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Fiber reinforced polymer composites (FRPCs) are valued for their high strength and lightweight and have found applications from aerospace to renewable energy. Additive manufacturing (AM, or 3D printing) of FRPCs is of great interest in recent years due to the manufacturing flexibility offered by AM. Direct ink write (DIW) 3D printing is a popular choice for FRPC 3D printing due to its low cost and open framework for broad material choices. However, previously explored techniques for AM of FRPCs are hindered by heavy reliance on fiber orientation dictated by extrusion toolpath and often require specialized hardware to print FRPCs with low viscosity and long cure time thermoset epoxy matrices. In this paper, we introduce a single-stream hybrid DIW AM technique for the creation of mechanically robust FRPC functional structures where the matrix is DIW 3D printed, and pre-epoxy impregnated (prepreg) woven carbon fiber (CF) fabrics are robotically placed. Additionally, functional components, such as conductive elements, can be readily integrated. We investigated the impact of prepreg woven CF reinforcement on a two-stage photo-thermal thermoset resin matrix on the mechanical characteristics of manufactured FRPCs. We also combined these efforts to fabricate functional structures, including strain sensors for in-situ deformation monitoring, heating elements, and embedded light sensors. This study found that the proposed single-stream hybrid DIW AM process could be a facile approach to fabricate high-strength FRPC functional structures.

We present a novel isogeometric collocation method for nonlinear dynamic analysis of three-dimensional, slender, elastic rods. The approach is based on the geometrically exact Cosserat model for rod dynamics. We formulate the governing nonlinear partial differential equations as a first-order problem in time and develop an isogeometric semi-discretization of position, orientation, velocity and angular velocity of the rod centerline as NURBS curves. Collocation then leads to a nonlinear system of first-order ordinary differential equations, which can be solved using standard time integration methods. Furthermore, our model includes viscoelastic damping and a frictional contact formulation. The computational method is validated and its practical applicability shown using several numerical applications of nonlinear rod dynamics.

Advancement of additive manufacturing is driving a need for design tools that exploit the increasing fabrication freedom. Multimaterial, three-dimensional (3D) printing allows for the fabrication of components from multiple materials with different thermal, mechanical, and “active” behavior that can be spatially arranged in 3D with a resolution on the order of tens of microns. This can be exploited to incorporate shape changing features into additively manufactured structures. 3D printing with a downstream shape change in response to an external stimulus such as temperature, humidity, or light is referred to as four-dimensional (4D) printing. In this paper, a design methodology to determine the material layout of 4D printed materials with internal, programmable strains is introduced to create active structures that undergo large deformation and assume a desired target displacement upon heat activation. A level set (LS) approach together with the extended finite element method (XFEM) is combined with density-based topology optimization to describe the evolving multimaterial design problem in the optimization process. A finite deformation hyperelastic thermomechanical model is used together with an higher-order XFEM scheme to accurately predict the behavior of nonlinear slender structures during the design evolution. Examples are presented to demonstrate the unique capabilities of the proposed framework. Numerical predictions of optimized shape-changing structures are compared to 4D printed physical specimen and good agreement is achieved. Overall, a systematic design approach for creating 4D printed active structures with geometrically nonlinear behavior is presented which yields nonintuitive material layouts and geometries to achieve target deformations of various complexities.

The recently developed dual-stage 3D printing reprocessable thermosets (3DPRTs) utilize acrylate functional groups to enable the ultra-violet based 3D printing (Stage I), and employ bond exchange reaction (BERs) to tailor the network structure for mechanical properties enhancement and impart the reshapeability, reparability, and recyclability into traditionally unprocessable thermosets (Stage II). 3DPRT provides a practical solution to address environmental challenges associated with the rapid increase in the consumption of 3D printing materials. However, due to the nascent state of development, fundamental understanding of the chemomechanics during the processing of 3DPRTs is still lacking. In this paper, we present detailed experimental and theoretical studies to understand the effect of thermal treatment condition at Stage II on the evolution of network structure and thermomechanical properties of 3DPRTs. A chemomechanics theory is defined to link the molecular-level BER kinetics to the macroscale thermomechanical properties of 3DPRTs during the thermal treatment. A thermo-viscoelastic multi-branched constitutive model is then established to capture the elastic and glass transition behaviors during the Stage II processing. The developed theory is able to capture the experimental observations on the mechanical properties enhancement and provide theoretical guidance for the network design and the selection of thermal treatment conditions to tailor the final mechanical properties of 3DPRTs.

Straight beams, rods and trusses are common elements in structural and mechanical engineering, but recent advances in additive manufacturing now also enable efficient freeform fabrication of curved, deformable beams and beam structures, such as microstructures, metamaterials and conformal lattices. To exploit this new design freedom for applications with nonlinear mechanical behavior, we introduce an isogeometric method for shape optimization of curved 3D beams and beam structures. The geometrically exact Cosserat rod theory is used to model nonlinear 3D beams subject to large deformations and rotations. The initial and current geometry are parameterized in terms of NURBS curves describing the beam centerline and an isogeometric collocation approach is used to discretize the strong form of the balance equations. Then, a nonlinear optimization problem is formulated in order to optimize the positions of the control points of the NURBS curve that describes the beam centerline, i.e., the geometry or shape of the beam. To solve the design problem using gradient-based algorithms, we introduce semi-analytical, inconsistent analytical and fully analytical approaches for calculation of design sensitivities. The methods are numerically validated and their performance is investigated, before the applicability and versatility of our 3D beam shape optimization method is illustrated in various numerical applications, including optimization of an auxetic 3D metamaterial.

