets: Constitutive Modeling and Numerical Integration

Abstract

Thermodynamics with internal variables provides a framework for constitutive modeling of elasto-plastic deformations. Within the scope of the theory, constitutive and evolution equations for ductile, elasto-plastic materials with mixed (isotropic and kinematic) hardening and anisotropic damage have been developed. Postulates within continuum damage mechanics were used in order to incorporate damage as an internal variable. Owing to this, and to a simplified definition of the inverted damage effect tensor, a general expression for degradation of the elastic properties in materials has been obtained. The corresponding numerical algorithm for integration of the constitutive equations is based on an elastic predictor -plastic/ damage corrector procedure. The plastic/damage corrector is uncoupled, which further simplifies and expedites the corrector procedure.KEY WORDS: constitutive modeling, anisotropic damage, small strain elasticity, large strain plasticity, mixed hardening, numerical integration.

The Evolution of Effective Elastic Properties of a Cold Formed Stainless Steel Sheet

“…7. As is also true in the case of the isotropic damage model, the substantially greater decrease of Young's modulus E Theory 3: Anisotropic damage [5,22] Another attempt to construct a physically objective elasto-plastic damage model was presented in [5] where damage evolution is defined by relation…”

“…In the case of isotropic damage, Y is defined with relation (5), but in anisotropic damage a corresponding mapping of (5), with respect to the actually considered principal damage axis, should be applied. In our computational approach we will substitute isotropic variables E and D in (5) with the corresponding anisotropic variables E ii and D ii , in order to estimate Y for the anisotropic model. In the coordinate system of principal damage axes, the anisotropic damage is represented by the eigenvalues of the damage tensor D ij :…”

“…In paper [5] the authors use the constitutive equations of the Cordebois and Sidoroff model [22], in which a dissipation potential is defined in the following way:…”

“…The last stage in the damage process is void coalescence and eventual rupture. In fact, a whole branch of mechanics, namely continuum damage mechanics, is basically founded with a focus on stiffness degradation [5]. Other theories posited as a cause of stiffness degradation microplastic strain [6], changes in the dislocations arrangement, and phase transformations [7].…”

Identification of material hardening parameters by three-point bending of metal sheets

“…Previous work by the first two authors [6,7] on constitutive and evolution equations for rate-dependent and -independent metal sheet behaviour provides a viscoplastic material model, exhibiting damage propagation and mixed hardening. In the present study, these models were simplified by excluding the damage part.…”