Stress-strain curve determined from a non-uniformly deformed specimen: An application of autonomous finite element analysis

Abstract

Stress-strain curve cannot be directly converted from force-displacement curve if the deformation is not uniform in test specimen. An automated inverse analysis is developed to select the candidate stress-strain curve whose force-displacement result in simulation has the best goodness of fit (GOF) to the test measurement. The candidate stress-strain curves are randomly generated by a Random Stress Strain Curve Generator (RSSCG) under several physical constrains without using test data or analytical formula. The process of finite element analysis (FEA) is packed into a white box function with stress-strain curve as input and its corresponding GOF as output. A Leveled Random Search (LRS) algorithm optimizes the shape of stress-strain curve for a better GOF value. LRS preforms several random probes at each search level. At next level, the size of search zone is reduced while the center of the search zone is repositioned to the best solution found so far. This process continues until a satisfactory result is found. LRS is designed to work with discontinuous response surface and overcome local minimal problem. As an optional feature, Human in the Loop (HITL) can be used to adjust the search zone for fast convergence. Examples in tension and compression test are provided to demonstrate the process. The concept of the automated inverse analysis is summarized as Autonomous Finite Element Analysis (AFEA). The fully automated computer program has been successfully used in material modeling of automobile crashworthiness, producing 40 beyond-necking point stress-strain curves in two weeks.