Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150041

150041 - Smooth Crack Band Model Based on Spress-Sprain Relation 

Inspired by the 2020 invention of the gap test (PNAS), the "sprain" tensor, representing the second-gradient of the displacement field vector and borrowed from orthopedic medicine, was introduced in the continuum modeling of softening material damage in quasibrittle materials. This tensor also served as a crucial localization limiter in finite element analysis of fracture. This computationally effective approach treated the displacement vector and its gradient as independent fields with the lowest (C₀) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as the microplane model M7 for concrete, the sprain model demonstrated the capability to address and eliminate the inherent limitations of the classical crack band model (CBM). These limitations include a fixed crack band width, uniform damage distribution, and crack growth that is locally biased by mesh lines. By incorporating the microplane model M7, the sprain model ensures a more accurate representation of softening behavior under triaxial stress states, providing a robust framework for analyzing concrete damage.

In this work, we compare the sprain model to popular strain-softening gradient-damage models. These models differ by missing the energy density that resists a material rotation gradient. Paradoxically, this implies that a finite difference in material rotations on two arbitrarily close parallel planes would not be resisted by any shear stresses. Finite Element (FE) comparisons using the same material constitutive model show negligible differences from the sprain model in the case of symmetric Mode I fractures but reveal significant differences for shear fractures, particularly Modes II and III. This suggests that while the sprain model aligns well with traditional methods for tensile fractures, it offers better accuracy for shear-dominated failures.

To gain full acceptance among practitioners, more experiments on Mode II and III fractures are necessary. These experiments would provide empirical validation of the theoretical advantages observed in the sprain model. From a theoretical standpoint, the necessity of incorporating material resistance to a rotation gradient supports the superiority of the sprain theory over traditional models. This approach better reflects the complexities of material behavior under varied loading conditions.

Additionally, it is important to highlight that this critique does not apply to strain-gradient plasticity, which operates under different principles and considerations. The sprain model's ability to incorporate realistic material behaviors and provide a more accurate analysis framework sets it apart from other models currently in use. Its application to finite element analysis of fracture in quasibrittle materials marks a significant advancement in the field, promising more precise and reliable results in practical engineering scenarios.

Presenting Author: Houlin Xu Northwestern University

Presenting Author Biography: Houlin Xu is a fourth-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