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Solution of a Hertzian Contact Mechanics Problem Using the Material Point Method

Solution of a Hertzian Contact Mechanics Problem Using the Material Point Method. Jason Sanchez Department of Mechanical Engineering University of New Mexico 18 March 2008. Nanoindentation Simulation of Blast Resistant Cement.

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Solution of a Hertzian Contact Mechanics Problem Using the Material Point Method

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  1. Solution of a Hertzian Contact Mechanics Problem Using the Material Point Method Jason Sanchez Department of Mechanical Engineering University of New Mexico 18 March 2008

  2. Nanoindentation Simulation of Blast Resistant Cement • DTRA blast resistant concrete investigation (UNM Dept. of Civil Engineering) • How well does a nanoindentation simulation reproduce experimental data for blast resistant cement? • Force vs. displacement response • Indenter impression • Material modeling of blast resistant concrete at micro-scale • Isotropic material to begin • elastic-plastic constitutive model • Possibly inhomogeneous material (fibers, other particles, etc. ) • Simulation method it the material point method (MPM)

  3. Work Breakdown • Perform a benchmark problem with MPM(Hertzian contact mechanics) • Constitutive modeling • Elastic-plastic constitutive model • Contact algorithm at indenter interface • compression only, friction at interface • decohesion • 3D MPM Birkovitch Indentation Simulation • Parallel MPM implementation necessary (use of HPC)

  4. Benchmark MPM Indentation Simulation • Hertzian contact of a rigid spherical indenter contacting a isotropic elastic material • Reproduce theoretical force vs. displacement response • MPM Implementation (references 1-3) • Explicit MPM • Momentum formulation • Plane axisymmetric formulation • Isotropic linear elasticity • Natural no-slip contact between material points • D. Sulsky, S. Zhou, and H.L. Schreyer, Application of a particle-in-cell method to solid mechanics, Comput. Phys. 87 (1995) 236-252 • D. Sulsky and H.L. Schreyer, MPM simulation of dynamic material failure with a decohesion constitutive model, European Journal of Mechanics A/Solids. 23 (2004) 423-445 • D. Sulsky, Z. Chen, and H.L. Schreyer, A particle method for history-dependent materials, Comput. Methods Appl. Mech.. 118 (1994) 179-196.

  5. spherical indenter R a d elastic material Hertzian Contact Mechanics Betweena Rigid Spherical Indenter and a Flat Specimen • local deformations at the contact • no consideration for bulk deformations or support of the bodies • small strains, linear elasticity

  6. MPM Contact Mechanics Simulation • isotropic elastic material, • 4 uniform quad meshes • 4 material points per element • slip at grid boundary • velocity prescribed to rigid material points (indenter) axis of symmetry spherical indenter sample

  7. MPM Indentation Simulation Results for aUniform Quad Mesh

  8. Locally Resolved Quad Mesh forMPM Indentation Simulation • 8520 elements • Resolved elements: dx = dy = 0.0185 cm • Coarse elements: dx = dy = 0.1667 cm • Best uniform grid simulation results correspond to 72000 elements with dx = dy = 0.03 cm

  9. MPM Contact Mechanics Simulation With Locally Resolved Mesh • isotropic elastic material • grid: 8520 4 node quad elements • 4 material points per element • slip at grid boundary • velocity prescribed to rigid material points

  10. Comparison of Numerical & Analytical Solution

  11. Comparison of Numerical & Analytical Solution (zoom in)

  12. Conclusions, current, and Future work • Conclusions • MPM reproduces analytical force vs. displacement results (Hertzian contact mechanics) • Highly resolved spatial mesh is necessary at indenter-material interface • Constitutive model for axisymmetric analysis (current work) • plasticity • Decohesion (initiation of cracking) • Contact algorithm at interface (current work) • compression only, friction at interface, decohesion • 3D MPM Indentation Simulation (summer / fall 08) • Parallel MPM implementation • Incorporate locally resolved mesh generator

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