Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers.

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Bibliographic Details
Title:	Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers.
Authors:	Zhang, Mengru^1,2 (AUTHOR), Xu, Mingzhu^1,2 (AUTHOR), Chen, Weiting^1,2 (AUTHOR) chenweiting@imech.ac.cn, Zhao, Yapu^1,2 (AUTHOR)
Source:	Applied Mathematics & Mechanics. Mar2025, Vol. 46 Issue 3, p423-446. 24p.
Subjects:	Steady state conduction, Curvilinear coordinates, Differential forms, Heat conduction, Path integrals
Abstract:	The initial stresses widely exist in elastic materials. While achieving a continuum stress-free configuration through compatible unloading is desirable, mechanical unloading alone frequently proves insufficient, posing challenges in avoiding virtual stress-free configurations. In this paper, we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain. Our focus is on initially stressed cylindrical and spherical elastomers, where we first derive the Saint-Venant, Beltrami-Michell, and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory. It is shown that for any given axially or spherically distributed initial stress, an equivalent temperature variation always exists. Furthermore, we propose two innovative initial stress forms based on the steady-state heat conduction. By introducing an equivalent temperature variation, the initial stress can be released through a compatible thermo-mechanical unloading process, offering valuable insights into the constitutive theory of initially stressed elastic materials. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	The initial stresses widely exist in elastic materials. While achieving a continuum stress-free configuration through compatible unloading is desirable, mechanical unloading alone frequently proves insufficient, posing challenges in avoiding virtual stress-free configurations. In this paper, we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain. Our focus is on initially stressed cylindrical and spherical elastomers, where we first derive the Saint-Venant, Beltrami-Michell, and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory. It is shown that for any given axially or spherically distributed initial stress, an equivalent temperature variation always exists. Furthermore, we propose two innovative initial stress forms based on the steady-state heat conduction. By introducing an equivalent temperature variation, the initial stress can be released through a compatible thermo-mechanical unloading process, offering valuable insights into the constitutive theory of initially stressed elastic materials. [ABSTRACT FROM AUTHOR]
ISSN:	02534827
DOI:	10.1007/s10483-025-3230-9