The solution of a solid mechanics problem involves the establishment of a statically admissible field (one which satisfies equilibrium internally and traction boundary conditions) and a kinematically admissible field (satisfaction of strain-displacement relations and displacement boundary conditions), and the satisfaction of material constitutive laws. Constitutive theory concerns the mathematical modeling of the physical response (output) of a material to a given stimulus (input); that input can be a generalized force or displacement. The importance of accurate constitutive relationships is illustrated in Figure 1; they form the primary link between stress (σ ij ) and strain (ε ij ) components at any point within a body. These relations may be simple (as in the case of linear elasticity) or extremely complex (as in the case of viscoplasticity), depending upon the materials composing the body and the conditions to which the body is subjected (e.g., temperature, loading, environment). Constitutive relations for a particular material are determined experimentally, and they may involve both physically (directly) measurable quantities (e.g., strain, temperature, time) and indirectly measurable internal parameters, often referred to as internal-state variables.Three types of experimentation are necessary to support the rational formulation of constitutive equations. These are (1) exploratory tests, which illuminate the salient response (e.g., time-dependence/timeindependence, sensitivity to hydrostatic stress field, material symmetry and/or anisotropy, etc.), identify fundamental deformation and damage mechanisms, and guide the mathematical structure of the model; (2) characterization tests, which provide the required database for determining the material-specific functional forms and associated parameters so as to represent a particular material over a given range of conditions; and (3) validation tests, often structural (multiaxial) in nature, which provide the prototypical response data that enable validation of a constitutive model through a comparison of structural response with predictions based on the model. Results from validation tests ideally provide feedback for subsequent developmental or refinement efforts.
AbstractMaterials property information such as composition and thermophysical/mechanical properties abound in the literature. Oftentimes, however, the corresponding response curves from which these data are determined are missing or at the very least difficult to retrieve. Further, the paradigm for collecting materials property information has historically centered on (1) properties for materials comparison/selection purposes and (2) input requirements for conventional design/analysis methods. However, just as not all materials are alike or equal, neither are all constitutive models (and thus design/ analysis methods) equal; each model typically has its own specific and often unique required materials parameters, some directly measurable and others indirectly measurable. Therefore, the type and extent ...