Efficient stochastic simulation of dynamic brittle strength using a random perturbation-based micromechanics model Graham-Brady, Lori L.; Liu, Junwei
Ceramic materials exhibit high strength against ballistic impact loads. The failure mechanism in this context is associated with crack growth and coalescence. The properties of preexisting flaws at the micro-scale, including the size, shape, orientations and clustering, have profound impact on the strength of such materials. Since the properties of pre-existing flaws are highly heterogeneous in space, the strength exhibits strong spatial variations, leading to localization of stress and subsequent failure. One approach to simulation of this spatial variability is to assign samples of the random flaw population statistics (e.g., flaw density and flaw size distribution) to each integration point of a macro-scale finite element analysis. Here we propose an up-scaling technique based on the micromechanics model proposed by Paliwal and Ramesh (2008)1. While in concept it is possible to perform a micromechanical analysis at each integration point individually, this becomes computationally prohibitive for macro-scale models with many elements. Instead, we propose a more efficient approach that applies a Taylor series expansion approximation to the constitutive behavior, based on the results of a single reference analysis from the micromechanics model. The reference parameters are taken from analysis of a typical parameter set for the pre-existing flaws. Peak strength and the corresponding strain, along with some necessary gradient results are recorded. Monte Carlo simulation of the material performance is therefore achieved by generating the random variables that represent the flaw population at every integration point, which typically require much less computational effort than stochastic simulation of representative constitutive property fields. With this approach a large-scale statistical study can be performed with high efficiency, with a speed up of approximately 2 orders of magnitude, while the relative error is satisfyingly low.
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