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Research Themes

Variational Multiscale Discontinuous Galerkin Framework

Framework for Deriving Computational Interface Methods for Contact, Fracture, and Material Joining

Under this thrust, our lab focuses on a variational formulation for interfaces, discontinuities, interphases, transitions; a mathematical framework for describing interfaces in mechanical systems; how they deform and transmit stress and other fields, and having a description that is variationally consistent, that evolves from a rigid behavior to an elastic behavior.

Having a stabilized method approach of modeling the fine scale field at the interface enables us a vehicle/approach to derive the method rather than design it. To found it on fine scale models we use a rational approach.

These methods are free from numerical tuning parameters and from inconsistencies. Rather, they contain only the physical material parameters. This removes guesswork, increases accuracy and fidelity.

We apply this method to a broad class of mechanics problems:

  • VMDG papers, debonding
  • MRDG, RVE models for stress distribution and fatigue
  • Contact mechanics
  • Mixture and porous and Melih stuff

Which then have application in a variety of materials and structures, including the simulation/modeling of them to design them and understand them.

Interfaces are everywhere. Wherever two dissimilar things are jointed, attached, or come in contact—or when cracks form and grow—we seek to address:

  • Creep in Grade 91, grain boundaries
  • MTR in Ti6242, process modeling, crystal plasticity
  • Composites, other stuff

Real-world applications include cavity growth on grain boundaries, cracks in composite materials in planes and cars, indentation of soft hydrogels or cartilage and the adhesion/friction coupling of those materials, damage in other materials, and superplasticity.

Current Projects

» Frictional Response of Bolted Metallic Surfaces
» Interface Integrity and Debonding in Polymer-Matrix Composites

Mechanical Modeling of Anisotropic or Crystalline or Directional Materials

This thrust is focused on helping to expose how that structure relates to bulk properties, what are observed in experiments; “ICME for directionally dependent materials” or materials with structure; simulating the creation, generation, manufacturing, and/or processing of materials (i.e. how to get the properties you want/need in an effective/reproducible manner); and their performance in service (such as discovering when they fail, their max capacity, etc.)

We focus on the deformation mechanisms of the materials and what microscale behavior of flaws gives rise to the observed response in:

  • Crystal plasticity; modeling the dislocation plasticity/motion in the material, the flow stress; depends on temperature and strain rate and the slip systems, and
  • Phase field fracture modeling in crystalline materials.

This is an area a lot of people work in broadly, from the study of mechanics of materials to how they deform or how they fail. This involves the most collaboration of our lab’s themes. Experimentalists and modelers work together to explain observations to enable future designs.

Current Projects

Performance Modeling:
» Creep-Life Prediction for Ferritic-Martensitic Steels Using Crystal Plasticity Modeling

Process Modeling:
» Ti6242

Multiscale and Stabilized Numerical Methods

It is well known that materials and structures have scales physically, but math models also have a filter induced by the mesh resolution, losing features below that length scale that is resolved. Capturing fine/microscale features has an effect on both accuracy and stability of simulations. Hence, we also develop methods to bridge scales in materials. Materials also may have interacting constituents, like mixtures. Things evolve.

Our lab focuses on considering problems with multiscale or multiphysics features, often expensive to fully resolve, by developing methods with either greater accuracy/fidelity or enabling the study of new classes of problems.

Current Projects

» Mixture
» Darcy Paper
» Mixed method and error estimation papers
» Modeling Heterogeneous Materials Using Low-Order Tetrahedral Elements