Vitrimers are a new class of thermosetting polymers that can be thermally processed through bond exchange reactions (BERs) without losing network integrity. In engineering applications, the tunability of their thermomechanical properties is highly desirable to meet the requirements of different working conditions. Here, we report a simple composite-based strategy that avoids complex chemistry to prepare vitrimer blends with tunable thermomechanical properties by virtue of the good weldability of base vitrimers. Effects of processing parameters (such as temperature and time) on the properties of recycled vitrimer blends are experimentally investigated. A computational model that accounts for the random distribution of component vitrimer particles is developed to predict the thermomechanical properties of the recycled vitrimer blends with various compositions. Good agreement is achieved between theoretical prediction and experiment. Parametric studies are further conducted by employing the computational model to explore the designability and provide some basic principles to guide the design of recycled vitrimer blends. Reasonable recyclability of the vitrimer blends is verified by multiple generations of recycling experiments.

Lattice structures are frequently found in nature and engineering due to their myriad attractive properties, with applications ranging from molecular to architectural scales. Lattices have also become a key concept in additive manufacturing, which enables precise fabrication of complex lattices that would not be possible otherwise. While design and simulation tools for stiff lattices are common, here we present a digital design and nonlinear simulation approach for additive manufacturing of soft lattices structures subject to large deformations and instabilities, for which applications in soft robotics, healthcare, personal protection, energy absorption, fashion and design are rapidly emerging. Our framework enables design of soft lattices with curved members conforming to freeform geometries, and with variable, gradually changing member thickness and material, allowing the local control of stiffness. We model the lattice members as 3D curved rods and using a spline-based isogeometric method that allows the efficient simulation of nonlinear, large deformation behavior of these structures directly from the CAD geometries. Furthermore, we enhance the formulation with a new joint stiffening approach, which is based on parameters derived from the actual node geometries. Simulation results are verified against experiments with soft lattices realized by PolyJet multi-material polymer 3D printing, highlighting the potential for simulation-driven, digital design and application of non-uniform and curved soft lattice structures.

The combination of scientific advances in additive manufacturing (AM) and smart materials (SMs) has enabled the development of a new interdisciplinary research area: 4D printing. This technology offers – via stimuli-responsive materials – promising transformation capabilities to objects whether at the functional, shape, or property levels. By considering such capabilities, researchers from multiple disciplines have investigated a large spectrum of stimuli-SMs associations with proofs-of-concept built from either commercial or custom 3D printers. Despite the abundant initiatives, 4D printing requires additional developments to meet robust system applications for the industry. The paper aims to highlight the status, inherent barriers, and challenges of 4D printing to be addressed from a product-systems design perspective. It firstly reminds the fundamentals of SMs, processes, stimulus, and AM to which a synthesis of significant research works related to 4D printing highlighting the current status as well as scientific, technical, and organizational limitations is provided. Beyond this comprehensive study, the paper emphasizes opportunities and challenges from multiple perspectives and draws a research roadmap for engineering design and cross-disciplinary design. The outcome of the work tends to structure research efforts for the next decade towards the development of smart products that meet use for humans and the industry.

Advanced manufacturing methods like multi-material additive manufacturing are enabling realization of multiscale materials with intricate spatially varying microstructures and thus, material properties. This blurs the boundary between material and structure, paving the way to lighter, stiffer, and stronger structures. Taking advantage of these tunable multiscale materials warrants development of novel design methods that effectively marry the concepts of material and structure. We propose such a design to manufacture workflow and demonstrate it with laminated continuous fiber-reinforced composites that possess variable stiffness enabled by spatially varying microstructure. This contrasts with traditional fiber-reinforced composites which typically have a fixed, homogenous microstructure and thus constant stiffness. The proposed workflow includes three steps: (1) Design automation—efficient synthesis of an optimized multiscale design with microstructure homogenization enabling efficiency, (2) Material compilation—interpretation of the homogenized design lacking specificity in microstructural detail to a manufacturable structure, and (3) Digital manufacturing—automated manufacture of the compiled structure. We adapted multiscale topology optimization, a mesh parametrization-based algorithm and voxel-based multimaterial jetting for these three steps, respectively. We demonstrated that our workflow can be applied to arbitrary 2D or 3D surfaces. We validated the complete workflow with experiments on two simple planar structures; the results agree reasonably well with simulations.

Vitrimers have the characteristics of shape-reforming and surface-welding, and have the same excellent mechanical properties as thermosets; so vitrimers hold the promise of a broad alternative to traditional plastics. Since their initial introduction in 2011, vitrimers have been applied to many unique applications such as reworkable composites and liquid crystal elastomer actuators. A series of experiments have investigated the effects of reprocessing conditions (such as temperature, time, and pressure) on recycled materials. However, the effect of particle size on the mechanical properties of recycled materials has not been reported. In this paper, we conducted an experimental study on the recovery of epoxy-acid vitrimers of different particle sizes. Epoxy-acid vitrimer powders with different particle size distributions were prepared and characterized. The effects of particle size on the mechanical properties of regenerated epoxy-acid vitrimers were investigated by dynamic mechanical analysis and uniaxial tensile tests. In addition, other processing parameters such as temperature, time, and pressure are discussed, as well as their interaction with particle size. This study helped to refine the vitrimer reprocessing condition parameter toolbox, providing experimental support for the easy and reliable control of the kinetics of the bond exchange reaction.

Three-dimensionally (3D) knitted technical textiles are spreading into industrial applications, since their geometric, structural and functional performance can be tailored and optimized on fibre-, yarn- and fabric levels by customizing yarn materials, knit patterns and geometric shapes. The ability to simulate their complex mechanical behaviour is thus an essential ingredient in the development of a digital workflow for optimal design and manufacture of 3D knitted textiles. Here, we present a multi-scale modelling and simulation framework for the prediction of the nonlinear orthotropic mechanical behaviour of single jersey knitted textiles and its experimental validation. On the meso-scale, representative volume elements (RVEs) of the fabric are modelled as single, interlocked yarn loops and their mechanical deformation behaviour is homogenized using periodic boundary conditions. Yarns are modelled as nonlinear 3D beam elements and numerically discretized using an isogeometric collocation method, where a frictional contact formulation is used to model inter-yarn interactions. On the macro-scale, fabrics are modelled as membrane elements with nonlinear orthotropic material behaviour, which is parameterized by a response surface constitutive model obtained from the meso-scale homogenization. The input parameters of the yarn-level simulation, i.e., mechanical properties of yarns and geometric dimensions of yarn loops in the fabrics, are determined experimentally and subsequent meso- and macro-scale simulation results are evaluated against reference results and mechanical tests of knitted fabric samples. Good agreement between computational predictions and experimental results is achieved for samples with varying stitch values, thus validating our novel computational approach combining efficient meso-scale simulation using 3D beam modelling of yarns with numerical homogenization and nonlinear orthotropic response surface constitutive modelling on the macro-scale.

