A materials characterization method models dynamic, non-linear, temperature-dependent stress, strain, hysteresis, creep, and loss of elasticity at high strain, both in test samples and in Finite Element Analysis (FEA). Incorporating universal properties of statistical mechanics and adapting domain models from ferromagnetics to the higher-dimensional realm of stress tensors, the model is applicable to polymers, rubbers, liquids, and metals in elastic and plastic deformation. The model quantifies the dynamics of both plastic and brittle failure. Apparatus and methods are shown for testing material samples and matching the computational model to sample characteristics, leading to a set of characterizing parameters and predictive simulations using those parameters. Though apparatus and testing protocols of the invention yield optimum characterizations, pre-existing data from conventional testing yield useful results.< / PTEXT>