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1

Distribution of crack-tip stresses during fatigue loading with an overload event: role of initial crack-tip shape, plastic compressibility and material softening

Pandey Satyabrat, Khan Debashis, Alam Intaf

Journal of Theoretical and Applied Mechanics

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2021

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Vol. 59 nr 2

239--250

EN

This paper deals with the influence of initial crack-tip shape, plastic compressibility and material or strain softening on near-tip stress-strain fields for mode I crack when subjected to fatigue loading with an overload event under plane strain and small scale yielding conditions. A finite strain elastic-viscoplastic constitutive equation with a hardening-softening- -hardening hardness function is taken up for simulation. For comparison, a bilinear hardening hardness function is also considered. It has been observed that the near-tip crack opening stress yy, crack growth stress xx, and hydrostatic stresses are noticeably controlled by the initial crack tip shape, plastic compressibility, material softening as well as the overload event. The distribution pattern of different stresses for a plastically compressible hardening- -softening-hardening solid appears to be very unusual and advantageous as compared to those of traditional materials. Therefore, the present numerical results may guide material scientists/engineers to understand the near-tip stress-strain fields and growth of a crack in a better way for plastically compressible solids, and thus may help to develop new materials with improved properties.

2

Numerical simulations of arteries with an adaptive finite element method

Fuksa A. K., Rachowicz W.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 4

917--925

EN

This paper presents applications of the adaptive FEM in computational biomechanics. The study involves finite deformation of artery walls built of layers of elastic, nearly incompressible (rubber-like) materials. The models are reinforced with nearly inextensible collagen fibres stretched along the directions close to the circumferential direction. A Total Lagrangian technique based on the displacement-pressure formulation is presented. Residual error estimates and finite element mesh adaptation strategies are developed. The procedures are illustrated for solutions of arteries under various load considerations.

3

Selective symmetrization of the slip-system interaction matrix in crystal plasticity

Petryk H., Kursa M.

Archives of Mechanics

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2011

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Vol. 63, nr 3

287-287

EN

The symmetry issue of the interaction matrix between multiple slip-systems in the theory of crystal plasticity at finite deformation is revisited. By appealing to possibly non-uniform distribution of slip-system activity in a representative space-time element of a crystal, symmetry of the slip-system interaction matrix for the representative element is derived under assumptions that have a physical meaning. This conclusion refers to active slip-systems only. Accordingly, for any given hardening law, a new symmetrization rule is proposed that is restricted to active slip-systems and leaves the latent hardening of inactive slip-systems unchanged. Advantages of the proposal in comparison with full symmetrization are illustrated by a simple example of uniaxial tension.

4

Influence of the crack tip model on results of the finite elements method

Graba M., Gałkiewicz J.

Journal of Theoretical and Applied Mechanics

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2007

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Vol. 45 nr 2

225-237

EN

The paper contains recommendations of finite element models of the crack tip neighborhood to obtain results independent of the finite element mesh. The recommendations are valid for elastic-plastic problems and finite strains. As an example, analysis of single edge notched specimens under bending is presented.

PL

W pracy przeprowadzono analizę wpływu modelu MES na wartość naprężeń przed frontem pęknięcia w materiałach sprężysto-plastycznych, wyznaczaną w sposób numeryczny wartość całki J oraz rozwarcie wierzchołka pęknięcia (RWP). Obliczenia prowadzono dla płaskiego stanu odkształcenia przy założeniu dużych odkształceń.

5

Constitutive relations for dynamic material instability at finite deformation

Beda P. B.

Archives of Mechanics

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2001

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Vol. 53, nr 4-5

319-331

EN

This paper aims to present a mathematically consistent formulation of the second gradient dependence in the constitutive equations for material instability phenomena in case of finite deformations. Thus the set of fundamental equations of the solid continuum (the kinematic equations, the Cauchy equations of motion and the constitutive equations) should also be written for finite deformations. Two basic properties are required: the existence and regular propagation of waves and the generic behavior at the loss of stability. Firstly, the wave dynamics is studied. To encounter the second gradient effects, we should use the third order waves here. Secondly, the system of fundamental equations completed with initial and boundary value conditions forms a dynamical system. Then, identifying material stability with Lapunov stability of a state of the continuus body, the loss of stability should be one of the two basic types of instabilities of dynamical systems: a static or a dynamic bifurcation. These instability modes should be strictly different for a generic dynamical system.