The cohesive element approach to dynamic fragmentation: The question of energy convergence

The cohesive element approach is getting increasingly popular for simulations in which a large amount of cracking occurs. Naturally, a robust representation of fragmentation mechanics is contingent to an accurate description of dissipative mechanisms in form of cracking and branching. A number of cohesive law models have been proposed over the years and these can be divided into two categories: cohesive laws that are initially rigid and cohesive laws that have an initial elastic slope. This paper focuses on the initially rigid cohesive law, which is shown to successfully capture crack branching mechanisms in simulations. The paper addresses the issue of energy convergence of the finite-element solution for high-loading rate fragmentation problems, within the context of small strain linear elasticity. These results are obtained in an idealized one-dimensional setting, and they provide new insight for determining proper cohesive zone spacing as function of loading rate. The findings provide a useful roadmap for choosing mesh sizes and mesh size distributions in two and three-dimensional fragmentation problems. Remarkably, introducing a slight degree of mesh randomness is shown to improve by up to two orders of magnitude the convergence of the fragmentation problem

Hydraulic-fracture growth in dipping anisotropic strata as viewed through the surface deformation field

In 1983 and 1984 Oak Rdige National Laboratory conducted a series of precision ground deformation measurements before, during, and after the generation of several large hydraulic fractures in a dipping member of the Cambrian Conasauga Shale. Each fracture was produced by the injection of approximately 500,000 L of slurry on a single day. Injection depth was 300 m. Leveling surveys were run several days before and several days after the injections. An array of eight high-precision borehole tiltmeters monitored ground deformations continuously for a period of several weeks. Analysis of the leveling and the tilt measurements revealed surface uplifts as great as 25 mm and tilts of tens of microradians during each injection. Furthermore, partial recovery (subsidence) of the ground took place during the days following an injection, accompanied by shifts in the position of maximum resultant uplift. Interpretation of the tilt measurements is consistent with stable widening and extension of hydraulic fractures with subhorizontal orientations. Comparison of the measured tilt patterns with fracture orientations established from logging of observation wells suggests that shearing parallel to the fracture planes accompanied fracture dilation. This interpretation is supported by measured tilts and ground uplifts that were as much as 100 percent greater than those expected from fracture dilation alone. Models of elastically anisotropic overburden rock do not explain the measured tilt patterns in the absence of shear stresses in the fracture planes. This work represents the first large-scale hydraulic-fracturing experiment in which the possible effects of material anisotropy and fracture-parallel shears have been measured and interpreted

Numerical convergence of the cohesive element approach in dynamic fragmentation simulations

The cohesive element approach is getting increasingly popular for simulations in which a large amount of cracking occurs. Naturally, a robust representation of fragmentation mechanics is contingent to an accurate description of dissipative mechanisms in form of cracking and branching. This paper addresses the issue of energy convergence of the finite-element solution for high-loading rate fragmentation problems. These results provide new insight for choosing mesh sizes and size distributions in two and three-dimensional fragmentation

High fidelity computational characterization of the mechanical response of thermally aged polycarbonate

A representative all-atom molecular dynamics (MD) system of polycarbonate (PC) is built and conditioned to capture and predict the behaviours of PC in response to a broad range of thermo-mechanical loadings for various thermal aging. The PC system is constructed to have a distribution of molecular weights comparable to a widely used commercial PC (LEXAN 9034), and thermally conditioned to produce models for aged and unaged PC. The MD responses of these models are evaluated through comparisons to existing experimental results carried out at much lower loading rates, but done over a broad range of temperatures and loading modes. These experiments include monotonic extension/compression/shear, unilaterally and bilaterally confined compression, and load-reversal during shear. It is shown that the MD simulations show both qualitative and quantitative similarity with the experimental response. The quantitative similarity is evaluated by comparing the dilatational response under bilaterally confined compression, the shear flow viscosity and the equivalent yield stress. The consistency of the in silico response to real laboratory experiments strongly suggests that the current PC models are physically and mechanically relevant and potentially can be used to investigate thermo-mechanical response to loading conditions that would not easily be possible. These MD models may provide valuable insight into the molecular sources of certain observations, and could possibly offer new perspectives on how to develop constitutive models that are based on better understanding the response of PC under complex loadings. To this latter end, the models are used to predict the response of PC to complex loading modes that would normally be difficult to do or that include characteristics that would be difficult to measure. These include the responses of unaged and aged PC to unilaterally confined extension/compression, cyclic uniaxial/shear loadings, and sawtooth extension/compression/shear

High fidelity computational characterization of the mechanical response of thermally aged polycarbonate

A representative all-atom molecular dynamics (MD) system of polycarbonate (PC) is built and conditioned to capture and predict the behaviours of PC in response to a broad range of thermo-mechanical loadings for various thermal aging. The PC system is constructed to have a distribution of molecular weights comparable to a widely used commercial PC (LEXAN 9034), and thermally conditioned to produce models for aged and unaged PC. The MD responses of these models are evaluated through comparisons to existing experimental results carried out at much lower loading rates, but done over a broad range of temperatures and loading modes. These experiments include monotonic extension/compression/shear, unilaterally and bilaterally confined compression, and load-reversal during shear. It is shown that the MD simulations show both qualitative and quantitative similarity with the experimental response. The quantitative similarity is evaluated by comparing the dilatational response under bilaterally confined compression, the shear flow viscosity and the equivalent yield stress. The consistency of the in silico response to real laboratory experiments strongly suggests that the current PC models are physically and mechanically relevant and potentially can be used to investigate thermo-mechanical response to loading conditions that would not easily be possible. These MD models may provide valuable insight into the molecular sources of certain observations, and could possibly offer new perspectives on how to develop constitutive models that are based on better understanding the response of PC under complex loadings. To this latter end, the models are used to predict the response of PC to complex loading modes that would normally be difficult to do or that include characteristics that would be difficult to measure. These include the responses of unaged and aged PC to unilaterally confined extension/compression, cyclic uniaxial/shear loadings, and sawtooth extension/compression/shear