김경종
112 lines
5.1 KiB
Markdown
112 lines
5.1 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: 2026-06-01
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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-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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- "[[Abaqus Element Library]]"
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- "[[Abaqus Element Selection and Formulation]]"
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- "[[Abaqus Continuum Element Families]]"
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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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- "[[Abaqus Hyperelastic and Viscoelastic Materials]]"
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sources:
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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source_refs:
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- source: "[[Abaqus Theory Manual]]"
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raw_path: ".raw/AbaqusTheoriesManual/"
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raw_files:
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- "AbaqusTheoriesManual_028.md"
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- "AbaqusTheoriesManual_029.md"
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md_indices:
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- 28
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- 32
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- 87
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- 29
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide3/"
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raw_files:
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md_indices:
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- 70
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide4/"
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raw_files:
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- "AbaqusAnalysisUserGuide4_010.md"
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- "AbaqusAnalysisUserGuide4_006.md"
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md_indices:
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match: "heuristic-heading-keyword"
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confidence: high
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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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[[Abaqus-Analysis-User-s-Guide-Volume-III|Volume III]] makes this practical for material selection. Nearly incompressible hyperelastic solids, especially confined rubberlike materials, often require hybrid continuum elements in Abaqus/Standard; Abaqus/Explicit cannot enforce exact incompressibility at each material point and therefore requires a compressible approximation.
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[[Abaqus-Analysis-User-s-Guide-Volume-IV|Volume IV]] makes the element-library side explicit: hybrid Abaqus elements are commonly marked with `H`, as in `C3D8H` or `B31H`, and are selected within continuum, beam, and truss families when incompressible or inextensible behavior would otherwise lock.
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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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- [[Abaqus Element Selection and Formulation]] explains how the `H` suffix appears in concrete Abaqus element names.
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- [[Abaqus Continuum Element Families]] shows the solid-element families where hybrid pressure treatment is common.
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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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- [[Abaqus Hyperelastic and Viscoelastic Materials]] is a common material class where hybrid or carefully compressible formulations matter.
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## Sources
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- [[Abaqus Theory Manual]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-III|Abaqus Analysis User's Guide Volume III]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]
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