The elastic stored energy of initially strained, or stressed, materials: restrictions and third-order expansions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916159683559424 |
|---|---|
| author | Gower, Artur L. Shearer, Tom Ciarletta, Pasquale Destrade, Michel |
| author_facet | Gower, Artur L. Shearer, Tom Ciarletta, Pasquale Destrade, Michel |
| contents | A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied forces. These initial stresses are due to initial strains or microstructural changes, such as thermal expansion, manufacturing processes, volumetric growth, remodelling, etc. A common constitutive choice for modelling such materials extends the classical approach in the field theory of continuum mechanics to include, explicitly, the initial stress or strain in the elastic stored energy function. Here, we discuss why these energy functions need to satisfy some restrictions to avoid unphysical behaviours, such as non-conservation of energy, {and we derive the required restrictions from the classical assumptions of elasticity.} To illustrate their need, we perform a rigorous asymptotic expansion for proving that these restrictions on stored energy functions that depend on the strain and initial stress are required for consistency with strain energy functions of classical third-order weakly nonlinear elasticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The elastic stored energy of initially strained, or stressed, materials: restrictions and third-order expansions Gower, Artur L. Shearer, Tom Ciarletta, Pasquale Destrade, Michel Soft Condensed Matter Classical Physics 74B05, 74B10, 74B15, 74B20 A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied forces. These initial stresses are due to initial strains or microstructural changes, such as thermal expansion, manufacturing processes, volumetric growth, remodelling, etc. A common constitutive choice for modelling such materials extends the classical approach in the field theory of continuum mechanics to include, explicitly, the initial stress or strain in the elastic stored energy function. Here, we discuss why these energy functions need to satisfy some restrictions to avoid unphysical behaviours, such as non-conservation of energy, {and we derive the required restrictions from the classical assumptions of elasticity.} To illustrate their need, we perform a rigorous asymptotic expansion for proving that these restrictions on stored energy functions that depend on the strain and initial stress are required for consistency with strain energy functions of classical third-order weakly nonlinear elasticity. |
| title | The elastic stored energy of initially strained, or stressed, materials: restrictions and third-order expansions |
| topic | Soft Condensed Matter Classical Physics 74B05, 74B10, 74B15, 74B20 |
| url | https://arxiv.org/abs/2403.09280 |