We present the design of a new compliant ratchet mechanism using a multi-material additive manufacturing technology. The design enables the elimination of springs and global movement of the pawl or gear that typically exist in classical ratchets. It is also taking advantage of recent advances in 3D printing technology to replace traditional mechanisms with multi-material mechanisms. This design is evaluated with computational finite element (FE) simulations and verified with physical tests of motion in two opposite directions. We also present a parametric study of the geometric and material properties of our current design and discuss how this basic design concept can be customized for specific applications.

3D printed active composites (PACs) are a new concept in active composite design and manufacturing where one or several active materials are used as fiber materials to create active shape changing composites that are determined by the design of fibers. Recent advances in multi-material 3D printing have enabled the rapid realization of these designs, many of which would not be possible without 3D printing. In addition, the integration of active materials with 3D printing also permits the novel concept of 4D printing, where the shape of an object can change after 3D printing. In the past, using printed active composites to create origami structures was demonstrated but was limited to simple folding patterns. In this paper, we study the relationship among folding angle, fiber orientation, and applied load during programming, in order to find the optimized fiber arrangement and loading directions for complicated folding patterns. Both experiments and finite element1 simulations were performed to optimize the fiber orientations in PAC in order to achieve the desired shape change, and good agreement was achieved. FEA was then used to help the design for some complicated, self-folding, active origami structures-including a miura-ori pattern, a table, a sailboat and a crane—in which the folding occurs in different directions. The successful implementation of these complicated patterns demonstrates the capability of using printed active composites for very complicated self-folding origami designs.

We present a novel method for the mechanical simulation of slender, elastic, spatial rods and rod structures subject to large deformation and rotation. We develop an isogeometric collocation method for the geometrically exact, nonlinear Cosserat rod theory. The rod centerlines are represented as spatial NURBS curves and cross-section orientations are parameterized in terms of unit quaternions as 4-dimensional NURBS curves. Within the isogeometric framework, the strong forms of the equilibrium equations of forces and moments of the discretized Cosserat model are collocated, leading to an efficient method for higher-order discretizations. For rod structures consisting of multiple, connected rods we introduce a formulation with rigid, quasi- G 1 -coupling. It is based on the strong enforcement of continuity of displacement and change of cross-section orientation at interfaces. We also develop a mixed isogeometric formulation, which is based on an independent discretization of internal forces and moments and alleviates shear locking for thin rods. The novel rod simulation methods are verified by numerical convergence studies. Further computational examples include realistic applications with large deformations and rotations, as well as a large-scale rod structure with several hundreds of coupled rods and complex buckling behavior.

3D printing of polymeric materials for various applications has been quickly developed in recent years. In contrast to thermoplastics, 3D printed thermosets, although desirable, are inherently non-recyclable due to their permanently crosslinked networks. As 3D printing is becoming more popular, it is desirable to develop recycling approaches for 3D printed parts in view of increasing polymer wastes. Here, we present a new thermosetting vitrimer epoxy ink and a 3D printing method that can 3D print epoxy into parts with complicated 3D geometries, which later can be recycled into a new ink for the next round of 3D printing. In the first printing cycle, a high-viscous ink is first slightly cured and is then printed at an elevated temperature into complicated 3D structures, followed by an oven cure using a two-step approach. To be recycled, the printed epoxy parts are fully dissolved in an ethylene glycol solvent in a sealed container at a high temperature. The dissolved polymer solution is reused for the next printing cycle using similar printing conditions. Our experiments demonstrate that the ink can be printed four times and still retains very good printability. In addition, the vitrimer epoxy can be used for pressure-free repairs for the 3D printed parts.

Voxel-based multimaterial jetting additive manufacturing allows fabrication of digital materials (DMs) at the meso-scale (∼1 mm) by controlling the deposition patterns of soft elastomeric and rigid glassy polymers at the voxel-scale (∼90 μm). The digital materials can then be used to create heterogeneous functionally graded material (FGM) structures at the macro-scale (∼10 mm) programmed to behave in a predefined manner. This offers huge potential for design and fabrication of novel and complex bespoke mechanical structures.\ud \ud This paper presents a complete design and manufacturing workflow that simultaneously integrates material design, structural design, and product fabrication of FGM structures based on digital materials. This is enabled by a regression analysis of the experimental data on mechanical performance of the DMs i.e., Young’s modulus, tensile strength and elongation at break. This allows us to express the material behavior simply as a function of the microstructural descriptors (in this case, just volume fraction) without having to understand the underlying microstructural mechanics while simultaneously connecting it to the process parameters.\ud \ud Our proposed design and manufacturing approach is then demonstrated and validated in two series of design exercises to devise complex FGM structures. First, we design, computationally predict and experimentally validate the behavior of prescribed designs of FGM tensile structures with different material gradients. Second, we present a design automation approach for optimal FGM structures. The comparison between the simulations and the experiments with the FGM structures shows that the presented design and fabrication workflow based on our modeling approach for DMs at meso-scale can be effectively used to design and predict the performance of FGMs at macro-scale.

