How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young's modulus and the Poisson's ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described b...

How to characterise a nonlinear elastic material ? A review on nonlinear constitutive parameters in isotropic finite elasticity

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterised by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. In contrast, the physical responses of nonlinear elastic materials are generally described b...

Nonlinear elastic inclusions in isotropic solids.

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construc...

The analysis of a Beam Made of Physical Nonlinear Material on Elastic Foundation Under a Harmonic Load

  ABSTRACT: A prismatic beam made of a behaviorally nonlinear material situated on nonlinear elastic foundation is analyzed under a moving harmonic load moving with a known velocity. The vibration equation of motion    is derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculat...

On Nonlinear Water Waves in a Channel