Continuum Mechanics: Elasticity, Plasticity, ViscoelasticityMost books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics. In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems. |
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a₁ base vectors body boundary conditions called Cijkm coefficients components consider constitutive functions constitutive relations continuum coordinate system covariant crack curvilinear coordinate defined deformation gradient denote depends determined deviatoric displacement e₁ e₂ eigenvalues eigenvectors elastic material equations fiber FIGURE finite element follows formula fourth-order tensor free energy hardening isotropic isotropic material linear elasticity mapping matrix mechanics n₁ n₂ nodal normal basis notation orthogonal P₁ parameters particle plane stress plastic loading plastic strain potential energy principal invariants real numbers reference configuration rotation tensor scalar shape functions shear skew-symmetric solution strain energy strain tensor stress tensor stress vector stress-strain relation stretch symmetric tensor T₁ temperature tensile test theorem theory thermodynamic unit vectors vector space viscoelastic yield criterion yield function yield stress yield surface zero α₁ θα ду дх