Current printing methods for continuous fiber-reinforced composites require the composites to quickly solidify during the printing, so the matrix is limited to thermoplastics or thermosets with fast curing mechanisms. This paper presents the first design of a 3D printer head for direct-ink-writing that can overcome the limitations on printable resins. It leverages the shear stress imposed on the fiber to enable the ready extrusion of composite filaments and is applicable to a wide variety of thermoset resins and commercially-available continuous fibers. The developed printing method can create thermally-curable composite components with covalently bonded interfaces and comparable mechanical strength as directly-molded samples. It also enables the free-standing 3D printing of UV-curable composites. Overall, the developed printing method allows the composite parts to be designed quickly to meet unique specifications, as well as provides new functions in 4D printing, biomedical printing, and the printing of functional devices.

We present a design optimization and manufacturing approach for the creation of complex three-dimensional (3D) curved rod structures with spatially variable material distributions that exhibit active deformation behavior, enabled by the shape memory effect (SME) of 3D printed photopolymers���so-called four-dimensional (4D) printing. Our framework optimizes the cross-sectional properties of a rod structure, in particular the Young's modulus, such that under given loading conditions it can obtain one or more target shapes resulting from geometrically nonlinear deformation, from which the structure can then actively deform back to the original shape due to the SME. Our approach includes a novel algorithm to generate physical realizations from the computational design model, which allows their direct fabrication via printing of shape memory composites with voxel-level compositional control with a multi-material 3D printer. Our design and manufacture digital toolchain allows the continuous variation of multiple active materials as a route to optimize mechanical as well as active behavior of a structure, without changing the original shape of the 3D rod structure, which is not possible with a single material. We demonstrate the entire design-fabrication-test approach and illustrate its capabilities with examples including 3D characters, personalized medical applications, and complex structures that exhibit instabilities during their nonlinear deformation.

Shape memory polymers (SMPs) are a class of active materials that have the capability of fixing a temporary shape and recovering to a permanent shape in response to environmental stimuli. While SMPs have been studied intensively, researchers paid comparatively fewer attentions to SMPs exhibiting anisotropic mechanical and shape memory behaviors by controlling the microscopic architectures. At the same time, the rapidly developed three-dimension (3D) printing technologies enable us to directly print complex 3D structures with multimaterials and provide possibilities to fabricate anisotropic shape memory polymer by precisely controlling the microstructure of fibers. In this paper, we present a new approach for fabricating printed anisotropic shape memory elastomeric composites (p-ASMECs) by taking advantage of 3D printing. In the fabrication process, an elastomer is first printed as matrix and the orientation of fibers is defined by the precisely printed channels. By interrupting the printing process, the printed channels are filled with the crystallizable polymeric fibers that endow the shape memory effect into the composite system. The p-ASMECs exhibit large, controllable anisotropy in both mechanical and shape memory behaviors that can be precisely controlled by geometric parameters of the microstructure such as fiber's volume fraction and position in space. To facilitate design of p-ASEMCs, we also developed a thermomechanical constitutive framework to describe the complex, anisotropic, larger deformation thermomechanical behaviors of p-ASEMCs. The developed constitutive model, used to explain the phenomenon that the lowest stiffness of p-ASEMCs occurs at the fiber orientation angle θ ≈ 55°, successfully predicts the anisotropic shape memory behavior of p-ASMECs, guides the design to enhance the temporary shape fixity, and simulates the shear deformation of the temporary shape after completely releasing the external constraints.

Graphene, the 2D form of carbon, has excellent mechanical, electrical and thermal properties and a variety of potential applications including NEMS, protective coatings, transparent electrodes in display devices and biological applications. Adhesion plays a key role in many of these applications. In addition, it has been proposed that the electronic properties of graphene can be affected by elastic deformation caused by adhesion of graphene to its substrate. In light of this, we present here a continuum mechanics based theoretical framework to understand the effect of nanoscale morphology of substrates on adhesion and mechanics of graphene. In the first part, we analyze the adhesion mechanics of graphene on 1 and 2D periodic corrugations. We carried out molecular statics simulations and found the results to be in good agreement with our theory. We modeled adhesive interactions surface forces described by Lennard-Jones 6-12 potential in both our analysis and simulations and in principle can be extended to any other interaction potential. The results show that graphene adheres conformally to substrates with large curvatures. We showed in principal that the theory developed here can be extended to substrates of arbitrary shapes that can be represented by a Fourier series. In the second part, we study the mechanics of peeling of graphene ribbons from 1D sinusoidally textured substrates. In the molecular statics simulations, we observed two key features in the peel mechanics of the ribbons: the ribbons slide over the substrate and undergo adhesion and peeling near the crack front in an oscillatory manner, the frequency of which reveals the wavelength of the underlying substrate. Our theory qualitatively captures these features of the peel mechanics and is general enough that it can be extended to other 2D materials like MoS2, BN etc and different kinds of interaction potentials., Comment: 45 pages, 21 figures, published in IJSS, 2016

Dynamic covalent network (or covalent adaptable network) polymers can rearrange their macromolecular chain network by bond exchange reactions (BERs) where an active unit replaces a unit in an existing bond to form a new bond. Such macromolecular events, when they occur in large amounts, can attribute to unusual properties that are not seen in conventional covalent network polymers, such as shape reforming and surface welding; the latter further enables the important attributes of material malleability and powder-based reprocessing. In this paper, a multiscale modeling framework is developed to study the surface welding of thermally induced dynamic covalent network polymers. At the macromolecular network level, a lattice model is developed to describe the chain density evolution across the interface and its connection to bulk stress relaxation due to BERs. The chain density evolution rule is then fed into a continuum level interfacial model that takes into account surface roughness and applied pressure to predict the effective elastic modulus and interfacial fracture energy of welded polymers. The model yields particularly accessible results where the moduli and interfacial strength of the welded samples as a function of temperature and pressure can be predicted with four parameters, three of which can be measured directly. The model identifies the dependency of surface welding efficiency on the applied thermal and mechanical fields: the pressure will affect the real contact area under the consideration of surface roughness of dynamic covalent network polymers; the chain density increment on the real contact area of interface is only dependent on the welding time and temperature. The modeling approach shows good agreement with experiments and can be extended to other types of dynamic covalent network polymers using different stimuli for BERs, such as light and moisture etc.

