Improved contact algorithm for the material point method and application to stress propagation in granular material

Journal ArticleContact between deformable bodies is a difficult problem in the analysis of engineering systems. A new approach to contact has been implemented using the Material Point Method for solid mechanics, Bardenhagen, Brackbill, and Sulsky (2000a). Here two improvements to the algorithm are described. The first is to include the normal traction in the contact logic to more appropriately determine the free separation criterion. The second is to provide numerical stability by scaling the contact impulse when computational grid information is suspect, a condition which can be expected to occur occasionally as material bodies move through the computational grid. The modifications described preserve important properties of the original algorithm, namely conservation of momentum, and the use of global quantities which obviate the need for neighbor searches and result in the computational cost scaling linearly with the number of contacting bodies. The algorithm is demonstrated on several examples. Deformable body solutions compare favorably with several problems which, for rigid bodies, have analytical solutions. A much more demanding simulation of stress propagation through idealized granular material, for which high fidelity data has been obtained, is examined in detail. Excellent qualitative agreement is found for a variety of contact conditions. Important material parameters needed for more quantitative comparisons are identified

Derivation of higher order gradient continuum theories in 2,3-d non-linear elasticity from periodic lattice models

localization of deformation (in the form of shear bands) at sufficiently high levels of strain, are frequently modeled by gradient type non-local constitutive laws, i.e. continuum theories that include higher order deformation gradients. These models incorporate a length scale for the localized deformation zone and are either postulated or justified from micromechanical considerations. Of interest here is the consistent derivation of such models from a given microstructure and the subsequent investigation of their localization and stability behavior under finite strains.In the interest of simplicity, the microscopic model is a discrete, periodic, non-linear elastic lattice structure in two or three dimensions. The corresponding macroscopic model is a continuum constitutive law involving displacement gradients of all orders. Attention is focused on the simplest such model, namely the one whose energy density includes gradients of the displacements only up to the second order. The relation between the ellipticity of the resulting first (local) and second (non-local) order gradient models at finite strains, the stability of uniform strain solutions and the possibility of localized deformation zones is discussed. The investigations of the resulting continuum are done for two different microstructures, the second one of which approximates the behavior of perfect monatomic crystals in plane strain. Localized strain solutions based on the continuum approximation are possible with the first microstructurc but not with the second. Implications for the stability of three-dimensional crystals using realistic interaction potentials are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31886/1/0000838.pd

Shear deformation in granular materials

An investigation into the properties of granular materials is undertaken via numerical simulation. These simulations highlight that frictional contact, a defining characteristic of dry granular materials, and interfacial debonding, an expected deformation mode in plastic bonded explosives, must be properly modeled. Frictional contact and debonding algorithms have been implemented into FLIP, a particle in cell code, and are described. Frictionless and frictional contact are simulated, with attention paid to energy and momentum conservation. Debonding is simulated, with attention paid to the interfacial debonding speed. A first step toward calculations of shear deformation in plastic bonded explosives is made. Simulations are performed on the scale of the grains where experimental data is difficult to obtain. Two characteristics of deformation are found, namely the intermittent binding of grains when rotation and translation are insufficient to accommodate deformation, and the role of the binder as a lubricant in force chains

Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock

Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Gr\"uneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.Comment: Figs.2,4,7,11 in JPG format; Accepted for publication in J. Phys. D: Applied Physic

Multi-disciplinary efforts to evaluate the therapeutic potential of CDK11, a novel transcription associated cyclin dependent kinase.

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On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models

Higher order gradient continuum theories have often been proposed as models for solids that exhibit localization of deformation (in the form of shear bands) at sufficiently high levels of strain. These models incorporate a length scale for the localized deformation zone and are either postulated or justified from micromechanical considerations. Of interest here is the consistent derivation of such models from a given microstructure and the subsequent comparison of the solution to a boundary value problem using both the exact microscopic model and the corresponding approximate higher order gradient macroscopic model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42682/1/10659_2004_Article_BF00043251.pd