skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • NSF Public Access
  • Search Results
  • Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness
Title: Controlling the fracture response of structures via topology optimization: From delaying fracture nucleation to maximizing toughness
It is now a well-established fact that even simple topology variations can drastically change the fracture response of structures. With the objective of gaining quantitative insight into this phenomenon, this paper puts forth a density-based topology optimization framework for the fracture response of structures subjected to quasistatic mechanical loads. One of the two key features of the proposed framework is that it makes use of a complete phase-field fracture theory that has been recently shown capable of accurately describing the nucleation and propagation of brittle fracture in a wide range of nominally elastic materials under a wide range of loading conditions. The other key feature is that the framework is based on a multi-objective function that allows optimizing in a weighted manner: ( ) the initial stiffness of the structure, ( ) the first instance at which fracture nucleates, and ( ) the energy dissipated by fracture propagation once fracture nucleation has occurred. The focus is on the basic case of structures made of a single homogeneous material featuring an isotropic linear elastic behavior alongside an isotropic strength surface and toughness. Novel interpolation rules are proposed for each of these three types of material properties. As a first effort to gain quantitative insight, the framework is deployed to optimize the fracture response of 2D structures wherein the fracture is bound to nucleate in three different types of regions: within the bulk, from geometric singularities (pre-existing cracks and sharp corners), and from smooth parts of the boundary. The obtained optimized structures are shown to exhibit significantly enhanced fracture behaviors compared to those of structures that are optimized according to conventional stiffness maximization. Furthermore, the results serve to reveal a variety of strengthening and toughening mechanisms. These include the promotion of highly porous structures, the formation of tension-compression asymmetric regions, and the removal of cracks and sharp corners. The particular mechanism that is preferred by a given structure, not surprisingly, correlates directly to the elastic, strength, and toughness properties of the material that is made of.  more » « less
Award ID(s):
2127134
PAR ID:
10492195
Author(s) / Creator(s):
; ;
Publisher / Repository:
ScienceDirect
Date Published:
Journal Name:
Journal of the Mechanics and Physics of Solids
Volume:
173
Issue:
C
ISSN:
0022-5096
Page Range / eLocation ID:
105227
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of the Mechanics and Physics of Solids)
    An experimental and theoretical study of delayed fracture of polydimethlsiloxane (PDMS) is presented. Previous works have demonstrated that delayed fracture in single edge notch specimens is caused by time dependent damage due to chain scission. Here we study the interactions between damage and the elastic field using different specimens and crack geometries with blunt and sharp cracks. Our experiments show that initial toughness is not well defined, as stable slow crack growth can occur over a range of applied loads. Our experiments demonstrate that there is a universal relation between crack growth rate and applied energy release rate. A model coupling the nonlinear elastic deformation and rate dependent bond scission is proposed and is in good agreement with experimental data. 
    more » « less
  2. ; (, Additive Manufacturing)
    Anisotropy in additive manufacturing (AM), particularly in the material extrusion process, plays a crucial role in determining the actual structural performance, including the stiffness and strength of the printed parts. Unless accounted for, anisotropy can compromise the objective performance of topology-optimized structures and allow premature failures for stress-sensitive design domains. This study harnesses process-induced anisotropy in material extrusion-based 3D printing to design and fabricate stiff, strong, and lightweight structures using a two-step framework. First, an AM-oriented anisotropic strength-based topology optimization formulation optimizes the structural geometry and infill orientations, while assuming both anisotropic (i.e., transversely isotropic) and isotropic infill types as candidate material phases. The dissimilar stiffness and strength interpolation schemes in the formulation allow for the optimized allocation of anisotropic and isotropic material phases in the design domain while satisfying their respective Tsai–Wu and von Mises stress constraints. Second, a suitable fabrication methodology realizes anisotropic and isotropic material phases with appropriate infill density, controlled print path (i.e., infill directions), and strong interfaces of dissimilar material phases. Experimental investigations show up to 37% improved stiffness and 100% improved strength per mass for the optimized and fabricated structures. The anisotropic strength-based optimization improves load-carrying capacity by simultaneous infill alignment along the stress paths and topological adaptation in response to high stress concentration. The adopted interface fabrication methodology strengthens comparatively weaker anisotropic joints with minimal additional material usage and multi-axial infill patterns. Furthermore, numerically predicted failure locations agree with experimental observations. The demonstrated framework is general and can potentially be adopted for other additive manufacturing processes that exhibit anisotropy, such as fiber composites. 
    more » « less
  3. ; ; ; ; (, International Journal for Numerical and Analytical Methods in Geomechanics)
    ABSTRACT Strongly anisotropic geomaterials, such as layered shales, have been observed to undergo fracture under compressive loading. This paper applies a phase‐field fracture model to study this fracture process. While phase‐field fracture models have several advantages—primarily that the fracture path is not predetermined but arises naturally from the evolution of a smooth non‐singular damage field—they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a recently developed phase‐field model that accounts for compressive traction across the crack face, this paper extends the model to the setting of anisotropic fracture. The key features of the model include the following: (1) a homogenized anisotropic elastic response and strongly anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase‐field fracture evolution calculations in a fully resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. Prior approaches to simulate wing cracks have treated the initial cracks as an external boundary, which makes them difficult to apply to general settings. Here, the effective crack response model enables us to treat the initial crack simply as a nonsingular damaged zone within the computational domain, thereby allowing for easy and general computations. 
    more » « less
  4. ; (, Journal of Geophysical Research: Biogeosciences)
    Abstract Infaunal organisms mix sediments through burrowing, ingestion and egestion, enhancing fluxes of nutrients and oxygen, yet the mechanisms underlying bioturbation remain unresolved. Burrows are extended through muddy sediments by fracture, and we hypothesize that the cohesive properties of sediments play an important but unexplored role in resisting bioturbation. Specifically, we suggest that crack branching, tortuosity, and microcracking are important in freeing particles from the cohesive matrix, and that the sediment properties that affect these processes are important predictors of bioturbation. We use finite element modeling and simplified, mechanics‐based models to explore the relative importance of sediment mechanical properties and worm behaviors in determining crack propagation paths. Our results show that crack propagation direction depends on variability in fracture toughness, and that applying more force to one side of the burrow wall, simulating “steering” behavior, has surprisingly little effect on crack propagation direction. Burrowers instead steer by choosing among crack branches. Paths created by burrowing worms in natural sediments are mostly straight with some crack branching, consistent with modeling results. Crack branching also requires sufficient stored elastic energy to drive two cracks, and worms can exert larger forces resulting in more stored energy in stiffer sediments. This implies that more crack branching and consequently more particle mixing occurs in heterogeneous sediments with low fracture toughness relative to stiffness. Whether sediments with greater potential for crack branching also experience higher bioturbation remains to be tested, but these results indicate that material properties of sediments may be important in resisting or facilitating bioturbation. 
    more » « less
  5. ; ; (, Limnology and Oceanography: Methods)
    Abstract Muddy marine sediments are elastic materials in which bubbles grow and worms extend their burrows by fracture. Bubble growth and burrowing behavior are dependent on the stiffness and fracture toughness (KIc) of these muds. This article describes a custom laboratory apparatus to measure the fracture toughness of muddy, cohesive sediments using a bubble injection method. The system induces fracture in sediment samples by incrementally injecting air through a needle inserted into the sediment. The increasing pneumatic pressure is monitored until it drops abruptly, indicating bubble formation. Fracture toughness is then calculated from the peak pressure at which fracture occurred, following cavitation rheology methods developed for soft gels. The system has produced measurements that compare well to previous data but with better spatial resolution, allowing for characterization of spatial heterogeneity on small scales. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email