title: 3D printing of bio-inspired, multi-material structures to enhance stiffness and toughness

authors: Zhang, Xinhan

subjects: Multi-material

abstract: In nature, many biological, multi-materials have complex microstructures and excellent mechanical properties. One shellfish material called nacre has received much attention due to its unique interlocking structure of alternating calcium carbonate tablet and soft organic matter filler. It has microstructure features such as waviness which provide high strength and toughness properties. As a popular topic in the study of bio-inspired structure, it is of great significance to study the ordered microstructure and toughening mechanism of nacre.

3D printing allows for the easy manufacture of complex structures. In this project, inspired by the high strength and toughness of natural nacre, 3D printing technology was used to prepare nacre-like, multi-material structure. Tensile tests, cyclic tensile test and fracture toughness tests were carried out to investigate the relationship between multi-material structure geometry and tensile properties, fracture modes and toughness behaviour.

In the experimental part of this thesis, specimens of the tablet-filler with different dovetail angles made by polylactic acid (PLA) and thermoplastic polyurethane (TPU) inspired by the microstructure of nacre structure were prepared through Fused filament fabrication (FFF)/ Fused Deposition Modelling (FDM) type of 3D printing technology. The multi-material dovetail PLA & TPU specimens exhibited multi-stage deformation under tensile testing. By comparing the tensile performance of structure made by dovetail PLA & PLA material as well as unidirectional pure PLA specimen, it was confirmed that the incorporation of soft TPU filler gave the opportunity for tablet sliding, resulting in a complex multi-stage deformation mechanism of the structures.

Two modes of failure mechanisms, tablet pull-out and tablet break, were observed for the multi-material PLA & TPU structure under tensile testing. The combination of tablet break and pull-out modes can lead to higher strength and modulus than tablet pull-out. In the tablet pull-out mode, transverse expansion was observed in the larger angle dovetail structure, and the occurrence of negative Poisson's ratio effect was determined by calculation. In addition, there is a distinct plateau stage in the tensile curve of multi-material PLA & TPU structure, through cyclic tensile tests identified the plateau as a yield point, generated by short interface between tablets and filler broken. The cyclic tensile tests also determined that the main deformation resistance of the PLA & TPU structure was provied by the long interface broken between tablets and filler, also the interlocking and shearing between the dovetail angle tablets. 

Multi-material PLA & TPU structures with larger dovetail angles produced greater plastic deformation and absorbed more energy during tensile testing. Multi-material PLA & TPU with 5˚ dovetail showed the highest ultimate tensile strength 11.46 MPa and Young’s modulus of 495.96 MPa, but 9˚ dovetail performed poorly with 6.51 MPa and 395.48 MPa, respectively. The value even below than 1˚ dovetail (ultimate tensile strength of 9.82 MPa, modulus of 453.38 MPa). The ultimate tensile strength and Young’s modulus of the multi-material PLA & TPU structure are not as high as those of unidirectional pure PLA and dovetail PLA & PLA specimen, but energy absorption performance is improved by soft TPU filler and dovetail angles. In fracture experiments, crack extension behaviour was observed in fracture toughness specimens.

In summary, the mechanical properties of the nacre-like, multi-material structure were investigated by tensile behavior, fracture mode and energy absorption analysis in this paper. It is demonstrated that the combination of stiff tablet material and soft filler material can effectively improve the toughness of the structure. The tensile strength of the multi-material structure can be improved by increasing the dovetail angle of the tablet. However, it has not been observed that increasing the dovetail angle can significantly increase stiffness. It is confirmed that the optimized design of the 3D printed, bio-inspired, multi-material structure can change the mechanical behavior of the structure and improve its mechanical properties, can provide new ideas for the development of composite materials with excellent mechanical properties.

text: 3D printing of bio-inspired, multi-material structures to enhance stiffness and toughness In nature, many biological, multi-materials have complex microstructures and excellent mechanical properties. One shellfish material called nacre has received much attention due to its unique interlocking structure of alternating calcium carbonate tablet and soft organic matter filler. It has microstructure features such as waviness which provide high strength and toughness properties. As a popular topic in the study of bio-inspired structure, it is of great significance to study the ordered microstructure and toughening mechanism of nacre.

3D printing allows for the easy manufacture of complex structures. In this project, inspired by the high strength and toughness of natural nacre, 3D printing technology was used to prepare nacre-like, multi-material structure. Tensile tests, cyclic tensile test and fracture toughness tests were carried out to investigate the relationship between multi-material structure geometry and tensile properties, fracture modes and toughness behaviour.

In the experimental part of this thesis, specimens of the tablet-filler with different dovetail angles made by polylactic acid (PLA) and thermoplastic polyurethane (TPU) inspired by the microstructure of nacre structure were prepared through Fused filament fabrication (FFF)/ Fused Deposition Modelling (FDM) type of 3D printing technology. The multi-material dovetail PLA & TPU specimens exhibited multi-stage deformation under tensile testing. By comparing the tensile performance of structure made by dovetail PLA & PLA material as well as unidirectional pure PLA specimen, it was confirmed that the incorporation of soft TPU filler gave the opportunity for tablet sliding, resulting in a complex multi-stage deformation mechanism of the structures.

