A Time-Adaptive Finite Element Phase-Field Model for Rate-Independent Fracture Mechanics

核心概念

The author presents a time-adaptive finite element phase-field model for rate-independent fracture mechanics, focusing on balanced viscosity solutions to predict physically reasonable energy trajectories.

要約

The content discusses the modeling of cracks using phase-field models in engineering and mathematics. It highlights the challenges of crack propagation, the importance of solution concepts like Balanced Viscosity solutions, and the numerical implementation of the proposed model. The paper emphasizes the predictive capabilities, efficiency, and robustness of the algorithm through numerical examples.

統計

"Focusing on a rate-independent setting, these models are defined by a unidirectional gradient-flow of an energy functional."
"Numerical examples highlight the predictive capabilities of the model and show the efficiency and robustness of the final algorithm."
"The energy defining the phase-field model of rate-independent fracture is non-convex."
"Global energetic solutions capture crack initiation but may predict it too early."
"An algorithm is proposed that avoids physically unreasonable predictions by approximating Balanced Viscosity solutions."

引用

抽出されたキーインサイト

A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics

by Feli... 場所 arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07461.pdf

深掘り質問

How does non-uniqueness in solution concepts impact practical applications

Non-uniqueness in solution concepts can have a significant impact on practical applications, especially in fields like fracture mechanics. When dealing with non-convex energy functionals, different solution concepts may lead to different predictions of crack propagation or material behavior. This can result in discrepancies in the predicted outcomes and make it challenging to determine the most accurate representation of the physical system. In practical applications, such as designing structures or materials, having multiple possible solutions can create uncertainty and make it difficult to make informed decisions.

What are potential limitations or drawbacks of relying on global energetic solutions

Relying solely on global energetic solutions in phase-field modeling for fracture mechanics has potential limitations and drawbacks. Global energetic solutions are based on global minimization procedures that aim to find the overall minimum energy state of the system. However, these solutions may not always capture localized phenomena accurately, such as crack initiation points or discontinuities in crack propagation. Additionally, global energetic solutions tend to predict crack initiation and propagation too early compared to experimental observations, leading to over-predictions.

How can advancements in phase-field modeling benefit other fields beyond fracture mechanics

Advancements in phase-field modeling techniques developed for fracture mechanics can benefit other fields beyond just predicting crack propagation behavior. The phase-field method provides a versatile framework for simulating complex material behaviors with evolving microstructures and damage patterns. By applying similar principles from fracture mechanics models to other areas such as material science, geophysics, or biological systems, researchers can gain insights into how materials deform under various conditions or how fractures propagate through heterogeneous media. This cross-disciplinary approach allows for a deeper understanding of structural integrity issues across different industries and scientific disciplines.