John T. Foster

A peridynamic formulation of pressure driven convective fluid transport in porous media

A general state-based peridynamic formulation is presented for convective single-phase flow of a liquid of small and constant compressibility in heterogeneous porous media. In addition to local fluid transport, possible anomalous diffusion due to non-local fluid transport is considered and simulated. The governing integral equations of the peridynamic formulation are computationally easier to solve in domains with discontinuities than the traditional conservation models containing spatial derivatives. A bond-based peridynamic formulation is also developed and demonstrated to be a special case of the state-based formulation. The non-local model does not assume continuity in the field variables, satisfies mass conservation over an arbitrary bounded body and approaches the corresponding local model as the non-local region goes to zero. The exact solution of the local model closely matches the non-local model for a classical two-dimensional flow problem with fluid sources and sinks and for both Neumann and Dirichlet boundary conditions. The model is shown to capture arbitrary flow discontinuities/heterogeneities without any fundamental changes to the model and with small incremental computational costs.

Constant strain rate testing of a G10 laminate composite through optimized Kolsky bar pulse-shaping techniques

Pulse-shaping techniques have been used for many years now in Kolsky bar testing of brittle materials. The use of pulse shapers allow the experimentalist to conduct high strain rate tests on brittle materials while ensuring that the sample will achieve a state of dynamic stress equilibrium before it fails, as well as to achieve a constant strain rate loading state for a large portion of the test. The process of choosing the appropriate pulse-shaper system has typically been one of trail-and-error, sometimes requiring many experimental trails to achieve optimal results. Advances in analytic modeling of Kolsky bar tests now make it possible, in an a priori fashion, to design a pulse-shaper system to produce a known constant strain rate experiment. This article describes the approach of coupling these analytic models to an optimization technique to quickly find a pulse-shaper system that will produce an experiment at a known constant strain rate. Experiments were conducted and the model predictions compared to resulting strain rate histories for a G10 material. Stress–strain curves for G10 are presented at three different strain rates in both the in-plane and out-of-plane loading configurations with respect to the laminate plys. The G10 material is not found to be rate sensitive in either its strength or failure properties.

Peridynamic beams and plates: A non-ordinary state-based model

While multiple peridynamic material models capture the behavior of solid materials, not all structures are conveniently analyzed as solids. Finite Element Analysis often uses 1D and 2D elements to model thin features that would otherwise require a great number of 3D elements, but peridynamic thin features remain underdeveloped despite great interest in the engineering community. This work presents non-ordinary state-based peridynamic models for the simulation of thin features. Beginning from an example non-ordinary state-based model proposed by Silling in 2007, lower dimensional peridynamic models of beams and plates are developed and shown to be energy equivalent to classical models for well-behaved deformations. The resulting plate model is initially restricted to a Poisson’s ratio of ν = 1/3, but is extended to arbitrary Poisson’s ratio via a bending state decomposition. Simple test cases demonstrate the model’s performance.Copyright

A Novel Torsional Kolsky Bar for Testing Materials at Constant-Shear-Strain Rates

Kolsky bars, also known as split-Hopkinson bars, have been widely used in the dynamic characterization of engineering materials for over 50 years. Kolsky bars can be made to test materials in compression, tension, or torsion, and until recently, have been generally employed in the testing of high-impedance ductile materials to collect rate-dependent stress-strain data during large-strain inelastic flow. The advancement of “pulse-shaping” techniques in the last decade has allowed Kolsky bars to be utilized for testing low-impedance and brittle materials as well. Pulse-shaping is a processes of tailoring the dynamic loading during a test, with consideration given to the material being tested, in order ensure that the sample achieves a state of dynamic stress equilibrium and constant strain-rate if desired. The most common design of torsional Kolsky bars currently in widespread use offer no way to incorporate pulse-shaping. This limits their use mostly to high-impedance, large-strain applications. A novel torsional Kolsky bar design is presented in this work, which allows for straightforward pulse-shaping, similar to the method employed in compression testing, that can be used to test brittle and low-impedance materials as well as to design experiments that ensure the sample is undergoing a constant-shear-strain-rate deformation. Details of the design as well as some preliminary data demonstrating the pulse shaping capabilities collected during tests are presented.

A Priori Pulse Shaper Design for Constant-Strain-Rate Tests of Elastic-Brittle Materials

Pulse shaping techniques have been used for many years now in Kolsky bar testing of brittle materials. The use of pulse shapers allow the experimentalist to conduct high-strain-rate tests on brittle materials while ensuring that the sample will achieve a state of dynamic stress equilibrium before it fails, as well as to achieve a constant-strain-rate loading state for a large portion of the test. The process of choosing the appropriate pulse shaper system has typically been one of trail-and-error, sometimes requiring many experimental trails to achieve optimal results. Advances in analytic modeling of Kolsky bar tests now make it possible, in an a priori fashion, to design a pulse shaper system to produce a known constant-strain-rate experiment. This paper describes the approach of coupling these analytic models to an optimization technique to quickly find a pulse shaper system that will produce an experiment at a known constant-strain-rate. Experiments were conducted and the model predictions compared to resulting strain-rate histories for a G-10 material.