Inspiring mechanical design from biological morphogenesis – BioDesign

The BioDesign project integrates numerical, experimental, and manufacturing approaches to develop and optimize bio-inspired mechanical joints. The methods used include allometric analysis to study the relationships between body mass and joint dimensions in quadrupedal mammals. This analysis, based on 3D tomographic scans and phylogenetic generalized least squares regressions, has helped define the starting points for a generative design algorithm.

The developed growth model mimics the biological processes of growth and adaptation of chondrocytes. In this model, growth is regulated by mechanical constraints, particularly hydrostatic and shear stresses, which influence the local volumetric expansion of mechanical parts. This model is inspired by the idea that cyclic hydrostatic stresses promote chondrocyte proliferation, while high shear stresses inhibit it. This results in a local volumetric expansion of the parts, proportional to the mechanical stresses experienced, thus allowing optimal adaptation of the joint surfaces.

The generative design algorithm was developed using Code_Aster, an open-source numerical solver. This code is available as open-source, allowing other researchers and engineers to use and modify it according to their needs. The manufacturing of the joints was carried out using powder bed fusion technology, a metal additive manufacturing method.

The evaluation of wear performance was conducted both numerically and experimentally. A numerical model was developed to predict the evolution of wear over time, using the wear coefficient determined experimentally. This numerical model was implemented in the finite element simulation software Code_Aster, which was used to perform stress and deformation analyses, as well as to simulate the wear of contact surfaces using specific algorithms. The meshes for the models were generated with GMSH, an open-source 3D mesh generator, allowing the creation of high-quality meshes for finite element simulations. Experimental tests were conducted on a test bench designed to evaluate the wear performance of bio-inspired joints under operational conditions.

The allometric analysis conducted to study the relationships between body mass and joint dimensions in quadrupedal mammals revealed that the average diameter and width of the distal humerus evolve proportionally to body mass. This relationship is crucial as it maintains a constant contact pressure and sliding speed across different sizes of mammals, which is essential for effective joint lubrication. Furthermore, the relationship between the diameter and width of the distal humerus is approximately 0.5, which is optimal for balancing load capacity and joint size.

A mathematical model has been developed to mimic the growth of biological tissues under mechanical contact conditions. This model integrates contact mechanics and uses finite element methods to simulate the growth and adaptation of contact surfaces. The algorithm employs growth rules inspired by the formation of synovial joints, where hydrostatic pressure promotes growth and shear inhibits it. Developed on Code_Aster, the algorithm has been tested under various boundary conditions and material properties, demonstrating its ability to generate contact interfaces with nearly uniform pressure distribution.

Several case studies have been conducted to evaluate the impact of model parameters on the uniformity of contact pressure, even under time-dependent loading conditions. The results have been compared with other studies, showing that the proposed algorithm generates high-quality contact interfaces in terms of pressure distribution.

The manufacturing of bio-inspired mechanical joints has been successfully achieved using powder bed fusion technology, a metal additive manufacturing method. This approach has enabled the production of complex and optimized joints in a single step, thereby simplifying the manufacturing process and reducing production costs.

Numerical and experimental evaluations have shown that bio-inspired joints exhibit more uniform wear and better distribution of contact stresses, resulting in increased durability. Numerical simulations have accurately predicted the evolution of wear over time, thus validating the theoretical models and generative designs.

One of the main perspectives is the processing of industrial applications. By adapting the developed methods and algorithms to industrial contexts, it would be possible to design more durable and efficient mechanical components. This could include optimizing parts for industrial machinery and improving the durability of equipment under variable load conditions, with expected consequences for reducing maintenance costs through better distribution of mechanical stresses.

The development of the algorithm for 3D cases represents another perspective of this project. Currently, simulations and designs are often limited to 2D models. By extending these capabilities to 3D environments, it would be possible to capture more complex and realistic mechanical behaviors. This would allow for a better understanding of the interactions between different parts of a mechanism and more precise optimization of the geometries of the parts.