Covalent adaptable networks (CANs; also known as dynamic covalent networks or vitrimers) are appealing for developing simple and efficient techniques for recycling thermosetting polymers. In this paper, ethylene glycol (EG) is used as a solvent to enable pressure-free surface welding, surface repair, and recycling of a malleable epoxy where the transesterification-type bond exchange reaction (BER) imparts a dynamic nature to the covalent network. At a high temperature, the EG molecules participate in the BER, leading to dissolution of the epoxy network. If the EG is allowed to evaporate, the dissolved epoxy can re-form into a solid. The effects of EG content, temperature, and catalyst concentration on EG-assisted BERs are investigated. It is found that the amount of EG can be adjusted to tune the solution/solid transformation: An excessive amount of EG is required to dissolve the epoxy; on the other hand, a shortage of EG can shift the reaction back to re-form the polymer. Furthermore, the catalyst concen...

Both environmental and economic factors have driven the development of recycling routes for the increasing amount of composite waste generated. This paper presents a new paradigm to fully recycle epoxy-based carbon fiber reinforced polymer (CFRP) composites. After immersing the composite in ethylene glycol (EG) and increasing the temperature, the epoxy matrix can be dissolved as the EG molecules participate in bond exchange reactions (BERs) within the covalent adaptable network (CAN), effectively breaking the long polymer chains into small segments. The clean carbon fibers can be then reclaimed with the same dimensions and mechanical properties as those of fresh ones. Both the dissolution rate and the minimum amount of EG required to fully dissolve the CAN are experimentally determined. Further heating the dissolved solution leads to repolymerization of the epoxy matrix, so a new generation of composite can be fabricated by using the recycled fiber and epoxy; in this way a closed-loop near 100% recycling paradigm is realized. In addition, epoxy composites with surface damage are shown to be fully repaired. Both the recycled and the repaired composites exhibit the same level of mechanical properties as fresh materials.

This study investigates the influence of print orientation and raster patterns on the mechanical behavior of Ultem 9085 and Antero 840CN03 (Electro-Static Dissipative Polyetherketoneketone; ESD-PEKK) used in fused filament fabrication printing. Samples were printed in Flat, Edge, and Vertical orientations, while the raster angle was altered from 0, to 45, to 90° with successive layers being either perpendicular or parallel. Monotonic testing revealed the mechanical strength of ESD-PEKK outperformed Ultem 9085 in flat (68.8 vs. 64.2 MPa), edge (95.7 vs. 76.1 MPa), and vertical (49.6 vs. 40.0 MPa) print orientations with a 45° perpendicular infill. The variation of raster angle and pattern was almost always detrimental to the mechanical properties compared to Edge print orientations with 45° perpendicular infill. Fatigue testing was also performed on all three orientations with a 45° perpendicular infill. The fatigue strength for the worst-case, vertically printed samples, was 3.5x higher for ESD-PEKK compared to Ultem (16 MPa vs. 4 MPa). All samples tested could be fitted with a power-law relationship, and each material showed low variability within their power-law exponents. This article discusses the performance of ESD-PEKK and Ultem 9085 and their potential use as aerospace and defense-grade polymers.

Among all three-dimensional (3D) printing materials, thermosetting photopolymers claim almost half of the market, and have been widely used in various fields owing to their superior mechanical stability at high temperatures, excellent chemical resistance as well as good compatibility with high-resolution 3D printing technologies. However, once these thermosetting photopolymers form 3D parts through photopolymerization, the covalent networks are permanent and cannot be reprocessed, i.e., reshaped, repaired, or recycled. Here, we report a two-step polymerization strategy to develop 3D printing reprocessable thermosets (3DPRTs) that allow users to reform a printed 3D structure into a new arbitrary shape, repair a broken part by simply 3D printing new material on the damaged site, and recycle unwanted printed parts so the material can be reused for other applications. These 3DPRTs provide a practical solution to address environmental challenges associated with the rapid increase in consumption of 3D printing materials., Thermosetting polymers are widely used in 3D printing owing to their superior mechanical stability, but once they are printed, the highly crosslinked polmyers cannot be reprocessed or repaired. Here the authors demonstrate a two-step polymerization strategy toward 3D printing of reprocessable thermosets.

In this paper, we demonstrate the feasibility of controlling the shape changing sequence of shape memory polymers created from digital manufacturing by exploiting multi-shape memory effects. We create shape memory polymer components with precise architectures by 3D printing. After subjecting them to model-based thermomechanical programming steps, the components assume specified configurations in a precisely controlled shape changing sequence. The use of the 3D printing technique enables the digital manufacturing route with the advantages of easy implementation, large design freedom, and high printing resolution of shape memory polymer components. The results in this paper provide a method for precisely controlling the shape recovery profile and enabling the manufacture of devices with complicated geometries and unprecedented multifunctional performance.

In this paper, we demonstrate the feasibility of using 3D printing technique to create functional graded shape memory polymers (SMPs) with both spontaneous and sequential shape recovery abilities. The created SMP components, with properly assigned spatial variation of the thermodynamical property distribution, react rapidly to a thermal stimulus, and return to a specified configuration in a precisely controlled shape changing sequence. The use of the 3D printing technique enables a manufacturing routine with merits of easy implementation, large design freedom, and high printing resolution, which promises to advance immediate engineering applications for low-cost, rapid, and mass production.

