Disequilibrium · disequilibrium:mechanical-stress

Mechanical stress or strain

A solid under load. Elastic energy can be released, and in polar or non-centrosymmetric materials the strain itself moves charge or magnetisation.

symbol σ, εClassical mechanicsenergy form mechanicalexergy positivealso: deformation, strain, compression, bending

Atlas record: 8 claims reference this disequilibrium — 7 established and 1 replicated.

Explorerelations · matrix context · routes · sources · cite

conditions: solid

8claims82enumerated routes7routes with complete-composition evidence28candidate routes not searched9cited sources

Relations

drives · 5

Mechanical stress or strain—drives→Direct piezoelectric effectestablished

a non-centrosymmetric crystal or a poled ferroelectric ceramic or polymer
stress below the depoling and fracture limits

D = d · σ · piezoelectric charge coefficient d [C/N]

Mechanical stress or strain—drives→Flexoelectric effectestablished

the required strain gradient may be generated mechanically (e.g. bending) or by spatially non-uniform thermal expansion; uniform strain alone does not produce bulk flexoelectric polarization in a centrosymmetric dielectric
coefficients are small in bulk (nC/m) and useful only at the nanoscale or in thin films

P = μ · ∇ε · flexoelectric coefficient μ [C/m]

Mechanical stress or strain—drives→Villari effectestablished

a magnetostrictive material under a bias field and cyclic stress

Mechanical stress or strain—drives→Elastic deformationestablished

σ = E · ε · Young's modulus E [Pa]

Mechanical stress or strain—drives→Elastocaloric effectreplicated

stress large enough to drive the martensitic transformation of a shape-memory alloy

produces · 3

Resonant vibration—produces→Mechanical stress or strainestablished

cyclic bending stress at the root of the cantilever

Elastic deformation—produces→Mechanical stress or strainestablished

the deformed member carries a cyclic stress or strain state that can drive a stress-driven conversion (flexoelectric
elastocaloric
piezoelectric)

Thermal expansion—produces→Mechanical stress or strainestablished

non-uniform thermal expansion is mechanically incompatible across adjacent regions of a solid, or is constrained by an adjoining material or structure, producing a strain or stress gradient; the constraining region may be the cooler part of the same continuous specimen rather than a separate stiffer body

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

C.01 Thermoelectric C.02 Thermionic C.03 Thermoacoustic C.04 Pyroelectric C.05 Thermogalvanic C.06 Thermomagnetic C.07 Thermophotovoltaic C.08 Heat engine (thermomechanical)C.09 Caloric (magneto/electro/elasto)C.10 Piezoelectric C.11 Flexoelectric C.12 Triboelectric C.13 Electrostatic (variable capacitance)C.14 Electromagnetic induction C.15 Magnetostrictive C.16 Magnetoelectric C.17 Spin caloritronic C.18 Photovoltaic C.19 Photoelectrochemical C.20 Photothermal C.21 Electrochemical C.22 Osmotic / salinity-gradient C.23 Electrokinetic C.24 Turbomachinery C.25 Magnetohydrodynamic C.26 Radiovoltaic C.27 Nuclear heat C.28 Rectenna C.29 Thermochemical C.30 Biological C.31 Fluctuation / information-driven C.32 Photon momentum C.33 Thermodiffusive C.34 Marangoni C.35 Acoustoelectric C.36 Photodiffusive C.37 Thermo-osmotic C.38 Electrohydrodynamic C.39 Radioluminescent C.40 Thermopolarization

Enumerated routes through this · 82 (showing 24)

