Session: 13-11-02: Friction, Fracture, and Damage II

Paper Number: 167002

Smooth Crack Band Model With Nonlinear Spress-Sprain Relationship 

The "sprain" tensor, representing the second-gradient of the displacement field vector and borrowed from orthopedic medicine, was introduced following the 2020 invention of the gap test (PNAS) to model softening damage in quasibrittle materials. This tensor functions as a crucial localization limiter in finite element fracture analysis. The computational approach treats displacement vector and its gradient as independent fields with C₀ continuity, constrained by a second-order Lagrange multiplier tensor.

When combined with the microplane model M7 for concrete, the sprain model effectively overcomes the inherent limitations of the classical crack band model (CBM): fixed crack band width, uniform damage distribution, and mesh-biased crack growth. The integration of the microplane model M7 ensures accurate representation of softening behavior under complex triaxial stress states, providing a comprehensive framework for concrete damage analysis.

Comparing the sprain model with conventional strain-softening gradient-damage models reveals a fundamental difference: the latter lack energy density that resists material rotation gradients. This theoretical gap implies that finite differences in material rotations between closely parallel planes would encounter no shear stress resistance—a physically implausible scenario. Finite Element comparisons using identical constitutive models demonstrate minimal differences for Mode I fractures but significant variations for shear fractures (Modes II and III).

While the sprain model performs comparably to traditional methods for tensile fractures, it demonstrates markedly superior accuracy for shear-dominated failures. This distinction highlights the model's versatility across different fracture mechanisms. Additional Mode II and III fracture experiments are needed to empirically validate the sprain model's theoretical advantages before achieving widespread acceptance among engineering practitioners.

From a theoretical perspective, the necessity of incorporating resistance to rotation gradients strongly supports the sprain theory's superiority over traditional models in capturing complex material behavior under various loading conditions. This enhanced theoretical foundation enables more realistic simulation of fracture processes that involve mixed-mode conditions. It should be noted that this critique specifically excludes strain-gradient plasticity, which operates on fundamentally different principles.

The sprain model's sophisticated capacity to incorporate realistic material behaviors provides a substantially more accurate analysis framework than current alternatives. Its application to finite element analysis of quasibrittle material fracture represents a significant advancement in computational mechanics, offering more precise and reliable results for challenging engineering applications. By addressing fundamental limitations in existing models while maintaining computational efficiency, the sprain model effectively bridges theoretical sophistication with practical implementation.

In conclusion, this innovative approach promises improved predictive capabilities for complex fracture phenomena in concrete and other quasibrittle materials, ultimately contributing to safer and more economical structural designs.

Reference:

▪ Xu, Houlin, Anh Tay Nguyen, and Zdeněk P. Bažant. "Sprain energy consequences for damage localization and fracture mechanics." Proceedings of the National Academy of Sciences 121.40 (2024): e2410668121.

▪ Nguyen, Anh T., Xu, Houlin, Matous, K., Bažant. Z.P. (2024). "Smooth Lagrangian crack band model based on spress-sprain relation and Lagrange multiplier constraint of displacement gradient." ASME J. of Applied Mechanics 91, 031007-1—10.

▪ Nguyen, Hoang T., Pathirage, M., Rezaei, M., Issa, M., Cusatis, G., and Bažant, Z.P. (2020). "New perspective of fracture mechanics inspired by gap test with crack-parallel compression." Proceedings of the National Academy of Sciences 117 (25), 14015--14020.

Presenting Author: Houlin Xu Northwestern University

Presenting Author Biography: Houlin Xu is a fifth-year Ph.D. candidate in Prof. Zdenek Bazant's group at Northwestern University, specializing in Multi-Physics Modeling and Fracture Mechanics. Throughout his academic journey, he has made several contributions to the field, including a remarkable 110x speed improvement in simulations and the introduction of the innovative Smooth Crack Band Model to address mesh sensitivity issues in fracture prediction models. Notably, Houlin participated in proposing the "Spress-Sprain" Theory, which promises to revolutionize material curvature understanding. His research projects also include improving fishnet failure probability estimates through innovative analysis methods, optimizing structural design processes using data-driven methodologies, and enhancing composite material failure prediction through automation and stability conditions.

Authors:

Houlin Xu Northwestern University
Anh Nguyen Northwestern University
Zdenek Bazant Northwestern University
Yang Zhao Northwestern University