김경종
55 lines
2.3 KiB
Markdown
55 lines
2.3 KiB
Markdown
---
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type: concept
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title: "Hybrid Incompressible Elements"
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complexity: advanced
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domain: computational-mechanics
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created: 2026-05-29
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updated: 2026-05-29
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address: c-000058
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aliases:
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- hybrid elements
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- hybrid incompressibility
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- displacement-pressure elements
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tags:
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- concept
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- finite-element-method
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- incompressibility
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- mixed-formulation
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status: current
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related:
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus Element Library]]"
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- "[[Mixed Finite Element Formulations]]"
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- "[[Reduced Integration and Hourglass Control]]"
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- "[[Isoparametric Finite Elements]]"
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sources:
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- "[[Abaqus Theory Manual]]"
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---
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# Hybrid Incompressible Elements
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## Definition
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Hybrid incompressible elements are mixed finite element formulations that introduce pressure-like variables in addition to displacement variables so incompressible or nearly incompressible materials do not lock.
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## How It Works
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Displacement-only solid elements can become too stiff when the material response strongly constrains volume change. Abaqus addresses partly incompressible behavior through selective reduced integration of the volumetric strain contribution, and fully incompressible behavior through hybrid formulations where hydrostatic pressure acts as an additional unknown or Lagrange multiplier.
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This separates deviatoric deformation from the incompressibility constraint. The element can represent shear deformation while enforcing the pressure or volume constraint through a mixed field rather than forcing the displacement interpolation to carry both roles.
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## Why It Matters
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Rubbers, elastomers, plastic flow with small elastic compressibility, and some large-deformation material models require stable incompressible treatment. Without a hybrid or otherwise stable mixed formulation, the mesh can show volumetric locking, poor convergence, or unphysical pressure behavior.
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## Connections
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- [[Mixed Finite Element Formulations]] gives the general multi-field stability setting.
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- [[Reduced Integration and Hourglass Control]] is related but not equivalent; reduced quadrature may relieve stiffness, while hybrid elements explicitly add pressure variables.
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- [[Abaqus Constitutive Integration]] provides the integration-point material response that supplies deviatoric stress and consistent tangent terms.
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## Sources
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- [[Abaqus Theory Manual]]
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