A primer in elasticity
type: Item
instance of: scholarly article
title: A primer in elasticity
zbMATH Open document ID: 0969.74003
DOI: 10.1023/A:1007672721487
author: Paolo Podio-Guidugli
published in: Journal of Elasticity
publication date: 2001-10-01T00:00:00Z
review text: With this publication, ``The Journal of Elasticity'' starts a series of invited review or tutorial articles from leading researchers. This advanced primer in elasticity gives a fundamental and concise account of the main elements of elasticity theory within the general theory of continuum mechanics. The text is especially well suited for a reader already familiar with classical physical fundamentals of elasticity and wishing to understand the modern approach to the subject, in particular, to the finite elasticity. The material is divided into 26 sections grouped into four chapters: 1. Strain (deformation, displacement, rigid deformations, pure strains, small strains, simple deformations, divergence identities); 2. Stress (forces, balances, dynamical processes, simple equilibrium solutions, normal and shear forces, alternative forms of basic balance laws, power, stress power, exact and linearized equilibrium theories); 3 Constitutive assumptions (linearly elastic materials, material symmetry, fourth-order tensors, classification and representation, internal constraints, constraints and material symmetry, interpretation of material moduli); 4. Equilibrium (classical, strong and weak formulations, variational formulation, principle of minimum potential energy, minimum complementary energy, variational principles, compatible field and boundary operators, generalized boundary conditions, elastic equilibrium with Cauchy relations, elastic equilibrium in the presence of internal constraints). Some sections are concluded with exercises closely related to the text.
Mathematics Subject Classification ID: 74-01
Mathematics Subject Classification ID: 74Bxx
Mathematics Subject Classification ID: 74A10
Mathematics Subject Classification ID: 74A05
zbMATH DE Number: 1556301
zbMATH Keywords: deformation
zbMATH Keywords: forces
zbMATH Keywords: linearly elastic materials
zbMATH Keywords: stress
zbMATH Keywords: displacement
zbMATH Keywords: rigid deformations
zbMATH Keywords: strains
zbMATH Keywords: divergence identities
zbMATH Keywords: balances
zbMATH Keywords: balance laws
zbMATH Keywords: stress power
zbMATH Keywords: linearized equilibrium theories
zbMATH Keywords: material symmetry
zbMATH Keywords: fourth-order tensors
zbMATH Keywords: internal constraints
zbMATH Keywords: material moduli
zbMATH Keywords: variational formulation
zbMATH Keywords: principle of minimum potential energy
zbMATH Keywords: minimum complementary energy
zbMATH Keywords: variational principles
zbMATH Keywords: elastic equilibrium
zbMATH Keywords: Cauchy relations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1556301