Peridynamic Thermal Stresses and Hypothetical Body Forces

ABSTRACT The present work aims to gain new insights into thermal stresses and force states in peridynamic elastic solids. The key findings from this study are: (1) A general micro‐potential‐based formulation is developed for peridynamic thermal stresses in elastic solids. It provides a route to develop and verify micro‐bond potential functions for materials with a known relationship between thermal stress and strain. As an example, a specific micro‐bond potential is introduced, and the corresponding peridynamic thermal stresses are derived, which take the same form as the linear relationship between stresses and strains in the classical theory of thermoelasticity. It indicates that the specific micro‐bond potential is applicable to linear thermoelasticity and might be further used to develop bond failure criteria for linear thermoelastic solids. (2) A peridynamic projection tensor is defined for the first time, based on which an exact relation between stresses and force states is established. This would provide a powerful way to incorporate more material models in peridynamics. (3) The peridynamic linear thermoelastic‐elastic correspondence principle is first developed by inspection of the constitutive force states and the basic peridynamic momentum equation. Peridynamic hypothetical body forces are formulated by taking into account the temperature effect on the motion. On this basis, the displacement solution to a linear thermoelastic problem could be replaced by a solution to a corresponding isothermal problem provided that the solid was subject to an additional hypothetical peridynamic body force. Besides, study shows that for material points away from solid boundaries, the hypothetical peridynamic body forces converge to those defined in the classical theory of linear thermoelasticity as the horizon approaches zero. The effectiveness of the present work is demonstrated through numerical examples, highlighting its ability to provide good predictions for displacements and thermal stresses in linear thermoelastic solids.