Modeling of Seismic Energy Dissipation in Elastic-Plastic Materials

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1 Modeling of in Elastic-Plastic Materials Instructor: Prof. Boris Jeremić University of California, Davis 15th IACMAG Wuhan, China Aug

2 Outline Introduction Modeling of Energy Dissipation Limitations of Traditional Methods Thermodynamics-Based Theory and Formulation FEM Implementation Real ESSI Simulator Illustrative Examples Summary

3 Introduction Modeling of Energy Dissipation FEM Implementation Summary Introduction Vajont Dam I I I Rapid collapse: Sliding mass moves at 100 km/h (62MPH) Vaporization of ground water during sliding Significant amount of energy dissipation (heat)

4 Limitations of Traditional Methods Outline Introduction Modeling of Energy Dissipation Limitations of Traditional Methods Thermodynamics-Based Theory and Formulation FEM Implementation Real ESSI Simulator Illustrative Examples Summary

5 Limitations of Traditional Methods Area of the Stress-Strain Loop Evolving loop? Monotonic loading?

6 Introduction Modeling of Energy Dissipation FEM Implementation Summary Limitations of Traditional Methods Use Incremental Equation: dφ = σij d pl ij I Negative incremental energy dissipation!

7 Limitations of Traditional Methods Negative incremental energy dissipation! Direct violation of the second law of thermodynamics Plastic Work (PW) is not Plastic Dissipation(PD) One important form of energy is missing! Plastic Free Energy = PW - PD

8 Thermodynamics-Based Theory and Formulation Outline Introduction Modeling of Energy Dissipation Limitations of Traditional Methods Thermodynamics-Based Theory and Formulation FEM Implementation Real ESSI Simulator Illustrative Examples Summary

9 Thermodynamics-Based Theory and Formulation Energy Transformation in Elastic-Plastic Material

10 Introduction Modeling of Energy Dissipation FEM Implementation Summary Thermodynamics-Based Theory and Formulation Plastic Free Energy I I Multi-scale effect of particle interlocking/rearrangement Physical nature strain energy on particle level

11 Thermodynamics-Based Theory and Formulation Plastic Free Energy and Dissipation Plastic Free Energy Related to hardening laws in classic plasticity theory Decomposed into isotropic and kinematic components Related to material state variables (back stress etc.) dψ iso pl = 1 k dk; dψ kin pl = 1 α ij dα ij κ 1 a 1 Energy Dissipation due to Plasticity Incremental dissipation should always be nonnegative dd P = dw P dψ pl = σ ij dɛ pl ij dψ pl 0

12 Real ESSI Simulator Outline Introduction Modeling of Energy Dissipation Limitations of Traditional Methods Thermodynamics-Based Theory and Formulation FEM Implementation Real ESSI Simulator Illustrative Examples Summary

13 Real ESSI Simulator Real ESSI Simulator Software, hardware and documentation system for 3D finite element modeling and simulation of Earthquake Soil/Rock Structure Interaction (ESSI) analysis of static and dynamic behaviors of infrastructure objects Extensive work on verification and validation High performance parallel computing Energy dissipation from various sources Probabilistic/Stochastic modeling and simulation Model building, mesh generation, results visualization

14 Real ESSI Simulator Real ESSI Simulator Features Finite Elements Dry/single-phase solids, fully saturated/two-phase solids, partially saturated/three-phase solids Truss, linear/nonlinear beams, nonlinear wall/shell Dry/Coupled contact elements Base isolator, energy dissipator Material Models Linear/nonlinear elastic Elastic-plastic: von Mises, Drucker Prager, Rounded Mohr-Coulomb, Modified Cam-Clay, SaniSand, SaniClay, Nested-surface models, PM4 Model (2D/3D), Tsinghua liquefaction model Nonlinear uniaxial fiber materials for concrete/steel Simulation Options Static: Load control, Displacement control, HyperSpherical constraint Dynamic: Newmark, Hilber Hughes Taylor (alpha method)

15 Illustrative Examples Outline Introduction Modeling of Energy Dissipation Limitations of Traditional Methods Thermodynamics-Based Theory and Formulation FEM Implementation Real ESSI Simulator Illustrative Examples Summary

16 Acceleration [g] Normal Stress [MPa] Illustrative Examples Steel Frame under Earthquake Loading 3 m 165 mm m Steel Fiber mm m A A A Section A - A Normal Strain [%] 3 m A Imposed Motion Time [s]

17 Energy [kj] Plastic Dissipation Illustrative Examples Steel Frame under Earthquake Loading Input Work Kinetic Energy Strain Energy Plastic Free Energy Story 3 Story Story Time [s]

18 Illustrative Examples Energy Dissipation in Large-Scale Model

19 Summary Concluding Remarks The calculation of energy dissipation should follow the basic principles of thermodynamics A system for energy analysis is developed and implemented in the Real ESSI Simulator Correct evaluation of energy dissipation can be used to improve design safety and economy Nonlinear/Inelastic Earthquake Soil Structure Interaction (ESSI) short course offered this fall in San Francisco, more info at

20 Summary Acknowledgement Strong support and instruction from Prof. Boris Jeremić Inspiring discussion with Prof. Yannis F. Dafalias This study is funded by US-DOE Collaborators: Mr. Sumeet K. Sinha, Mr. Yuan Feng, Mr. Hexiang Wang, Mr. Maxime Lacour, Ms. Fatemah Behbehani