On the reducibility of failure theories for composite materials

This paper reports on the initiation of an effort to address three ontological aspects of failure criteria as they are applicable to composite materials applications. The first attempts to clarify “what a criterion really is” from the perspective of physical objectivity. The second attempts to clarify “how a criterion relates with another” in terms of their main semantic attributes. The third attempts to identify “how one criterion is related to another” in terms of their syntactic representation in the context of term calculus especially from the perspective of polynomial association with the strain energy density. Under the first aspect the non-physical nature of a theory is exposed when it is used as a criterion and is evaluated from its semantic perspective. The human role on the formation of any failure criterion is shown to have a foundationally subjective character, thus, rendering the corresponding criterion as non-objective. Under the second aspect the creation of classification ontology in terms of the semantic projections of failure criteria in their structural heritage and usage contexts is given. The common attributes of failure criteria are utilized to identify the bases of the attribute space that can be used to enable their ontological classification. Web ontology software is utilized for visual interpretation of the ontological context. Under the third aspect the syntactic reducibility of the various known failure theories to one another is addressed. Thermodynamically founded strain energy density expansion leads to the creation of various generalized strain energy based criteria. Two theorems are proposed and proved to show that under specific conditions failure criteria and theories of certain polynomial structure are constrained renderings of criteria based on strain energy density. Examples are given to demonstrate how a critical energy density criterion represents the least upper bound in the partial ordered set of many well known failure criteria.