Abstract
The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two centuries ago in the school of mathematical physics in France. While the latter approach – fundamentally based on the Navier displacement equation of motion – remains the conventional setting for analysis of wave propagation in elastic bodies, the stress-based formulation and the advantages it offers in elastodynamics and its various extensions remain much less known. Since the key mathematical results of that formulation, as well as a series of applications, originated with J. Ignaczak in 1959 and 1963, the key relation is named the Ignaczak equation of elastodynamics. This review article presents the main ideas and results in the stress-based formulation from a common perspective, including (i) a history of early attempts to find a pure stress language of elastodynamics, (ii) a proposal to use such a language in solving the natural traction initial-boundary value problems of the theory, and (iii) various applications of the stress language to elastic wave propagation problems. Finally, various extensions of the Ignaczak equation of elastodynamics focused on dynamics of solids with interacting fields of different nature (classical or micropolar thermoelastic, fluid-saturated porous, piezoelectro-elastic) as well as nonlinear problems are reviewed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3674-3713 |
| Number of pages | 40 |
| Journal | Mathematics and Mechanics of Solids |
| Volume | 24 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 1 2019 |
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Keywords
- Elasticity
- elastodynamics
- stress formulation
- wave propagation
ASJC Scopus subject areas
- Mathematics(all)
- Materials Science(all)
- Mechanics of Materials
Cite this
Ignaczak equation of elastodynamics. / Starzewski, Martin Ostoja.
In: Mathematics and Mechanics of Solids, Vol. 24, No. 11, 01.11.2019, p. 3674-3713.Research output: Contribution to journal › Review article
}
TY - JOUR
T1 - Ignaczak equation of elastodynamics
AU - Starzewski, Martin Ostoja
PY - 2019/11/1
Y1 - 2019/11/1
N2 - The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two centuries ago in the school of mathematical physics in France. While the latter approach – fundamentally based on the Navier displacement equation of motion – remains the conventional setting for analysis of wave propagation in elastic bodies, the stress-based formulation and the advantages it offers in elastodynamics and its various extensions remain much less known. Since the key mathematical results of that formulation, as well as a series of applications, originated with J. Ignaczak in 1959 and 1963, the key relation is named the Ignaczak equation of elastodynamics. This review article presents the main ideas and results in the stress-based formulation from a common perspective, including (i) a history of early attempts to find a pure stress language of elastodynamics, (ii) a proposal to use such a language in solving the natural traction initial-boundary value problems of the theory, and (iii) various applications of the stress language to elastic wave propagation problems. Finally, various extensions of the Ignaczak equation of elastodynamics focused on dynamics of solids with interacting fields of different nature (classical or micropolar thermoelastic, fluid-saturated porous, piezoelectro-elastic) as well as nonlinear problems are reviewed.
AB - The development of linear elastodynamics in pure stress-based formulation began over half-a-century ago as an alternative to the classical displacement-based treatment that came into existence two centuries ago in the school of mathematical physics in France. While the latter approach – fundamentally based on the Navier displacement equation of motion – remains the conventional setting for analysis of wave propagation in elastic bodies, the stress-based formulation and the advantages it offers in elastodynamics and its various extensions remain much less known. Since the key mathematical results of that formulation, as well as a series of applications, originated with J. Ignaczak in 1959 and 1963, the key relation is named the Ignaczak equation of elastodynamics. This review article presents the main ideas and results in the stress-based formulation from a common perspective, including (i) a history of early attempts to find a pure stress language of elastodynamics, (ii) a proposal to use such a language in solving the natural traction initial-boundary value problems of the theory, and (iii) various applications of the stress language to elastic wave propagation problems. Finally, various extensions of the Ignaczak equation of elastodynamics focused on dynamics of solids with interacting fields of different nature (classical or micropolar thermoelastic, fluid-saturated porous, piezoelectro-elastic) as well as nonlinear problems are reviewed.
KW - Elasticity
KW - elastodynamics
KW - stress formulation
KW - wave propagation
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U2 - 10.1177/1081286518757284
DO - 10.1177/1081286518757284
M3 - Review article
AN - SCOPUS:85044787654
VL - 24
SP - 3674
EP - 3713
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
SN - 1081-2865
IS - 11
ER -