We measured the work of separation of single and few-layer MoS

A 4D printing method is developed where the shape of a 3D-printed part can change rapidly into a new permanent one by heating., We describe an approach to print composite polymers in high-resolution three-dimensional (3D) architectures that can be rapidly transformed to a new permanent configuration directly by heating. The permanent shape of a component results from the programmed time evolution of the printed shape upon heating via the design of the architecture and process parameters of a composite consisting of a glassy shape memory polymer and an elastomer that is programmed with a built-in compressive strain during photopolymerization. Upon heating, the shape memory polymer softens, releases the constraint on the strained elastomer, and allows the object to transform into a new permanent shape, which can then be reprogrammed into multiple subsequent shapes. Our key advance, the markedly simplified creation of high-resolution complex 3D reprogrammable structures, promises to enable myriad applications across domains, including medical technology, aerospace, and consumer products, and even suggests a new paradigm in product design, where components are simultaneously designed to inhabit multiple configurations during service.

A frictionless contact formulation for spatial rods is developed within the framework of isogeometric collocation. The structural mechanics is described by the Cosserat theory of geometrically nonlinear spatial rods. The numerical discretization is based on an isogeometric collocation method, where the geometry and solution fields are represented as NURBS curves and the strong forms of the equilibrium equations are collocated at Greville points. In this framework, a frictionless rod-to-rod contact formulation is proposed. Contact points are detected by a coarse-level and a refined search for close centerline points and reaction forces are computed by the actual penetration of rod surface points, so that the enforcement of the contact constraints is performed with the penalty method. An important aspect is the application of contact penalty forces as point loads within the collocation scheme, and methods for this purpose are proposed and evaluated. The overall contact algorithm is validated by and applied to several numerical examples. This is the authors' accepted and refereed manuscript to the article. Locked until 01 July 2019 due to copyright restrictions

Thermally malleable polymers which undergo covalent bond exchange reactions (BERs) have been shown to be able to rearrange their network topology at high temperatures without impairing the network integrity. At low temperatures, the BERs are so sluggish that the materials behave like traditional thermosetting polymers. In this paper, we demonstrated that the temperature dependent BER rate could be tuned by adjusting the stoichiometry of monomers. As the ratio of hard segments in the epoxy thermoset network is increased, the material's glass transition temperature (Tg) is increased, with a corresponding increase in the temperature required to achieve a given stress relaxation rate. The material stress relaxation behavior was studied from both a theoretical and experimental point of view. Based on the kinetics of BERs, we derived the detailed expression of stress relaxation time, which reveals an Arrhenius type dependency of material relaxation behavior on the applied temperature. Subsequently, from the experimental stress relaxation curves, we determined the energy barrier for the BERs in different networks. With the Tg being elevated from 30.3 °C to 63.0 °C, the BER energy barrier is linearly increased from 68.2 kJ mol−1 to 97.3 kJ mol−1. Such a correlation between these two thermomechanical behaviors provides an additional design parameter (beyond catalyst choice) which can aid in achieving highly tunable service conditions for practical engineering applications of thermally malleable thermosets.

Light activated polymers (LAPs) are a class of contemporary materials that when irradiated with light respond with mechanical deformation. Among the different molecular mechanisms of photoactuation, here we study radical induced bond exchange reactions (BERs) that alter macromolecular chains through an addition-fragmentation process where a free chain whose active end group attaches then breaks a network chain. Thus the BER yields a polymer with a covalently adaptable network. When a LAP sample is loaded, the macroscopic consequence of BERs is stress relaxation and plastic deformation. Furthermore, if light penetration through the sample is nonuniform, resulting in nonuniform stress relaxation, the sample will deform after unloading in order to achieve equilibrium. In the past, this light activation mechanism was modeled as a phase evolution process where chain addition-fragmentation process was considered as a phase transformation between stressed phases and newly-born phases that are undeformed and stress free at birth. Such a modeling scheme describes the underlying physics with reasonable fidelity but is computationally expensive. In this paper, we propose a new approach where the BER induced macromolecular network alteration is modeled as a viscoplastic deformation process, based on the observation that stress relaxation due to light irradiation is a time-dependent process similar to that in viscoelastic solids with an irrecoverable deformation after light irradiation. This modeling concept is further translated into a finite deformation photomechanical constitutive model. The rheological representation of this model is a photoviscoplastic element placed in series with a standard linear solid model in viscoelasticity. A two-step iterative implicit scheme is developed for time integration of the two time-dependent elements. We carry out a series of experiments to determine material parameters in our model as well as to validate the performance of the model in complex geometrical and loading configurations. The comparison between the finite element simulations and experiments shows that the model can accurately capture the response of the LAP under a wide range of coupled photo-mechanical loading conditions, such as light induced stress relaxation, creep in tension, and bending. Furthermore, we demonstrate the versatility of the model by simulating a series of examples that exhibit complex three-dimensional, time-dependent photodeformation, including photoorigami, photoforming, and photobulge tests.

Shape memory polymers (SMPs) have gained strong research interests recently due to their mechanical action that exploits their capability to fix temporary shapes and recover their permanent shape in response to an environmental stimulus such as heat, electricity, irradiation, moisture or magnetic field, among others. Along with interests in conventional “dual-shape” SMPs that can recover from one temporary shape to the permanent shape, multi-shape SMPs that can fix more than one temporary shapes and recover sequentially from one temporary shape to another and eventually to the permanent shape, have started to attract increasing attention. Two approaches have been used to achieve multi-shape shape memory effects (m-SMEs). The first approach uses polymers with a wide thermal transition temperature whilst the second method employs multiple thermal transition temperatures, most notably, uses two distinct thermal transition temperatures to obtain triple-shape memory effects (t-SMEs). Recently, one of the authors’ group reported a triple-shape polymeric composite (TSPC), which is composed of an amorphous SMP matrix (epoxy), providing the system the rubber-glass transition to fix one temporary shape, and an interpenetrating crystallizable fiber network (PCL) providing the system the melt-crystal transition to fix the other temporary shape. A one-dimensional (1D) material model developed by the authors revealed the underlying shape memory mechanism of shape memory behaviors due to dual thermal transitions. In this paper, a three-dimension (3D) finite deformation thermomechanical constitutive model is presented to enable the simulations of t-SME under more complicated deformation conditions. Simple experiments, such as uniaxial tensions, thermal expansions and stress relaxation tests were carried out to identify parameters used in the model. Using an implemented user material subroutine (UMAT), the constitutive model successfully reproduced different types of shape memory behaviors exhibited in experiments designed for shape memory behaviors. Stress distribution analyses were performed to analyze the stress distribution during those different shape memory behaviors. The model was also able to simulate complicated applications, such as a twisted sheet and a folded stick, to demonstrate t-SME.

