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Multiscale Constitutive Modelling of the Influence of Anisotropy E?ects on Fracture Phenomena in Inelastic Solids

Perzyna P. P.

Engineering Transactions

2012

Vol. 60, iss. 3

225-225

The main objective of the present paper is the consistent development of the thermodynamical theory of elasto-viscoplasticity within the framework of a unique constitutive materialstructure. The focus of attention on the description of the influence of anisotropy effects on fracture phenomena is proposed. In the first part a general principle of determinism is formulated and a unique constitutive material structure is developed. The original conception of the intrinsic state of a particle X during motion of a body B has been assumed. A notion of the method of preparation of the deformation-temperature con?guration of a particle X has been proposed as a simple way of the gathering information for the description of the internal dissipation. As the basis of the thermodynamical requirements the dissipation principle in the form of the Clausius-Duhem inequality is assumed. By particular assumption of the method of preparation space for a unique constitutive material structure the internal state variable material structure has been constructed. In the second part the thermodynamical theory of elasto-viscoplasticity within the framework of the internal state variable material structure is formulated. Introduction of a finite set of the internal state variables is based on multiscale considerations in analysis of the physical foundations of inelastic solids and experimental observation results. Particular attention is focused on the determination of the evolution laws for the introduced internal state variables. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is proposed.

Adaptive analysis of inelastic problems with Bodner-Partom constitutive model

Cecot W.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 4

513-521

The Bodner-Partom elastic-visco-plastic constitutive eąuations [4] were used for numerical analysis of inelastic problems. This rate-dependent model makes it possible to describe elastic, plastic and viscous processes in metals, including temperaturę and continuum damage effects. The adaptive finite element method [9] was applied to approximate solution of the governing eąuations with two a posteriori error es-timates that control accuracy of time and space discretization of displacements and internal variables. The paper addresses a further development of the methodology proposed by the author in previous works [7, 8] and used in [6]. We present here certain additional theoretical background and propose a novel strategy of adaptation as well as verify the method of solution transfer.