Two modes of failure mechanisms, tablet pull-out and tablet break, were observed for the multi-material PLA & TPU structure under tensile testing. The combination of tablet break and pull-out modes can lead to higher strength and modulus than tablet pull-out. In the tablet pull-out mode, transverse expansion was observed in the larger angle dovetail structure, and the occurrence of negative Poisson's ratio effect was determined by calculation. In addition, there is a distinct plateau stage in the tensile curve of multi-material PLA & TPU structure, through cyclic tensile tests identified the plateau as a yield point, generated by short interface between tablets and filler broken. The cyclic tensile tests also determined that the main deformation resistance of the PLA & TPU structure was provied by the long interface broken between tablets and filler, also the interlocking and shearing between the dovetail angle tablets. 

Multi-material PLA & TPU structures with larger dovetail angles produced greater plastic deformation and absorbed more energy during tensile testing. Multi-material PLA & TPU with 5˚ dovetail showed the highest ultimate tensile strength 11.46 MPa and Young’s modulus of 495.96 MPa, but 9˚ dovetail performed poorly with 6.51 MPa and 395.48 MPa, respectively. The value even below than 1˚ dovetail (ultimate tensile strength of 9.82 MPa, modulus of 453.38 MPa). The ultimate tensile strength and Young’s modulus of the multi-material PLA & TPU structure are not as high as those of unidirectional pure PLA and dovetail PLA & PLA specimen, but energy absorption performance is improved by soft TPU filler and dovetail angles. In fracture experiments, crack extension behaviour was observed in fracture toughness specimens.

In summary, the mechanical properties of the nacre-like, multi-material structure were investigated by tensile behavior, fracture mode and energy absorption analysis in this paper. It is demonstrated that the combination of stiff tablet material and soft filler material can effectively improve the toughness of the structure. The tensile strength of the multi-material structure can be improved by increasing the dovetail angle of the tablet. However, it has not been observed that increasing the dovetail angle can significantly increase stiffness. It is confirmed that the optimized design of the 3D printed, bio-inspired, multi-material structure can change the mechanical behavior of the structure and improve its mechanical properties, can provide new ideas for the development of composite materials with excellent mechanical properties.

year: 2021

title: Monoids with tests and the algebra of possibly non-halting programs

authors: Jackson, Marcel

subjects: Science & Technology

abstract: We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, if-then-else and while-do defined in terms of a Boolean algebra of conditions. It has previously been shown that there is no finite axiomatisation of algebras of partial functions under these operations alone, and this holds even if one restricts attention to transformations (representing halting programs) rather than partial functions, and omits while-do from the signature. In the halting case, there is a natural “fix”, which is to allow composition of halting programs with conditions, and then the resulting algebras admit a finite axiomatisation. In the current setting such compositions are not possible, but by extending the notion of if-then-else, we are able to give finite axiomatisations of the resulting algebras of (partial) functions, with while-do in the signature if the state space is assumed finite. The axiomatisations are extended to consider the partial predicate of equality. All algebras considered turn out to be enrichments of the notion of a (one-sided) restriction semigroup

text: Monoids with tests and the algebra of possibly non-halting programs We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, if-then-else and while-do defined in terms of a Boolean algebra of conditions. It has previously been shown that there is no finite axiomatisation of algebras of partial functions under these operations alone, and this holds even if one restricts attention to transformations (representing halting programs) rather than partial functions, and omits while-do from the signature. In the halting case, there is a natural “fix”, which is to allow composition of halting programs with conditions, and then the resulting algebras admit a finite axiomatisation. In the current setting such compositions are not possible, but by extending the notion of if-then-else, we are able to give finite axiomatisations of the resulting algebras of (partial) functions, with while-do in the signature if the state space is assumed finite. The axiomatisations are extended to consider the partial predicate of equality. All algebras considered turn out to be enrichments of the notion of a (one-sided) restriction semigroup

year: 2015-03

title: PIWeCS: enhancing human/machine agency in an interactive composition system

authors: Whalley, Ian

abstract: This paper focuses on the infrastructure and aesthetic approach used in PIWeCS: a Public Space Interactive Web-based Composition System. The concern was to increase the sense of dialogue between human and machine agency in an interactive work by adapting Paine's (2002) notion of a conversational model of interaction as a ‘complex system’. The machine implementation of PIWeCS is achieved through integrating intelligent agent programming with MAX/MSP. Human input is through a web infrastructure. The conversation is initiated and continued by participants through arrangements and composition based on short performed samples of traditional New Zealand Maori instruments. The system allows the extension of a composition through the electroacoustic manipulation of the source material.

text: PIWeCS: enhancing human/machine agency in an interactive composition system This paper focuses on the infrastructure and aesthetic approach used in PIWeCS: a Public Space Interactive Web-based Composition System. The concern was to increase the sense of dialogue between human and machine agency in an interactive work by adapting Paine's (2002) notion of a conversational model of interaction as a ‘complex system’. The machine implementation of PIWeCS is achieved through integrating intelligent agent programming with MAX/MSP. Human input is through a web infrastructure. The conversation is initiated and continued by participants through arrangements and composition based on short performed samples of traditional New Zealand Maori instruments. The system allows the extension of a composition through the electroacoustic manipulation of the source material.

year: 2004