Engineering Software Research & Development

In mechanical and structural engineering, strength criteria are commonly expressed as allowable limits on scalar measures derived from the stress tensor field in a linear elasticity problem. These limits are determined from experimental observations and engineering safety requirements. We must remember that continuum mechanics assumes materials have no microstructure and therefore treats them as capable of subdivision without limit. Real materials do not satisfy this assumption. Consequently, pointwise stresses computed from a continuum model should be interpreted as averages over a representative volume element (RVE). As long as the stress field varies smoothly, such that the stress changes only slightly across an RVE, continuum theory may be understood as providing RVE-averaged stresses.  In the following, we consider situations in which the averaging process must be made explicit.

Reliable strength prediction in laminated composites requires the simultaneous control of discretization and model-form errors. Conventional plate and shell formulations cannot generally provide this control. The hp-version of the finite element method offers a practical solution.

"From Legacy Finite Element Modeling to Explainable Simulation: Technical Requirements for XAI in Computational Mechanics", a technical paper authored by ESRD Co-founder and Chairman Dr. Barna Szabó, was recently published in Computational Mechanics and is available to all as an open-access article. This paper discusses technical requirements posed by Explainable AI (XAI), methods for controlling both model-form and discretization errors in AI-assisted simulation, and model-centric vs. element-centric implementations.