---
type: concept
title: "Reduced Integration and Hourglass Control"
complexity: advanced
domain: computational-mechanics
created: 2026-05-29
updated: 2026-06-01
address: c-000057
aliases:
  - reduced integration
  - hourglass control
  - under-integration
tags:
  - concept
  - finite-element-method
  - numerical-integration
  - locking
status: current
related:
  - "[[Abaqus Theory Manual]]"
  - "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
  - "[[Abaqus Element Library]]"
  - "[[Abaqus Element Selection and Formulation]]"
  - "[[Abaqus Continuum Element Families]]"
  - "[[Isoparametric Finite Elements]]"
  - "[[Solid Element Stiffness Integration]]"
  - "[[Shell Locking Phenomenon]]"
  - "[[Hybrid Incompressible Elements]]"
sources:
  - "[[Abaqus Theory Manual]]"
  - "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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---

# Reduced Integration and Hourglass Control

## Definition

Reduced integration evaluates an element with fewer integration points than full quadrature. Hourglass control adds stabilization to suppress spurious zero-energy deformation modes that reduced integration can introduce.

## How It Works

Reduced integration can reduce computational cost and, in some element families, improve accuracy at special strain-sampling locations. It can also soften elements that otherwise become overly stiff in bending-dominated or nearly incompressible situations.

The risk is rank deficiency: some displacement patterns can produce little or no strain energy at the reduced integration points. These patterns appear as hourglass or zero-energy modes. Abaqus controls them by adding artificial stiffness or related stabilization terms so the element remains usable without losing the intended benefits of reduced quadrature.

[[Abaqus-Analysis-User-s-Guide-Volume-IV|Volume IV]] shows how this becomes a naming and selection issue. Many Abaqus element names use `R` to mark reduced integration, such as `C3D8R` and `S4R`, and the element family determines which hourglass-control assumptions are appropriate.

## Why It Matters

Reduced integration is not just a cheaper quadrature rule. It changes the numerical behavior of the element and must be judged together with element topology, mesh distortion, material behavior, contact, and expected deformation mode.

## Connections

- [[Isoparametric Finite Elements]] supplies the quadrature framework.
- [[Abaqus Element Library]] places reduced integration among full, selective, and hybrid element choices.
- [[Abaqus Element Selection and Formulation]] connects reduced integration to element suffixes and analysis-product availability.
- [[Abaqus Continuum Element Families]] shows where reduced-integration solid and coupled-field variants appear.
- [[Shell Locking Phenomenon]] is one reason under-integration or assumed-strain methods are introduced.
- [[Hybrid Incompressible Elements]] is a more explicit mixed alternative for incompressible response.

## Sources

- [[Abaqus Theory Manual]]
- [[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]