| A unified constitutive equation with the effect of compression strain rate, tension strain, and shear strain for materials with very low Poisson's ratio has been developed. The unified equation combines strain, creep, and relaxation into a single unified strain which is time dependent. This approach results in a single equation describing the relationship among strain rate, stress, strain, and state variables. The equation as developed satisfies the coordinate invariance requirement and material objectivity requirements for all of the parameters. The mathematical derivation based on the principles of continuum mechanics is described in detail. To numerically solve for the parameters of the equation, a matrix with 18 linear equations has been derived and a computer program has been written.; The test data of two types of energy absorbing foam materials are used for correlation study: the polyurethane foam which was tested at five compressive strain rates and the polypropylene foam which was tested for the quasi-static compressive, tension, and shear. Good correlations have been concluded for both cases. The foam material model #57 of LS-DYNA3D was developed jointly by the author, his colleagues, and Livermore Software Technology Corporation (LSTC). Using this material model to simulate various shapes of FEA structural models is also presented in detail. The lack of strain rate effect in model #57 limits the usage to the quasi-static simulation for foam materials. The newly developed unified equation would expand the capability of an FEA method into the strain rate sensitive type of foam material simulation once it is incorporated into an FEA software. |