The implementation of a generative design module for the structural part of the components, integrating the bone remodeling law, is an interesting perspective. By drawing inspiration from biological bone remodeling processes, where bones adapt based on the mechanical stresses they undergo, it would be possible to develop algorithms capable of evolving mechanical structures as well as their contact interfaces automatically.

The development of the algorithm for multicomponent cases, where all parts of a mechanical system are shaped simultaneously, is another perspective. In nature, the bones of a skeletal system evolve simultaneously, with complex interactions between different segments. By reproducing this behavior in mechanical systems, it would be possible to design mechanisms where all parts adapt and evolve together, thus optimizing the overall performance of the system. This could lead to significant advances in the design of complex mechanical systems.

Arroyave-Tobon, S.; Hernandez-Aristizabal, D.; Diperi, J.; Linares, J. M. Bio-inspired non-assembly joints: Design, fabrication and wear performance. CIRP Annals. 2024.

Marquez-Florez, K.; Arroyave-Tobon, S.; Tadrist, L.; Linares, J. M. Elbow dimensions in quadrupedal mammals driven by lubrication regime. Scientific Reports. 2024, 14(1), 2177.

Hernandez-Aristizabal, D.; Arroyave-Tobon, S.; Garzon-Alvarado, D. A.; Linares, J. M. Stress-adaptive design of 2D contact interfaces with uniform pressure: A bio-inspired approach. International Journal of Solids and Structures. 2023, 270, 112238.

Marquez-Florez, K.; Arroyave-Tobon, S.; Linares, J. M. From biological morphogenesis to engineering joint design: a bio-inspired algorithm. Materials & Design. 2023, 225, 111466.

For many years, mechanical design has been based on parts defined from canonical geometries (e.g. cylinders and planes). Today, simulation, prototyping and manufacturing means are no longer constraints for the development of new concepts. Calculation means and new modelling formalisms, such as numerical twins, allow a detailed and realistic mechanical analysis of complex systems (mechanical and biological). Current manufacturing technologies, such as additive manufacturing and 5-axis CNC machining, make it possible to obtain parts with complex surfaces. Additive manufacturing opens up new possibilities for obtaining already assembled mechanisms. In this way, technological barriers have been removed, opening up new avenues for the development of new design paradigms.

Bio-inspiration, as a research paradigm, aims to understand natural structures and processes to guide scientific research in non-biological sciences. In the struggle for survival, natural systems have achieved extraordinary properties by exploiting multi-scale and multiphase structures. From a mechanical perspective, nature has generated specialized structures and joints whose mechanical properties exceed those created by humans. So why not inspire the design of mechanical systems for biological processes?

Theories and numerical models have been developed to reproduce the processes of morphogenesis and bone growth. However, these theories and models have not yet been explored as a source of inspiration for the design and dimensioning of mechanical systems and parts. A link between bone growth theories and mechanical design methodologies is missing. The adaptation of these biological theories in a technological context could provide an opportunity to formulate new approaches to mechanical design.

BioDesign project will investigate the hypothesis that the biological mechanisms of endoskeleton growth can be mimicked in an engineering context to automate the design of the mechanisms. In order to test this hypothesis, the overall objective of this project is to formulate new design methodologies and to implement numerical tools inspired by bone growth theories for the development of engineering applications. In other words, the aim is to learn how nature makes matter grow, in a context of limited resources, in order to realize functional mechanical systems. The idea is to capitalize on the possibilities of additive manufacturing to obtain mechanisms with complex geometry that are already assembled.

The input data for the methodology will be the external mechanical loads and the topology of the system under study. The algorithm, mimicking the processes of biological morphogenesis, will shape elementary parts according to the mechanical stresses generated during operation. In an iterative formulation, all parts will be shaped simultaneously while simulating the system operation. The result of the methodology will be the optimized external geometry of the elementary parts of the system. Algorithms will be developed in the form of a demonstrator. Experimental and numerical evaluations will be performed. Open source software will be used for the implementation of the demonstrator: Salome/Code Aster for finite element mechanical analysis, SimTK for multibody dynamic analysis and OpenCascade for geometric modeling. In line with an open science approach, developed software tools will be also open-source for diffusion in the scientific community.