Titlebook: Spatial and Material Forces in Nonlinear Continuum Mechanics; A Dissipation-Consis Paul Steinmann Book 2022 The Editor(s) (if applicable) a

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Mechanical Balances,This chapter details the generic balances for the case of mechanical balances of mass, spatial momentum, and its vector and scalar moment, respectively, with emphasis on their global and local formats and the distinction between material and spatial control volumes.

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Consequences of Mechanical Balances,This chapter explores the consequences of the mechanical balances by elaborating on local and global formats of the balance of kinetic energy and the balance of material momentum and its vector and scalar moments, thereby differentiating between spatial and material control volumes.

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Virtual Work,This chapter capitalizes on the referential setting when introducing the notions of spatial and material virtual displacements and discussing the accompanying spatial and material virtual work principles.

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Variational Setting,This chapter expands on the variational setting in terms of extended Hamilton and Dirichlet principles for conservative elasto-dynamic and elasto-static cases, respectively, and carefully analyzes the resulting spatial and material Euler-Lagrange equations.

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