Abstract
We consider a classical derivation of a continuum theory, based on the fundamental balance laws of mass and momenta, for a body with internal corner and surface contact interactions. The balances of mass and linear and angular momentum are applied to the arbitrary parts of a continuum which supports non-classical internal corner and surface contact interactions. The form of the specific corner contact interaction force measured per unit length of the corner is derived. A generalized form of Cauchy’s stress theorem is obtained, which shows that the surface traction on an oriented surface depends in a specific way on both the oriented unit normal as well as the curvature of the surface. An explicit form of the surface-couple traction which acts on every oriented surface is obtained. Two fields in the continuum, which are denoted as stress and hyperstress fields, are shown to exist, and their role in representing the surface traction and the surface-couple traction is identified. Finally, the field equations for this theory are determined, and a fundamental power theorem is derived. In the absence of internal corner and surface-couple traction interactions, the equations of classical continuum mechanics are recovered. There is no appeal to any ‘principle of virtual power’ in this work.
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Communicated by Victor Eremeyev, Peter Schiavone and Francesco dell'Isola.
To David Steigmann in recognition of the depth and breadth of his research contributions and his unwavering dedication to the advancement of fundamental continuum mechanics.
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Fosdick, R. A generalized continuum theory with internal corner and surface contact interactions. Continuum Mech. Thermodyn. 28, 275–292 (2016). https://doi.org/10.1007/s00161-015-0423-8
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DOI: https://doi.org/10.1007/s00161-015-0423-8