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Balance Laws Stress and Field Equations
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according applied arbitrary associated basis becomes bifurcation body boundary conditions called Cartesian Cauchy components consider constant constitutive coordinate corresponding cylinder deduce defined definition deformation deformation gradient denote depends derivative described determined differentiable direction discussion elastic elastic material elements equal equation equivalent Eulerian example existence expressible field fixed follows force further given Grad hence holds incompressible incremental independent inequality isotropic Lagrangean leads linear loading material Mechanics motion normal notation Note objective observer obtain orthogonal particular physical plane positive possible principal Problem properties pure reference configuration relation relative replaced respectively restriction rotation satisfying scalar second-order tensor Section shear simple solid solution space strain strain-energy function stress stretches surface symmetry tensor theory traction transformation uniqueness unit values vector write written