On stress-based piecewise elasticity for limited strain extensibility materials

• A one-dimensional stress-based elasticity model with limited strain extensibility is developed.
• Such nonlinear elastic models can be used to model certain rubber-like and biological materials with limiting chain extensibility.
• The derived constitutive function is a non-smooth piecewise expression, which can be regularized for numerical or physical considerations.
• This non-smooth constitutive expression is derived from a Gibbs potential.
• A three-dimensional extension of this stress-based model is also proposed.
• Some simple structural examples are investigated for a bar composed of this non-smooth elastic body with concentrated and distributed forces.

A one-dimensional stress-based elasticity model with limited strain extensibility is developed in this paper, based on thermodynamics arguments. Such nonlinear elastic models can be used to model certain rubber-like and biological materials with limiting chain extensibility. The derived constitutive function is a non-smooth piecewise expression, which can be regularized for numerical or physical considerations. This non-smooth constitutive expression is derived from a Gibbs potential. A three-dimensional extension of this stress-based model is also proposed in the paper. Some simple structural examples are investigated for a bar composed of this non-smooth elastic body. A homogeneous bar composed of this new class of nonlinear elastic material that is loaded is studied for different tension states, namely for concentrated or distributed axial loading. It is shown that the displacement limit extensibility can be observed at the structural scale, with finite or infinite axial load parameters.