Optimization of fiber-reinforced materials to passively control strain-stress response

Abstract

The intricate and nonlinear nature of material behavior, characterized by a progressively changing stress-strain relationship, is a fundamental and indispensable property governing the behavior of numerous mechanical systems. Examples of these mechanical systems include rubber components in automobile suspensions and engine mounts, soft tissues and organs in bio-mechanics and medical engineering, as well as packaging materials such as foam, paper, and plastics. Components used for the construction of these mechanical systems often need to meet specific stiffness requirements which can be influenced by the composition of the employed material, see Steinbrecher et al. [Computational Mechanics, 69 (2022)].

On the macro or micro level, such materials can often be classified as fiber-reinforced materials, i.e., thin and long fibers embedded inside a matrix material. One way to control the stress-strain relationship of fiber-reinforced materials is to alter the geometry of the reinforcements, thus creating passive materials with a highly nonlinear stress-strain response. This can be a viable method for the development of optimized system components or meta-materials.

This method can be explored with a single beam embedded in a softer matrix. If the embedded beam is straight, the stress increase would be approximately linear with increasing strain. Bending the beam inside the matrix will lower the starting stress rate. The stress rate increases until the encased beam is straight, at which point the stress rate will not increase further. By manipulating the initial geometry of the beam, the evolution of the strain rate can be influenced.

Previously, Reinforcement Learning based shape optimization has been used to optimize structures in the context of fluid dynamics, see Fricke et al. [Advances in Computational Science and Engineering, 1 (2023)]. This approach is different from classical optimization methods, as it trains an agent to solve a specific task inside a defined problem set. While the training is computationally more expensive than a single optimization, the trained agent is able to optimize a problem inside the learned problem set with less effort.

Applying the RL-based shape optimization method to the beam geometry, an agent is trained to identify optimal beam geometries for a set of starting stress rates and ending stress rates.