# Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

# Mixed Variational Methods: Considerations on Numerical Applications

• Massimo Cuomo
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_181-1

## Definitions

Mixed variational principles are multi-field principles that involve all or some of the field variables of the physical model examined. The solution of the problem is characterized as an optimum point of the functional. Mixed methods are largely used in computational mechanics for obtaining accurate solutions and for removing locking and instability phenomena.

## Introduction

Irreducible formulations in solid mechanics are the most commonly employed, both for continuum and discrete models. However irreducible formulations require some of the field equations to be exactly satisfied, and this poses very strong conditions on the functional spaces where the field variables are defined. These are particularly severe when numerical solutions based on interpolations are used. The inability of the interpolating spaces to exactly fulfill some of the field equations gives rise to the phenomenon of locking. Mixed formulations turn out to...

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## Authors and Affiliations

1. 1.Department of Civil Engineering and ArchitectureUniversity of CataniaCataniaItaly

## Section editors and affiliations

• Francesco dell’Isola
• 1
• 2
1. 1.DISGUniversity of Rome La SapienzaRomeItaly
2. 2.International Research Center M&MoCSUniversity of L’AquilaL’AquilaItaly