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vol. 54, no. 5-6 (2002)
vol. 55, no. 2 (2003)
Archives of Mechanics
Archiwum Mechaniki Stosowanej
A Bimonthly Journal
Appears since 1949
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vol. 54, no. 5-6 (2002) |
vol. 55, no. 1 (2003)
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vol. 55, no. 2 (2003) |
- A general framework for the analysis of heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic viscodamage evolution is formulated for-impact related problems within the framework of thermodynamic laws and nonlinear continuum mechanics. The proposed formulations include thermo-elasto-viscoplastici- ty with anisotropic thermo-elasto-viscodamage, a dynamic yield criterion of a von Mises type and a dynamic viscodamage criterion, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. That is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The evolution laws are impeded in a finite deformation framework based on the multiplicative decomposition of the deformation gradient into elastic, viscoplastic, and viscodamage parts. Since the material macroscopic thermomechanical response under high-impact loading is governed by different physical mechanisms on the macroscale level, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic hardening), and crack and void interactions (damage hardening). The non-local theory of viscoplasticity and viscodamage that incorporates macroscale interstate variables and their higher-order gradients is used here to describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of the evolution-related viscoplasticity and viscodamage hardening variables. The gradients are introduced here in the hardening internal state variables and are considered to be independent of their local counterparts. It also incorporates the thermomechanical coupling effects as well as the internal dissipative effects through the rate-type covariance constitutive structure with a finite set of internal state variables. The model presented in this paper can be considered as a framework, which enables one to derive various non-local and gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions.
A framework is derived for the proper and consistent description of a discontinuity (a crack) as the result of a damaging process in a continuous medium. The damaging process in the continuous medium is described using a gradient-enhanced damage theory, so that well-posedness of the boundary-value problem is maintained until the damage process is completed and a discontinuity arises. At that moment the partition-of-unity property of finite element shape functions is exploited to partition the displacement field into two continuous fields, separated via a Heaviside function. It is demonstrated that the additional boundary conditions that arise in a gradient-enhanced damage theory, can be accounted for in a natural and transparent manner.
A numerical integration algorithm for thermo-elasto-viscoplastic constitutive equations is presented. This algorithm satisfies the principle of material objectivity with respect to the total motion (translation, rotation and strain) of a material element. For this purpose, the properties of convective description are used. The explicit-implicit integration scheme for the plastic flow rule plays the crucial role in the proposed algorithm. The method of determining the stress state for inelastic deformations is based on the iterative solution of the dynamic yield condition with respect to the norm of the viscoplastic deformation rate tensor. The constitutive model being the subject of numerical analyses is described. Results of numerical calculations, which show an excellent performance of the proposed procedure, are presented.
Reprints of the full papers may be obtained from their authors. Contact Editorial Office in case you need the address of the respective author.The equations of second order elasticity theory are applied. In this approximation three constants of the second order and six constants of the third order characterize the crystal. The stress for three shearing planes and three directions for each plane has been calculated. The stresses have been calculated separately for each material constant. For copper, the shearing planes and shearing directions for which stress reaches extreme values have been determined. The extreme values for each component of the traction have been calculated.
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