Exact simulation for direction-dependent large elastic strain responses of soft fibre-reinforced composites

An explicit form of the elastic strain-energy function for direction-dependent large elastic strain behaviors of soft fiber-reinforced composites is first presented based upon a decoupled approach for simulating complex nonlinear coupling effects.From this form,the exact closed-form solutions are then obtained for the uniaxial tension responses in the fiber and cross-fiber directions.With such exact solutions,the issue of simultaneously simulating strongly coupling nonlinear responses in the fiber and cross-fiber directions may be reduced to the issue of separately treating each decoupled uniaxial stress-strain response,thus bypassing usual complexities and uncertainties involved in identifying a large number of strongly coupled adjustable parameters.The numerical examples given are in good agreement with the experimental data for large strain responses.

Further study of rubber-like elasticity: elastic potentials matching biaxial data

By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multi axial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders （Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII： experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251-288 （1951））. Good agreement is achieved with these extensive data.

Work conjugate strain of virial stress

Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor.Virial stress is widely accepted as the stress measurement in molecular dynamics(MD).However,its conjugate strain is not yet identified.An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at 0 K temperature.The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density.This conclusion is numerically verified with(1)Coulomb-Buckingham potential,Lenard-Jones potential,or arbitrary nonlinear pair potential and(2)randomly generated atomic configurations and deformation gradients.Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation.The result shows that the atomic logarithmic strain is identical to engineer-ing strain when deformation is small.

Work conjugate pair of stress and strain in molecular dynamics

Certain stress and strain form a thermodynamic conjugate pair such that their strain energy equals to a scalar-valued potential energy.Different atomistic stresses and strains are analytically derived based on the work conjugate relation.It is numerically verified with both two-body and three-body potentials that the atomistic Kirchhoff stress,first-order Piola–Kirchhoff stress and second-order Piola–Kirchhoff stress are conjugates to atomistic logarithmic strain,deformation gradient and Lagrangian strain,respectively.Virial stress at 0 K based on original volume is the special form of atomistic Kirchhoff stress for pair potential.It is numerically verified that Hencky strain is not conjugate to any stress.

OBTAINING MULTI-AXIAL ELASTIC POTENTIALS FOR RUBBER-LIKE MATERIALS VIA AN EXPLICIT,EXACT APPROACH BASED ON SPLINE INTERPOLATION

An explicit, exact approach is proposed to obtain multi-axial elastic potentials for isotropic rubber-like materials undergoing large incompressible deformations. By means of two direct, explicit procedures, this approach reduces the problem of determining multi-axial poten- tials to that of determining one-dimensional elastic potentials. To this end, two one-dimensional potentials for uniaxial case and simple shear case are respectively determined via spline inter- polation and, then, the two potentials are extended to generate a multi-axial elastic potential using a novel method based on certain logarithmic invariants. Eventually, each of the multi-axial potentials will exactly match the finite strain data from four benchmark tests.