Visualization of finite element data of a multi-phase concrete model M. Ritter 1, M. Aschaber 1, W. Benger 2, G. Hofstetter 1 1 University of Innsbruck, Austria 2 Louisiana State University, USA , Vienna Center for Comput- ation and Technology IBK

Outline – Motivation – Numerical Simulation – Data Modeling – Visualization – Conclusion & Future Work

Motivation: by Neal Stone Scientific Visualization Techniques and Research Engineering Simulation Tools and Visualization Gap Motivation

Motivation: by Neal Stone Scientific Visualization Techniques and Research Engineering Simulation Tools and Visualization Motivation

Motivation: Simulation techniques are used more frequently Produced data sets growing Data complexity is increasing Simulation techniques are used more frequently Produced data sets growing Data complexity is increasing Visualization used for data interpretation of results is important. Motivation

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Aim: – More realistic simulation of drying shrinkage Application: – Strengthening of a RC structure by adding an overlay Numerical Simulation New top concrete layer Old concrete structure

Drying shrinkage: – Long term drying process in concrete – Decrease of relative pore humidity – Increase of capillary pressure – Capillary pressure results in volumetric shrinkage Numerical Simulation concrete drying

Drying Shrinkage: Numerical Simulation New top concrete layer Old concrete structure Different internal stresses Critical region at joint Drying shrinkage Swelling concrete

Numerical Simulation: – Finite element simulation on multiple grids of concrete specimen – Hexahedral Mesh of 9 x 9 x 13 Cells Numerical Simulation 100 x 100 x 56 mm

Numerical Simulation: – Finite element simulation on multiple grids of concrete specimen – Hexahedral Mesh of 9 x 9 x 13 Cells Numerical Simulation Undeformed linear elementDeformed quadratic element The element has curved faces

Multiphase concrete model Solid, water, and gas phase (dry air and water vapor) Coupled hygral-thermo-mechanical model Numerical Simulation: Balance equations Mass Enthalpy Linear Momentum Linear kinematic relations Constitutive equations Governing equations: Numerical Simulation

Multiple solution variables (Data fields) Gas pressurescalar Capillary pressurescalar Displacementsvector Temperaturescalar Derived data fields Strain2 nd order tensor Stress2 nd order tensor

Numerical Simulation

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Before doing data visualization one has to deal with data Many different kinds Many formats Data management and handling is crucial in computational sciences Reusability of methods and techniques Sustainability Exchangeability of data (collaborations) We propose using a concept based on mathematics to systematically organize data Data Modeling

Separation of Geometry (Grids) and Datafield (Fields) Inspired by concepts of: TopologyDifferential GeometryGeometric Algebra Fiber Bundle Data Model Data Modeling

Manifold describing the base space Topology Refinement level Coordinate representation Vertex positions in representation Neighborhood Grid the base space Data Modeling

Dataset holding numerical data per k-cell on the grid (vertex, edge, cell, … ) Array of arbitrary type, for example: Scalar Vector, BiVector, … Tensor Any other user defined type Field the fiber space Data Modeling

Hierarchical structure:

Supported Grid types: Uniform Grid Curvilinear Grid Rectilinear Grid Adaptive Mesh Refinement Grid (AMR) Point Cloud Lines Triangular/Quad and Mixed Surfaces Grids can be fragmented (Blocks) having Ghost ZonesGrids can have refinement levelsWork in progress: Hexahedral Grid FEM Grid Connected Graph Data Full Waveform LIDAR Laser Data Data Modeling

Data at Vertices: (optional)

Data Modeling Data at Integration Points: No positions  can be computed

Data Modeling Sets of Nodes and Sets of Elements: Indices of vertices in named fragments Indices of integration points in named fragments Indices of integration points in named fragments

Data Modeling Linked groups for alternative data access: – E.g. time frames and time steps in ABAQUS No data stored

Data Modeling HDF5 Based Data format:  independent, free, open, data browser HDF5 Based Data format:  independent, free, open, data browser FEM - Example

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Visualization framework Highly modular design – Small Core – Plug-Ins Mainly developed by Werner Benger – Currently about 8 people are actively contributing C++, OpenGL Open Academic License Runs on Linux, Windows (and MacOS) Visualization Shell VISH Visualization

Colored Cages – Show FE grid Positive Negative – Shaded colored surface – Illustrates data at vertices – One scalar field via color-map – One vector field via displacement – Can be combined with other visualization techniques Visualization

Colored Cages – Integration point data is extrapolated and averaged on demand Visualization Extrapolation from integration points Averaged, smoothed Averaged, smoothed Over-scaled deformation

Tensor analysis: – Shape factors by [Westin97] – Stress/strain are 3x3 symmetric tensors – 3 Eigen-Values: – Shape factors: [BBHKS06] Visualization

Direct stress tensor visualization: – Ellipsoids representing the shape factors – Tensor Splats [BengerHege04] -> barycentric Visualization

Direct stress tensor visualization: – Ellipsoids representing the shape factors – Tensor Splats [BengerHege04] -> barycentric Visualization Works only for positive Eigenvalues! Works only for positive Eigenvalues!

Direct stress tensor visualization: – Ellipsoids representing the shape factors – Tensor Splats [BengerHege04] -> barycentric [BBHKS06] Visualization Works only for positive Eigenvalues! Works only for positive Eigenvalues!  Enhancement: Color a splat in blue, when any Eigenvalues is negative  Enhancement: Color a splat in blue, when any Eigenvalues is negative

Visualization Drying simulation: – Tensor splats: Biaxial tension Uniaxial tension Pressure region + Multiple stress directions + Tension vs pressure regions + Multiple stress directions + Tension vs pressure regions

Scalar fields by volume rendering: – Texture based volume rendering ( requires resampling on uniform grid  to be improved) – Shows inner structure of data fields – Example: tri-axial compression of a cuboid Visualization

Dual volume rendering: – One scalar field controls color – Another controls transparency

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Fiber bundle data model for FEM Captures many other types of scientific data Comes with an HDF5 based data format (big data)  Good for collaborations and transparent data storageVisualization: Colored cages Direct tensor field visualization Scalar fields via volume rendering Dual volume rendering Future work: Enhancing the direct tensor field visualization Volume rendering on the FEM grid (GPU raycasting) Support more FEM data (also shells)

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Balance equations of the multiphase model Mass of the water w Mass of the steam gw Mass of the dry air ga Mass of the solid phase s Enthalpy of the whole system Impulse of the whole system Numerical Simulation