Energy dissipation analysis of elastic–plastic materials

Yang, Han; Sinha, Sumeet Kumar; Yuan, Feng; McCallen, David; Jeremić, Boris

doi:10.1016/j.cma.2017.11.009

Cited by 55 publications

(29 citation statements)

References 36 publications

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“…Note that E S and E P correspond to elastic and plastic parts of free energy Ψ el and Ψ pl , respectively, defined by softening plasticity potential from (19). As indicated in [36], it is important to distinguish between energy dissipation D P and plastic work W Pl , where plastic work represents the combination of plastic dissipation and plastic free energy. Namely, only one part of this non-recoverable plastic work is dissipated and converted into heat.…”

Section: Plastic Softeningmentioning

confidence: 99%

“…The remaining part of the plastic work, also known as stored energy of cold work, is stored as internal energy and occurs as a consequence of rearrangement of microstructural crystals [37]. Details on energy dissipation analysis in various plasticity hardening models can be found in [36]. Energy balance equation 24can also be recovered by using the theorem of expended stress power (see [8]) combined with energy dissipation which stateṡ…”

Section: Plastic Softeningmentioning

confidence: 99%

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Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Nikolić

Nam

Ibrahimbegović

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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In this work we propose and compare the two models for crack propagation in dynamics. Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms. The first one is based on discrete lattice approach, where the domain is discretized with Voronoi cells held together prior to crack occurrence by cohesive links represented in terms of Timoshenko beams. The second one is based on constant strain triangular solid element. In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities. The latter remain localized inside the element, regulated by the localized traction separation behavior defined through exponential softening law. Thus, the both models provide the result that remain mesh-independent, with fracture energy as the model parameter. We show that implementation in dynamics framework can be obtained by adding inertial effects without modifying the existing quasi-statics models. In order to provide reliable results, classical implicit Newmark algorithm can be used for time integration. The two presented models are subjected to dynamic crack propagation benchmarks, where detailed analysis on strain, kinetic, plastic free and dissipated energy during simulation is verified by comparison to the amount of total work which is introduced into the system. The main strength of the proposed approach is that cracks initiation, propagation, their coalescence, merging and branching are automatically obtained without any tracking algorithms. In addition, since the discontinuities remain localized inside elements, accurate results can be obtained even with coarser grids, leading to efficient methodology capable of capturing complex crack patterns in dynamics.

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Section: Plastic Softeningmentioning

confidence: 99%

Section: Plastic Softeningmentioning

confidence: 99%

Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Nikolić

Nam

Ibrahimbegović

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…a purely elastic form. In accordance with the principle of conservation of mechanical energy, the peak elastoplastic strain energy ΔU peak around the opening during the first cycle of vibration is in the most conservative case effectively equal to the peak elastic strain energy, ΔU ′ E,peak , in the same domain derived from an equivalent elastic system, as depicted in Figures 4(c) and 4(d) [34,35]. us, the concentrated peak bending moments can be solved by evaluating the bending moments corresponding to ΔU ′ E,peak :…”

Section: Analysis Methodsmentioning

confidence: 68%

“…is is under the supposition that the development of localized plasticity around the opening is the failure criterion. Specifically, the kinetic energy of the plate-like structure may progressively dissipate or build up as plastic strain energy around the opening, potentially resulting in large deformations, rupture, or dynamic fracture during the initial cycle or subsequent oscillations [34][35][36].…”

Section: Discussionmentioning

confidence: 99%

“…e response of the plate-like structure may be adversely influenced if any localized plasticity around the opening is allowed to form and grow over subsequent cycles of free vibration. Specifically, the kinetic energy of the plate-like structure may be progressively dissipated or stored as plastic strain energy around the opening, potentially resulting in large deformations, rupture, or dynamic fracture during the initial cycle or subsequent oscillations, as depicted in Figure 4(b) [34][35][36]. e use of oversimplified analytical methods for calculating the stress concentrations may result in an overly conservative design of the reinforcement.…”

Section: Introductionmentioning

confidence: 99%

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Analysis Method for Reinforcing Circular Openings in Isotropic Homogeneous Plate-Like Structures Subjected to Blast Loading

Mendes

Cao

2018

Advances in Civil Engineering

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An analysis method is formulated to predict the peak bending stress concentrations around a small circular opening in an idealized isotropic homogeneous, linear elastic-perfectly plastic plate-like structure subjected to uniform blast loading. The method allows for the determination of corresponding concentrated bending moments adjacent to the opening for the design of reinforcement that can prevent the formation of localized plasticity around the opening during a blast event. The rapid formation and growth of localized plasticity around the opening can lead to a drastic reduction of the plate-like structure’s local and global stability, which could result in catastrophic failure of the structure and destruction of the entity it is protecting. A set of elemental formulas is derived considering one-way and two-way rectangular plate-like structures containing a single small circular opening located where flexure predominates. The derived formulas are applicable for elastic global response to blast loading. Abaqus was employed to conduct numerical verification of the derived formulas considering various design parameters including material properties, plate dimensions, position of opening, and explosive charge size. The formulas demonstrate a good correlation with FEA albeit with a conservative inclination. The derived formulas are intended to be used in tandem with dynamic SDOF analysis of a blast load-structure system for ease of design. Overall, the proposed method has the potential to be applicable for many typical conditions that may be encountered during design.

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A phase‐field approach for compaction band formation due to grain crushing

Borja

2022

Num Anal Meth Geomechanics

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Compaction bands are tabular regions of localized compressive deformation with little or no shear offset. Often observed in high‐porosity rocks, they can be classified into several subtypes based on their pattern and orientation with respect to the maximum principal stress. The combined effects of material properties and loading conditions on the type of compaction bands that develop are not fully understood, and realistic simulations of their formation are not always successful. In this study, a phase‐field approach for capturing the formation and propagation of compaction bands is proposed. The fracture energy utilized in classic phase‐field formulations is interpreted to be driven by grain crushing and is herein characterized by breakage mechanics theory. A new decomposition of the free energy function is introduced in which the energy stored by plastic compactive flow drives grain crushing. Depending on the value of the energy release rate, the model predicts different styles of compaction bands that are remarkably consistent with those observed in the field. Numerical simulations demonstrate the role of confining pressure, plasticity, and critical breakage energy on the styles of the predicted compaction bands.

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Energy dissipation analysis of elastic–plastic materials

Cited by 55 publications

References 36 publications

Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Analysis Method for Reinforcing Circular Openings in Isotropic Homogeneous Plate-Like Structures Subjected to Blast Loading

A phase‐field approach for compaction band formation due to grain crushing

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