Peridynamic stress is the static first Piola–Kirchhoff Virial stress

Li, Jun; Li, Shaofan; Lai, Xinmin; Liu, Lisheng

doi:10.1016/j.ijsolstr.2022.111478

Cited by 29 publications

(7 citation statements)

References 35 publications

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“…There are multiple approaches that can be utilized to interrogate the stress state that arises within the composite due to the combination of the thermal residual stress from processing and the applied stress state during testing, including approaches such as peridynamics 28 and finite element analysis 29 . However, such methods, while excellent at evaluating individual configurations, often come at a higher computational cost.…”

Section: Methodsmentioning

confidence: 99%

Microstructural and thermal stress effects on mechanical properties of boron carbide particle‐reinforced silicon carbide

Shoulders,

Guziewski,

Swab

2023

J Am Ceram Soc.

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Ceramic composites consisting of a silicon carbide matrix and boron carbide particles of various sizes and weight percentages were produced, characterized, and mechanically tested to elucidate the effect of microstructure on the mechanical response. All samples were observed to have flexural strength values lower than either of the constituent phases; however, blends with finer B4C particles (<10 μm) exhibited improved fracture toughness. Residual stresses from the mismatch in thermal expansion of the materials are found to be fundamental to these variations in mechanical response, resulting in either microcracking during processing or producing an initial stress state within the composite prior to testing. Microcracks were observed in samples with larger B4C particles (∼77 μm), causing a significant reduction in mechanical properties, while the finer B4C particles were found to be microcrack free. Residual stress measurements via X‐ray diffraction and Raman spectroscopy show increasing compressive stresses within the SiC matrix as the weight percentage of boron carbide increases, however both flexural strength and fracture toughness are found to decrease, indicating that the boron carbide particles that are in a tensile stress state are an important strength‐limiting feature. This is corroborated by fracture analysis. The results of both characterization and mechanical testing compare well with those predicted by micromechanics models.

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Section: Methodsmentioning

confidence: 99%

Microstructural and thermal stress effects on mechanical properties of boron carbide particle‐reinforced silicon carbide

Shoulders,

Guziewski,

Swab

2023

J Am Ceram Soc.

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show abstract

“…Peridynamics has also attracted considerable research attention as a new non-local theory [11,12], and has been applied to many engineering problems, such as the stress analysis in the vicinity of the crack tip [13], fracture modelling of reinforced concrete [14,15], and the inelastic fracture [16], etc. The governing equations in peridynamics are integral-differential equations rather than partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

ABAQUS and ANSYS Implementations of the Peridynamics-Based Finite Element Method (PeriFEM) for Brittle Fractures

Han¹,

Li²,

Zhang³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this study, we propose the first unified implementation strategy for peridynamics in commercial finite element method (FEM) software packages based on their application programming interface using the peridynamics-based finite element method (PeriFEM). Using ANSYS and ABAQUS as examples, we present the numerical results and implementation details of PeriFEM in commercial FEM software. PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically. It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM. Therefore, this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional FEM. An implicit algorithm is used for both ANSYS and ABAQUS; however, different convergence criteria are adopted owing to their unique features. In ANSYS, APDL enables users to conveniently obtain broken-bond information from UPFs; thus, the convergence criterion is chosen as no new broken bond. In ABAQUS, obtaining broken-bond information is not convenient for users; thus, the default convergence criterion is used in ABAQUS. The codes integrated into ANSYS and ABAQUS are both verified through benchmark examples, and the computational convergence and costs are compared. The results show that, for some specific examples, ABAQUS is more efficient, whereas the convergence criterion adopted in ANSYS is more robust. Finally, 3D examples are presented to demonstrate the ability of the proposed approach to deal with complex engineering problems.

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“…Based on coupled thermo-mechanical peridynamic theory, Song et al [26] established a coupled thermal mechanical periodic model with modified failure criterion suitable for de-icing technology. Li et al [27] proposed an improved peridynamic stress expression, which can well predict the stress state at the crack tip.…”

Section: Introductionmentioning

confidence: 99%

The Coupled Thermo-Chemo-Mechanical Peridynamics for ZrB2 Ceramics Ablation Behavior

Li¹,

Liu²,

Liu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The ablation of ultra-high-temperature ceramics (UTHCs) is a complex physicochemical process including mechanical behavior, temperature effect, and chemical reactions. In order to realize the structural optimization and functional design of ultra-high temperature ceramics, a coupled thermo-chemo-mechanical bond-based peridynamics (PD) model is proposed based on the ZrB 2 ceramics oxidation kinetics model and coupled thermomechanical bond-based peridynamics. Compared with the traditional coupled thermo-mechanical model, the proposed model considers the influence of chemical reaction process on the ablation resistance of ceramic materials. In order to verify the reliability of the proposed model, the thermo-mechanical coupling model, damage model and oxidation kinetic model are established respectively to investigate the applicability of the proposed model proposed in dealing with thermo-mechanical coupling, crack propagation, and chemical reaction, and the results show that the model is reliable. Finally, the coupled thermo-mechanical model and coupled thermo-chemo-mechanical model are used to simulate the crack propagation process of the plate under the thermal shock load, and the results show that the oxide layer plays a good role in preventing heat transfer and protecting the internal materials. Based on the PD fully coupled thermo-mechanical model, this paper innovatively introduces the oxidation kinetic model to analyze the influence of parameter changes caused by oxide layer growth and chemical growth strain on the thermal protection ability of ceramics. The proposed model provides an effective simulation technology for the structural design of UTHCs.

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Peridynamic stress is the static first Piola–Kirchhoff Virial stress

Cited by 29 publications

References 35 publications

Microstructural and thermal stress effects on mechanical properties of boron carbide particle‐reinforced silicon carbide

Microstructural and thermal stress effects on mechanical properties of boron carbide particle‐reinforced silicon carbide

ABAQUS and ANSYS Implementations of the Peridynamics-Based Finite Element Method (PeriFEM) for Brittle Fractures

The Coupled Thermo-Chemo-Mechanical Peridynamics for ZrB2 Ceramics Ablation Behavior

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