Design optimization for functionally graded battery electrodes is shown to improve the usable energy capacity of Li batteries predicted by computational simulations and numerically optimizing the electrode porosities and particle radii. A multi-scale battery model which accounts for nonlinear transient transport processes, electrochemical reactions, and mechanical deformations is used to predict the usable energy storage capacity of the battery over a range of discharge rates. A multi-objective formulation of the design problem is introduced to maximize the usable capacity over a range of discharge rates while limiting the mechanical stresses. The optimization problem is solved via a gradient based optimization. A LiMn 2 O 4 cathode is simulated with a PEO–LiCF 3 SO 3 electrolyte and both a Li Foil (half cell) and LiC 6 anode. Studies were performed on both half and full cell configurations resulting in distinctly different optimal electrode designs. The numerical results show that the highest rate discharge drives the simulations and the optimal designs are dominated by Li + transport rates. The results also suggest that spatially varying electrode porosities and active particle sizes provides an efficient approach to improve the power-to-energy density of Li + batteries. For the half cell configuration, the optimal design improves the discharge capacity by 29% while for the full cell the discharge capacity was improved 61% relative to an initial design with a uniform electrode structure. Most of the improvement in capacity was due to the spatially varying porosity, with up to 5% of the gains attributed to the particle radii design variables.

It was recently reported that thermally malleable polymers with bond exchange reactions (BERs) can rearrange their microscopic network topology without impairing the network integrity. Besides, two pieces of polymers were shown to be able to weld together upon heating without introducing additional monomers or chemicals on the interface, enabling thermoforming, self-healing, and reprocessing of the polymer, which has drawn significant interest in the study of this type of polymers. This new breakthrough also opens an avenue to recycle thermoset polymers that traditionally are very difficult to recycle. This paper experimentally studies the reprocessing and recycling ability of a thermoset polymer (an epoxy thermosetting network) with exchangeable bonds in a pulverous state. Due to the large surface area and small size of polymer particles, their handling, transportation, and storage can offer convenience in comparison with traditional polymer scrap in bulk form, which can advance their immediate industrial applications in thermoset recycling, structure rehabilitations and component rework. A detailed investigation was performed to study the effect of reprocessing conditions (such as time and pressure) on the material mechanical performance. The reprocessing routine was also repeated multiple times (representing multiple generations of recycling) to manufacture complex objects and to join two separate bulk polymers.

We present a general framework that digitally integrates the workflow for optimal design and fabrication of novel multiscale laminated fiber-based composites with spatially varying microstructure in each lamina of a flat or curved laminate. Given a design problem, our framework consists of three key components: 1) Design automation, 2) Material compilation, and 3) Digital fabrication. Design automation involves efficient simultaneous synthesis of optimal macroscale topology and spatially varying fibrous microstructure in a laminated composite, whereas digital fabrication comprises manufacture of the optimal structure. Material compilation is an intermediate process that translates the multiscale results of the design automation step to a digitally manufacturable arrangement of matrix and fibers within each layer of a laminate. These components constitute a digital thread and can be initialized by any method or process of choice. In this paper, we develop a multiscale topology optimization approach for design automation, new computational geometry algorithms for material compilation, and voxel-based material jetting for digital fabrication. We demonstrate and experimentally validate the extensive capabilities of our framework with various plate and shell structures that have potential applications in architecture, aerospace and soft robotics.

Active composites are a class of materials that have environmentally responsive components within them. One key advantage of active composites is that through mechanics design, a variety of actuation can be achieved. The development of active composites has been significantly enhanced in recent years by multimaterial 3D printing where different materials can be precisely placed in 3D space, enabling the achievement of shape-shifting of 3D printed parts, or 4D printing. In practical applications, it is highly desirable that the part shape can change in a pre-described manner, which requires the careful design of where to place different materials. However, designing an active composite structure to achieve a target shape change is challenging because it requires solving an inverse problem with spatially heterogenous, highly nonlinear (active) material behavior within a potentially complex boundary value problem. In this paper we present a machine learning approach to the design of active composite structures that can achieve target shape shifting responses. Our strategy is to combine the finite element method with an evolutionary algorithm. In order to achieve a target shape, we compose the structures of equally sized voxel units that are made of either a passive or an active material and optimize the distribution of these two material phases. The optimization method is tested against several illustrative examples in active composite design to show the agreement between the target shape and the best machine learning solution obtained.

