---
type: concept
title: "Shell Locking Phenomenon"
complexity: advanced
domain: computational-mechanics
aliases:
  - shell locking
  - locking phenomenon
  - membrane locking
  - shear locking
created: 2026-05-28
updated: 2026-05-28
address: c-000045
tags:
  - concept
  - finite-element-method
  - shell-elements
  - locking
status: current
related:
  - "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
  - "[[Assumed Transverse Shear Strain Interpolation]]"
  - "[[MITC4 Shell Element]]"
  - "[[Displacement-Based Finite Element Formulation]]"
  - "[[Shell Structure Asymptotic Behavior]]"
  - "[[Uniform Optimal Convergence]]"
sources:
  - "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
---

# Shell Locking Phenomenon

## Definition

Shell locking is a thickness-dependent finite element error in which a shell element becomes artificially stiff as the shell becomes thin. It appears as underpredicted displacements, stresses, strains, and strain energy, and as poor convergence in thin-shell bending or mixed-dominated problems.

## How It Works

The source connects locking to [[Shell Structure Asymptotic Behavior]]. Displacement-based shell elements may fail to approximate the pure bending displacement space of the [[Basic Shell Mathematical Model]]. The result is parasitic membrane or transverse shear strain in states that should be nearly strain-free in those modes.

The paper distinguishes membrane locking from shear locking. Membrane locking appears in curved shells, while transverse shear locking can appear regardless of curvature when the interpolation cannot represent the thin-shell bending constraint.

## Remedies

Common remedies include reduced integration, incompatible or non-conforming modes, ANS, EAS, and MITC-style mixed interpolation. The source treats MITC as a particularly effective family because it interpolates selected tensorial strain components at tying points while trying to retain consistency and ellipticity.

## Connections

- [[Assumed Transverse Shear Strain Interpolation]] is the targeted shear-locking remedy used in the four-node shell thread.
- [[MITC4 Shell Element]] is the practical low-order shell element thread that uses mixed interpolation to control locking.
- [[Uniform Optimal Convergence]] is the desired behavior after locking has been controlled.
- [[Shell Element Benchmark Testing]] describes how locking should be exposed using convergence curves and thickness variation.

## Sources

- [[On-the-Finite-Element-Analysis-of-Shell-Structures]]