Fracture of disordered three-dimensional spring networks: A computer simulation methodology

Chung, Jae‐Hyun; Roos, Arjen; Hosson, de Jeff; Giessen, van der Erik

doi:10.1103/physrevb.54.15094

Cited by 28 publications

(25 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1) suggest that disordered elastic networks [15] may be used to model TAs. Our initial studies were conducted on a square network of linear springs.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Model for Bone Strength and Osteoporotic Fractures

et al. 2002

View full text Add to dashboard Cite

Inner porous regions play a critical role in the load bearing capability of large bones. We show that an extension of disordered elastic networks [Chung et al., Phys. Rev. B 54, 15 094 (1996)] exhibits analogs of several known mechanical features of bone. The "stress backbones" and histograms of stress distributions for healthy and weak networks are shown to be qualitatively different. A hereto untested relationship between bone density and bone strength is presented.

show abstract

“…1) suggest that disordered elastic networks [15] may be used to model TAs. Our initial studies were conducted on a square network of linear springs.…”

mentioning

confidence: 99%

“…Externally imposed deviations increased the potential energy of the network via a combination of elastic [ contributions. Here Dl and Du are changes in the length of a spring and the bond angle between adjacent springs, respectively [15]. The differences between trabeculae are modeled by assigning random values for k and…”

mentioning

confidence: 99%

Model for Bone Strength and Osteoporotic Fractures

et al. 2002

View full text Add to dashboard Cite

show abstract

“…In Ref. [8], it was proposed that a system to model mechanical properties of a TA can be obtained by adapting a disordered network of fragile elastic elements [9]. The model system includes potential energy contributions from elasticity and from changes in bond angles between adjacent springs.…”

mentioning

confidence: 99%

Estimating the strength of bone using linear response

Gunaratne

2002

Phys. Rev. E

View full text Add to dashboard Cite

Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., http://xyz.lanl.gov]. It is shown that the ratio Γ of responses of such a network to static and periodic strain can be used to estimate its ultimate (or breaking) stress. Since bone fracture in older adults results from the weakening of porous bone, we discuss the possibility of using Γ as a non-invasive diagnostic of osteoporotic bone.Osteoporosis is a major socio-economic problem in an aging population [1]. Unfortunately, therapeutic agents which can prevent and even reverse osteoporosis often induce adverse side effects [2]. Thus, non-invasive diagnostic tools to determine the necessity of therapeutic intervention are essential for effective management of osteoporosis. Bone Mineral Density (BMD), or the effective bone density is the principal such investigative tool [3]. Ultrasound transmission through bone [4] and geometrical characteristics of the inner porous region or trabecular architecture (TA) [5][6][7] are being studied as complementary diagnostics.In older adults, weakening of the TA is the principal cause of increased propensity for bone fracture [4]. Analysis of models can complement mechanical studies of bone in aiding the identification of precursors of the weakening of a TA. In Ref. [8], it was proposed that a system to model mechanical properties of a TA can be obtained by adapting a disordered network of fragile elastic elements [9]. The model system includes potential energy contributions from elasticity and from changes in bond angles between adjacent springs. Furthermore, springs that are strained beyond (a predetermined value) ǫ and bond angles that change more than δ are assumed to fracture and are removed from the network. The inertia of the network is modeled by placing masses at the vertices. When in motion, each mass experiences a dissipative force proportional to its speed. Osteoporosis is modeled by random removal of a fraction ν of springs from the network, and the bone density is estimated by the fraction of remaining links. Therapeutic regeneration is introduced by strengthening springs that experience large strain (as suggested by Wolff's law [10]).Numerical studies of the system show analogs of several mechanical properties of bone including, (1) an initially linear stress vs. strain curve that becomes nonlinear beyond the fracture of elastic elements, (2) an exponential reduction of the ultimate (or breaking) stress with decreasing BMD, and (3) a dramatic increase of bone strength following therapeutic regeneration [8]. Together they support the conjecture that elastic networks are a suitable model of mechanical properties of bone. In this Letter we use results from a numerical study of the model to introduce a possible diagnostic tool for osteoporosis. FIG. 1. The stress distributions on networks of size 60 × 60 with (a) ν = 10%, and (b) ν = 30% representing "healthy" and "osteoporotic" bone respectively. For clarity only the compressed bonds...

show abstract

“…Within the past decade many papers have been published on the subject of the simulation of brittle 1 fracture. A commonly used approach in these papers is the lattice model (Arabi [1], Chung [3], Donze [4]). This method models objects as a lattice of points or pointmasses connected by stiff springs.…”

Section: Introductionmentioning

confidence: 99%

“…(Even with the use of implicit integration methods, the simulation of a lattice of stiff springs entails a computational cost as least equal to that of Lagrange multipliers.) For example, in Chung [3], the simulation of an object with 2701 lattice-links is done in 137 time-steps, each taking 86 seconds on a 75MHz MIPS R8000, for a total of three and a half hours. A comparable simulation with our method on the same hardware would take roughly five and a half 1 The term "brittle," as used in materials science literature (and in this paper) means that the substance does not undergo significant plastic (reversible) deformation before breaking [2].…”

Section: Introductionmentioning

confidence: 99%

Fast and Controllable Simulation of the Shattering of Brittle Objects

Smith¹,

Witkin²,

Baraff³

2001

Computer Graphics Forum

View full text Add to dashboard Cite

We present a method for the rapid and controllable simulation of the shattering of brittle objects under impact. An object to be broken is represented as a set of point masses connected by distance-preserving linear constraints. This use of constraints, rather than stiff springs, gains us a significant advantage in speed while still retaining fine control over the fracturing behavior. The forces exerted by these constraints during impact are computed using Lagrange multipliers. These constraint forces are then used to determine when and where the object will break, and to calculate the velocities of the newly created fragments. We present the details of our technique together with examples illustrating its use.

show abstract

Fracture of disordered three-dimensional spring networks: A computer simulation methodology

Cited by 28 publications

References 8 publications

Model for Bone Strength and Osteoporotic Fractures

Model for Bone Strength and Osteoporotic Fractures

Estimating the strength of bone using linear response

Fast and Controllable Simulation of the Shattering of Brittle Objects

Contact Info

Product

Resources

About