We develop a thermodynamics and mechanics theory for polymers that when irradiated with light, undergo photochemical reactions that alter their macromolecular structure, e.g., by bond breaking and/or reformation, and in turn affect their mechanical and physical behavior. This emerging class of highly-engineered active materials shows great promise for myriad applications and is a subset of a broader class of polymers with covalent bonds that can be dynamically tuned with various environmental stimuli. We formulate a general thermodynamic and kinetic framework to model the complex photochemical–thermal–mechanical coupling in these materials. Our theory considers the behavior of a polymer that is subjected to the combination of mechanical and thermal loading while simultaneously irradiated by light with multiple frequency components and directions. We introduce an approach to model the photochemical reactions that can change the network topology, resulting chemical species transport, heat conduction and finite deformation. We describe the interaction of the material with light via a radiometric description and show how it can be linked to a full electromagnetic treatment when appropriate and if desired. Our approach is sufficiently general to permit the modeling of various materials that operate via different photochemical reaction mechanisms. After formulating the general theory, we specialize it to a polymer that when irradiated with light undergoes a series of photochemical reactions that cause chain scission and reformation which continuously rearrange the polymer network into a stress-free configuration. Based on the operant physical mechanisms we develop a constitutive model using a polymer chain decomposition and evolution approach to track the molecular structure changes during simultaneous irradiation and mechanical loading. In the special case of isothermal conditions with monochromatic and unidirectional irradiation, we recover a previous model based on intuitive ad-hoc assumptions and thus put it on strong thermodynamic footing. Finally we use our model to simulate the behavior of a polymer that is biaxially stretched and then irradiated with light from one side. We simulate the process and emphasize the spontaneous bending that occurs due to inhomogeneous photoinduced stress relaxation. From our theory, we obtain an analytical expression of a characteristic time for photo-induced stress relaxation in terms of the dominating system parameters.

Covalent adaptable network (CAN) polymers can rearrange their macromolecular network by bond exchange reactions (BERs), where an active unit attaches to and then replaces a unit in an existing bond and forms a new bond. When such macromolecular events occur on the interface, they can contribute to surface welding, self-healing, and recycling of thermosetting polymers. In this paper, we study the interfacial welding and failure of CANs involving both interfacial normal and shear stresses. To do this, we incorporate our recently developed multiscale model for surface welding of CANs with a cohesive zone modeling approach in finite-element method (FEM) simulation. The developed FEM paradigm involves a multiscale model predicting the interfacial chain density and fracture energy, which are transferred to a cohesive zone model to establish the surface traction-separation law. The simulations show good agreement with experimental results on the modulus and strength of welded samples. They also provide understanding of the interactions between surface welding and material malleability in determining the final mechanical properties of polymer structures. The developed FEM model can be applied to study other complex welding problems, such as polymer reprocessing with nonregular particle size and shape.

The creation of reversibly-actuating components that alter their shapes in a controllable manner in response to environmental stimuli is a grand challenge in active materials, structures, and robotics. Here we demonstrate a new reversible shape-changing component design concept enabled by 3D printing two stimuli responsive polymers—shape memory polymers and hydrogels—in prescribed 3D architectures. This approach uses the swelling of a hydrogel as the driving force for the shape change, and the temperature-dependent modulus of a shape memory polymer to regulate the time of such shape change. Controlling the temperature and aqueous environment allows switching between two stable configurations – the structures are relatively stiff and can carry load in each – without any mechanical loading and unloading. Specific shape changing scenarios, e.g., based on bending, or twisting in prescribed directions, are enabled via the controlled interplay between the active materials and the 3D printed architectures. The physical phenomena are complex and nonintuitive, and so to help understand the interplay of geometric, material, and environmental stimuli parameters we develop 3D nonlinear finite element models. Finally, we create several 2D and 3D shape changing components that demonstrate the role of key parameters and illustrate the broad application potential of the proposed approach.

Recent research using 3D printing to create active structures has added an exciting new dimension to 3D printing technology. After being printed, these active, often composite, materials can change their shape over time; this has been termed as 4D printing. In this paper, we demonstrate the design and manufacture of active composites that can take multiple shapes, depending on the environmental temperature. This is achieved by 3D printing layered composite structures with multiple families of shape memory polymer (SMP) fibers – digital SMPs - with different glass transition temperatures (Tg) to control the transformation of the structure. After a simple single-step thermomechanical programming process, the fiber families can be sequentially activated to bend when the temperature is increased. By tuning the volume fraction of the fibers, bending deformation can be controlled. We develop a theoretical model to predict the deformation behavior for better understanding the phenomena and aiding the design. We also design and print several flat 2D structures that can be programmed to fold and open themselves when subjected to heat. With the advantages of an easy fabrication process and the controllable multi-shape memory effect, the printed SMP composites have a great potential in 4D printing applications.

Bending rigidity and Gaussian bending stiffness are the two key parameters that govern the rippling of suspended graphene-an unavoidable phenomenon of two-dimensional materials when subject to a thermal or mechanical field. A reliable determination about these two parameters is of significance for both the design and the manipulation of graphene morphology for engineering applications. By combining the density functional theory calculations of energies of fullerenes and single wall carbon nanotubes with the configurational energy of membranes determined by Helfrich Hamiltonian, we have designed a theoretical approach to accurately determine the bending rigidity and Gaussian bending stiffness of single-layered graphene. The bending rigidity and Gaussian bending stiffness of single-layered graphene are 1.44 eV (2.31 × 10(-19) N m) and -1.52 eV (2.43 × 10(-19) N m), respectively. The bending rigidity is close to the experimental result. Interestingly, the bending stiffness of graphene is close to that of lipid bilayers of cells about 1-2 eV, which might mechanically justify biological applications of graphene.

SUMMARY The capacity of lithium ion batteries can be improved through the use of functionally graded electrodes. Here, we present a computational framework for optimizing the layout of electrodes using a multiscale lithium ion battery cell model. The model accounts for nonlinear transient transport processes and mechanical deformations at multiple scales. A key component of the optimization methodology is the formulation of the adjoint sensitivity equations of the multiscale battery model. The efficient solution of the adjoint equations relies on the decomposition of the multiscale problem into multiple, computationally small problems associated with the individual realizations of the microscale model. This decomposition method is shown to significantly reduce the computational time needed for sensitivity analysis versus numerical finite differencing. The potential of the proposed optimization framework is illustrated with numerical problems involving both macroscale and microscale performance criteria and design variables. The usable capacity of a lithium ion battery cell is maximized while limiting the stress level in the electrode particles through manipulation of the local porosities and particle radii. The optimization results suggest that optimal functionally graded electrodes improve the performance of a battery cell over using uniform porosity and particle radius distributions. Copyright © 2012 John Wiley & Sons, Ltd.