Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity
Most 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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applies behavior body called coefficients components consider constitutive functions constitutive relations continuum coordinate system curvilinear coordinate defined deformation gradient deformed configuration denote depends determined deviatoric differential equation dissipation eigenvalues eigenvectors elastic material entropy expressed fiber FIGURE finite element follows formula fourth-order tensor free energy given hardening heat flux history of strain indices integration isotropic material linear elasticity mapping material constants mathematical mechanics motion nodal forces node normal basis notation occurs orthogonal parameters partial derivatives plane stress plastic loading plastic strain potential energy principal invariants real numbers reference configuration relaxation modulus representation rotation tensor satisfy scalar shape functions shear skew-symmetric small deformations solution strain energy strain measure strain tensor stress tensor stress vector stress-strain relation stretch symmetric tensor temperature tensile test theorem thermodynamic tractions unit vectors variables vector space viscoelastic yield criterion yield function yield stress yield surface zero