Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Dornowski, W.; Perzyna, P.

doi:10.1016/s0020-7683(02)00405-5

Cited by 15 publications

(4 citation statements)

References 21 publications

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“…Based on the possible linear transformations defined by Eqs. (12), (13), (19), and (20), and by analogy to the classical results, we have…”

Section: Downloaded By [North Dakota State University] At 20:32 19 Nomentioning

confidence: 72%

Thermoelasticity in the Framework of the Fractional Continuum Mechanics

Sumelka

2014

Journal of Thermal Stresses

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Fractional continuum mechanics is the generalization of classical mechanics utilizing fractional calculus. Contrary to classical theory, the obtained description is non-local, which is inherently the consequence of the fractional derivative definition based on the interval. So, all fields obtained in the framework of this new formulation, such as temperature, thermal stresses, total stresses, displacements, etc., at the specific point of interest, depend on the information from its surroundings. The dimensions of these surroundings and the ways of influencing the results are governed by the fractional differential operator applied. In this article, the application of the fractional continuum mechanics to thermoelasticity is presented. A classical solution is obtained as a special case.

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“…Based on the possible linear transformations defined by Eqs. (12), (13), (19), and (20), and by analogy to the classical results, we have…”

Section: Downloaded By [North Dakota State University] At 20:32 19 Nomentioning

confidence: 72%

Thermoelasticity in the Framework of the Fractional Continuum Mechanics

Sumelka

2014

Journal of Thermal Stresses

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“…This has been done by assumption that the stress intensity invariants for nucleation and growth depend on the three invariants of stress tensor, cf. It has been shown by Dornowski and Perzyna [17], [18], [19], [20] that this modification helps to describe the accumulation of damage during dynamic loading cyclic process. (25) and (26).…”

Section: Influence Of Stress Triaxiality On the Evolution Of Microdamagementioning

confidence: 99%

Constitutive Modelling of Dissipative Solids for Application in Modern Manufacturing Processes

Perzyna¹

2004

AIP Conference Proceedings

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Articles you may be interested inA force-based large increment method for 2D continuum solids and the mesh convergence study AIP Conf.Abstract. The main objective of this paper is to survey some recent developments in the constitutive modelling of inelastic polycrystalline solids, which may be used for the description of important problems in modern manufacturing processes. This description is needed for the investigation by using the numerical methods how to avoid unexpected plastic strain localization and fracture phenomena in manufacturing technology. Since modern manufacturing processes lead to very complex state of stress and deformation for a solid body under consideration then in the description we have to take into account the influence of stress triaxiality and plastic spin effects. In this lecture emphasis is laid on experimental and physical foundations as well as on mathematical constitutive modelling for the description of localization of plastic deformation and various modes of fracture phenomena in polycrystalline solids. The description of kinematics of finite deformations and the stress tensors is given. The development of a thermo-elasto-viscoplastic model within the thermodynamic framework of the rate type covariance constitutive structure with finite set of the internal state variables is presented. Particular attention is focused on the determination of the evolution laws for the internal state variables. Fracture criterion based on the evolution of microdamage is formulated. By assuming that the mechanical relaxation time is equal to zero the thermo-elasto-plastic (rate independent) response of the damaged material can be accomplished. The thermodynamical theory of elasto-viscoplasticity of polycrystalline solids presented has important features as follows: (i) invariance with respect to diffeomorphism; (ii) finite plastic deformation and plastic spin effects; (iii) plastic non-normality; (iv) softening effects generated by microdamage mechanism; (v) plastic deformation induced anisotropic effects; (vi) thermomechanical couplings (thermal plastic softening and thermal expansion); (vii) influence of stress triaxiality on the evolution of microdamage; (viii) rate sensitivity; (ix) length scale sensitivity; (x) regularization of the evolution problem; (xi) dissipation and dispersion effects; (xii) synergetic effects generated by cooperative phenomena. All these fundamental features have been carefully discussed. It should be noted that the very important part of the constitutive modelling is the identification procedure for the material functions and constants involved in the constitutive equations proposed.

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“…explicit [Borst and Pamin, 1996, Fleck and Hutchinson, 1997, Aifantis, 1999, Voyiadjis and Abu Al-Rub, 2005, Polizzotto, 2011] (e.g. via classical strain gradients) or implicit [Perzyna, 1998, Łodygowski and Perzyna, 1997, Dornowski and Perzyna, 2002, Sumelka and Łodygowski, 2011, Sumelka and Łodygowski, 2013, Voyiadjis and Faghihi, 2013, Sumelka, 2013c (i.e. via relaxation time in Perzyna's type viscoplasticity).…”

Section: Introductionmentioning

confidence: 99%

Non-local fractional model of rate independent plasticity

Sumelka

2013

Preprint

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In the paper the generalisation of classical rate independent plasticity using fractional calculus is presented. This new formulation is non-local due to properties of applied fractional differential operator during definition of kinematics. In the description small fractional strains assumption is hold together with additive decomposition of total fractional strains into elastic and plastic parts. Classical local rate independent plasticity is recovered as a special case.

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Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Cited by 15 publications

References 21 publications

Thermoelasticity in the Framework of the Fractional Continuum Mechanics

Thermoelasticity in the Framework of the Fractional Continuum Mechanics

Constitutive Modelling of Dissipative Solids for Application in Modern Manufacturing Processes

Non-local fractional model of rate independent plasticity

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