Energy-based modeling of localization and necking in plasticity

In this paper two different non-local plasticity models are presented and compared to describe the necking and fracture through a non-convex energy, where fracture is regarded as the extreme localization of the plastic strain. The difference between the models arises from the evolution of plastic deformation. The first (rate-dependent) approach, proposed in Yalcinkaya et al. (2011) follows the principle of virtual work to get balance equations and the dissipation inequality, in order to obtain the plastic evolution equation. The free-energy is given by the sum of a non-convex plastic term, and two quadratic terms with respect to the elastic deformation and the plastic deformation gradient. In the second (rate-independent) model, developed in Del Piero et al. (2013a), the plastic evolution is determined by incremental minimization of an energy functional which is equal to the free-energy of the previous model. The numerical example considers a convex-concave plastic energy to address the response of a tensile steel bar, where plastic strains localize intrinsically up to fracture. The numerical results exhibit good agreement between the two models. The solutions provided by the rate-dependent model approach those of the rate independent model, as the imposed deformation rate reduces.


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Lancioni, Giovanni; Yalçınkaya, Tuncay (2014-05-09)
Plastic deformation induces various types of dislocation microstructures at different length scales, which eventually results in a heterogeneous deformation field in metallic materials. Development of such structures manifests themselves as macroscopic hardening/softening response and plastic anisotropy during strain path changes, which is often observed during forming processes. In this paper we present two different non-local plasticity models based on non-convex potentials to simulate the intrinsic rate-...
Non-convex rate dependent strain gradient crystal plasticity and deformation patterning
Yalçınkaya, Tuncay; Geers, M.G.D. (2012-09-15)
A rate dependent strain gradient crystal plasticity framework is presented where the displacement and the plastic slip fields are considered as primary variables. These coupled fields are determined on a global level by solving simultaneously the linear momentum balance and the slip evolution equation, which is derived in a thermodynamically consistent manner. The formulation is based on the 1D theory presented in Yalcinkaya et al. (2011), where the patterning of plastic slip is obtained in a system with no...
Ternary nanocomposites of low density, high density and linear low density polyethylenes with the compatibilizers E-MA-GMA and E-BA-MAh
Işık Coşkunses, Fatma; Yılmazer, Ülkü; Department of Chemical Engineering (2011)
The effects of polyethylene, (PE), type, compatibilizer type and organoclay type on the morphology, rheological, thermal, and mechanical properties of ternary low density polyethylene (LDPE), high density polyethylene (HDPE), and linear low density polyethylene (LLDPE), matrix nanocomposites were investigated in this study. Ethylene – Methyl acrylate – Glycidyl methacrylate terpolymer (E-MAGMA) and Ethylene – Butyl acrylate- Maleic anhydrate terpolymer (E-BA-MAH) were used as the compatibilizers. The organo...
Güler, Baran; Efe, Mert (2018-06-22)
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Thermal stress problem for an FGM strip containing periodic cracks
Köse, Ayşe; Kadıoğlu, Fevzi Suat; Department of Mechanical Engineering (2013)
In this study the plane linear elastic problem of a functionally graded layer which contains periodic cracks is considered. The main objective of this study is to determine the thermal stress intensity factors for edge cracks. In order to find an analytic solution, Young’s modulus and thermal conductivity are assumed to be varying exponentially across the thickness, whereas Poisson ratio and thermal diffusivity are taken as constant. First, one dimensional transient and steady state conduction problems are ...
Citation Formats
T. Yalçınkaya, “Energy-based modeling of localization and necking in plasticity,” 2014, vol. 3, Accessed: 00, 2020. [Online]. Available: