Archetype-blending continuum theory

We propose a modular approach for generalized computational mechanics in mesostructured continua, namely the archetype blending continuum (ABC) theory. The theory’s modularity derives from its mathematical constructors: archetypes, or building blocks that all multi-component material laws are generated from. These archetypes are the means used to discretize a description of material motion that relies on the fundamental theorem of calculus, an approach that contrasts the Taylor series expansions that underlie previous generalized continuum kinematics. All enhanced continuum methods to date assume embedded scales may be seen as separable material points in larger domains, an assumption that creates unnecessary restrictions on the constitutive modeler and makes the additional stress tensors introduced far less physical. The ABC theory removes that assumption and provides mesostructural basis for higher order stress quantities by attributing them separately to archetypes and their interactions. In this manner, ABC is a bridge between generalized continuum mechanics and micromechanics, two well-established fields. Thus, a multi-component material design space may be probed with the ABC theory by adding and removing archetype modules or by refining archetypes themselves. This work presents the mathematics and ingredients for finite element implementation of the theory so that others may build on the specific demonstrations for solid mechanics explored here: multi-component elasticity and multi-crystal plasticity. Abstract extensions of the ABC theory into stochastic space and multiphysics problems are also briefly propounded.