Fracture roughness in three-dimensional beam lattice systems

We study the scaling of three-dimensional crack roughness using large-scale beam lattice systems. Our results for prenotched samples indicate that the crack surface is statistically isotropic, with the implication that experimental findings of anisotropy of fracture surface roughness in directions parallel and perpendicular to crack propagation is not due to the scalar or vectorial elasticity of the model. In contrast to scalar fuse lattices, beam lattice systems do not exhibit anomalous scaling or an extra dependence of roughness on system size. The local and global roughness exponents (ζloc and ζ, respectively) are equal to each other, and the three-dimensional crack roughness exponent is estimated to be ζloc=ζ=0.48±0.03. This closely matches the roughness exponent observed outside the fracture process zone. The probability density distribution p[Δh(ℓ)] of the height differences Δh(ℓ)=[h(x+ℓ)−h(x)] of the crack profile follows a Gaussian distribution, in agreement with experimental results.Peer reviewe

An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks

{\it Critical slowing down} associated with the iterative solvers close to the critical point often hinders large-scale numerical simulation of fracture using discrete lattice networks. This paper presents a block circlant preconditioner for iterative solvers for the simulation of progressive fracture in disordered, quasi-brittle materials using large discrete lattice networks. The average computational cost of the present alorithm per iteration is $O(rs log s) + delops$, where the stiffness matrix ${\bf A}$ is partioned into $r$-by-$r$ blocks such that each block is an $s$-by-$s$ matrix, and $delops$ represents the operational count associated with solving a block-diagonal matrix with $r$-by-$r$ dense matrix blocks. This algorithm using the block circulant preconditioner is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing down} that is especially severe close to the critical point. Numerical results using random resistor networks substantiate the efficiency of the present algorithm.Comment: 16 pages including 2 figure

AISI/DOE Technology Roadmap Program: TRP 9732Steel Processing Properties and Their Effect on Impact Deformation of Lightweight Structures

The objective of the research was to perform a comprehensive computational analysis of the effects of material and process modeling approaches on performance of Ultra Light Steel Auto Body (ULSAB) vehicle models. The research addressed numerous material related effects, impact conditions as well as analyzed the performance of the ULSAB vehicles in crashes against designs representing the current US vehicle fleet. Crash modeling simulations show a clear effect of strain-rate sensitivity on high strength steel (HSS) intensive vehicle. The influence of a strain-rate model can be an incremental sensitivity due to the increased flow stress when similar structure collapse modes are predicted. However, significant differences in crash energy management capacity can be predicted if the change in loading on members alters the predicted collapse mode of the structure. From the material substitution study it can be concluded that HSS material substitution cannot be performed on the basis of the material yield point only and that, especially for advanced HSS vehicle designs, the entire region of material plastic response has to be considered. However, the problem of modeling of the overall dynamic crush process still remains open and requires further experimental and theoretical investigation. Crash modeling simulations show a moderate effect of forming on overall crash performance. The design is the determining factor on the vehicle performance and, therefore, the results of this research cannot provide measures that can be used in a general case. However, it has been shown that for materials that have modest strain hardening, the forming effect is observable and that when more complex forming operations are used, especially in combination with rapid strain hardening materials, forming effects should be taken in the consideration in the computational crash models. crash compatibility study between ULSAB and cars of similar geometric characteristics have shown that the U LSAB design is compatible with the conventional designs of existing cars with similar inertia and geometric characteristics. The structural-performance characteristics of the vehicles involved in a car-to-car collision when one of the cars is the ULSAB are governed by the stiffness and geometry of the crush zone in the vehicles. The effects of mass could not be evaluated because of the similar mass of the vehicle models used in the analysis. Within the constraints of the current analysis it appears that, for the ULSAB, the effects of stiffness dominate the compatibility aspects for collisions with similar vehicles