Bending-actuated NiTi elastocaloric air cooler1/2 est · demonstrated
Regenerative elastocaloric heat pump1/2 est · demonstrated
Bimetallic-strip piezoelectric harvester5/5 est · demonstrated
Piezoelectric vibration harvester5/5 est · demonstrated
Flexoelectric vibration harvester5/5 est · demonstrated
Magnetostrictive vibration harvester7/7 est · demonstrated
Flow-induced-vibration piezoelectric harvester7/7 est · demonstrated
Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work3/3 est · extends a recorded pathway
Mechanical stress or strain → Flexoelectric effect → Separated surface charge → Electrical work3/3 est · extends a recorded pathway
Temperature gradient → Thermal expansion → Mechanical stress or strain → Elastocaloric effect → Cooling3/4 est · same energy form
Temperature gradient → Thermal expansion → Mechanical stress or strain → Elastocaloric effect → Useful heat3/4 est · same energy form
Pressure gradient → Elastic deformation → Mechanical stress or strain → Elastocaloric effect → Cooling3/4 est · extends a recorded pathway
Pressure gradient → Elastic deformation → Mechanical stress or strain → Elastocaloric effect → Useful heat3/4 est · extends a recorded pathway
Mechanical vibration → Resonant vibration → Mechanical stress or strain → Elastocaloric effect → Cooling3/4 est · candidate
Mechanical vibration → Resonant vibration → Mechanical stress or strain → Elastocaloric effect → Useful heat3/4 est · candidate
Vibration-driven elastocaloric cooler (proposed)3/4 est · candidate
Mechanical vibration → Elastic deformation → Mechanical stress or strain → Elastocaloric effect → Useful heat3/4 est · candidate
Thermal-expansion flexoelectric thermopolarization5/5 est · candidate
Pressure gradient → Elastic deformation → Mechanical stress or strain → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Pressure gradient → Elastic deformation → Mechanical stress or strain → Flexoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Mechanical stress or strain → Villari effect → Changing magnetic flux → Electromagnetic induction → Charge carriers → Electrical work5/5 est · extends a recorded pathway
Mechanical stress or strain → Elastic deformation → Elastic stress → Direct piezoelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Mechanical stress or strain → Elastocaloric effect → Temporal temperature change → Pyroelectric effect → Separated surface charge → Electrical work5/5 est · extends a recorded pathway
Mechanical vibration → Resonant vibration → Mechanical stress or strain → Flexoelectric effect → Separated surface charge → Electrical work5/5 est · candidate

Cited sources · 9

[1]
J. Curie, P. Curie. Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées (1880)
Bulletin de la Société minéralogique de France 3, 90–93 · doi:10.3406/bulmi.1880.1564 · crossref ✓ 2026-09-19 · record
[2]
J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)
Oxford University Press · book, no DOI · record
[3]
A. Erturk, D. J. Inman. Piezoelectric Energy Harvesting (2011)
Wiley · doi:10.1002/9781119991151 · crossref ✓ 2026-09-19 · record
[4]
P. Zubko, G. Catalan, A. K. Tagantsev. Flexoelectric effect in solids (2013)
Annual Review of Materials Research 43, 387–421 · doi:10.1146/annurev-matsci-071312-121634 · crossref ✓ 2026-09-19 · record
[5]
S. Iwakiri, Y. Miyata, T. Mori. Observation of universal thermopolarization effect in insulators (2026)
arXiv:2605.17224 (17 May 2026), National Institute for Materials Science, Tsukuba · arxiv.org/abs/2605.17224 · record
[6]
E. Villari. Ueber die Aenderungen des magnetischen Moments, welche der Zug und das Hindurchleiten eines galvanischen Stroms in einem Stabe von Stahl oder Eisen hervorbringen (1865)
Annalen der Physik 202, 87–122 · doi:10.1002/andp.18652020906 · crossref ✓ 2026-09-19 · record
[7]
L. Wang, F. G. Yuan. Vibration energy harvesting by magnetostrictive material (2008)
Smart Materials and Structures 17, 045009 · doi:10.1088/0964-1726/17/4/045009 · crossref ✓ 2026-09-19 · record
[8]
J. Tušek et al.. A regenerative elastocaloric heat pump (2016)
Nature Energy 1, 16134 · doi:10.1038/nenergy.2016.134 · crossref ✓ 2026-09-19 · record
[9]
X. Moya, S. Kar-Narayan, N. D. Mathur. Caloric materials near ferroic phase transitions (2014)
Nature Materials 13, 439–450 · doi:10.1038/nmat3951 · crossref ✓ 2026-09-19 · record

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