Desired Stiffness Research Articles

Energy Dissipation and Toughening of Covalent Networks via a Sacrificial Conformation Approach.

Covalent polymer networks find wide utility in diverse engineering applications owing to their desirable stiffness and resilience. However, the rigid covalent chemical structure between crosslinking points imposes limitations on enhancing their toughness. Although the incorporation of sacrificial chemical bonds has shown promise in improving toughness through energy dissipation, composite networks struggle to maintain both rapid recovery and stiffness. Consequently, a significant challenge persists in achieving a covalent network that combines high strength, stiffness, toughness, and fast recovery performance. To address this challenge, we propose a novel sacrificial structure termed "sacrificial conformation." In this approach, β-cyclodextrin is covalently embedded into the network skeleton as the sacrificial conformation element. Compared to traditional covalent networks (LCN), well-designed cyclodextrin-embedded covalent network (CCN) exhibit a 100-fold increase in Young's modulus and a 60-fold increase in toughness. Importantly, CCN maintains excellent elasticity, ensuring swift recovery after deformation. This sacrificial conformational strategy enables efficient energy dissipation without necessitating the rupture of chemical bonds, thereby overcoming the limitations of traditional approaches. This advancement holds great promise for the design and fabrication of advanced elastomers and hydrogels with superior mechanical properties and dynamic behavior.

Energy Dissipation and Toughening of Covalent Networks via a Sacrificial Conformation Approach

Covalent polymer networks find wide utility in diverse engineering applications owing to their desirable stiffness and resilience. However, the rigid covalent chemical structure between crosslinking points imposes limitations on enhancing their toughness. Although the incorporation of sacrificial chemical bonds has shown promise in improving toughness through energy dissipation, composite networks struggle to maintain both rapid recovery and stiffness. Consequently, a significant challenge persists in achieving a covalent network that combines high strength, stiffness, toughness, and fast recovery performance. To address this challenge, we propose a novel sacrificial structure termed "sacrificial conformation." In this approach, β‐cyclodextrin is covalently embedded into the network skeleton as the sacrificial conformation element. Compared to traditional covalent networks (LCN), well‐designed cyclodextrin‐embedded covalent network (CCN) exhibit a 100‐fold increase in Young's modulus and a 60‐fold increase in toughness. Importantly, CCN maintains excellent elasticity, ensuring swift recovery after deformation. This sacrificial conformational strategy enables efficient energy dissipation without necessitating the rupture of chemical bonds, thereby overcoming the limitations of traditional approaches. This advancement holds great promise for the design and fabrication of advanced elastomers and hydrogels with superior mechanical properties and dynamic behavior.

Poly(vinyl alcohol)/graphene nanoplatelet nanocomposites: Elucidation of the nanofiller, dispersing agent, and interphase effects on thermomechanical properties

AbstractPoly(vinyl alcohol) (PVA)/graphene nanoplatelet (GnP) nanocomposite films were fabricated by a solution casting method. High loadings (30–40 wt.%) of two GnP grades, that is, xGnP C300 (low surface area/large size) and C750 (high surface area/small size), were utilized in combination with three commercial dispersing agents, that is, DISPERBYK‐161, DISPERBYK‐162 TF, and DISPERBYK‐2014, to yield films with desirable stiffness and energy dissipation characteristics (dynamic mechanical analysis, DMA), as well as thermal properties (thermogravimetric analysis, TGA) for potential impact resistance applications. The addition of GnPs and dispersing agents to PVA leads to a maximum six‐fold increase in its Young's modulus for the PVA sample containing 40 wt.% C300 GnPs and DISPERBYK‐162 TF. However, the modulus of resilience drops dramatically for the same sample (about 18‐fold decrease), as expected. Also, C300 GnPs yield nanocomposites with higher Young's moduli that those obtained using C750 GnPs. The atomic force microscopy stiffness maps illustrate that C300 GnPs disperse better in the PVA matrix. Furthermore, the average interphase thickness in the PVA‐C300 nanocomposites (~300 nm) is almost double that of PVA‐C750 nanocomposites. Based on the TGA results, the addition of GnPs and dispersing agent to the PVA matrix leads to a moderate increase (an average of 3.5%) in the value of the neat PVA, while its char yield increases by an average 8.5‐fold. Specifically, the PVA/GnP nanocomposites containing DISPERBYK‐162 TF yield the largest and char yield values than the other systems. The insights gained in this work can guide the design of coatings for impact resistance applications.

410 Improving Patient Outcomes through Design of Biodegradable Implants for Long Bone Fractures

OBJECTIVES/GOALS: Current long bone fracture standard of care uses inert metal intramedullary nails (IMN), 10x stiffer than femur cortex. Consequent “stress-shielding” bone loss sees >5% of patients needing revision surgery. To improve nonunion healing, we develop automated design optimization methods for biodegradable Mg alloy IMNs to control local reloading. METHODS/STUDY POPULATION: Finite element analysis (FEA) is performed on 3D bone-IMN representations to establish this study’s baseline strain states for existing inert IMN geometries within QCT-informed femoral models under simulated biomechanical loading. FEA with Mg alloy properties for same IMN designs simulate transient IMN material loss through discrete time-step models with experimental in vivo Mg corrosion rates and strain-based bone density evolution using remodeling algorithms from literature. Transient stability and strength metrics, fracture zone stress profiles under gradual reloading and manufacturing constraints are formulated through gradient-based sensitivity analysis into a topology optimization framework (TOF) incorporating a reaction-diffusion degradation model to generate IMN topologies. RESULTS/ANTICIPATED RESULTS: TOF designs for Mg alloy IMNs with transient allowable strength constraints, using safety factors to prevent IMN failure, demonstrate higher compliance than standard inert IMNs with mechanical properties closer to native cortical bone. The biodegradation model within the TOF, informed by corrosion behavior from bone-IMN FEA study, predicts how potential design evolutions affect transient strain states of the system. Thus, local fracture region stress states are controlled by the algorithm optimizing for desirable transient stiffness profiles based on a minimum variance objective of fracture zone stress compared to a target bone stress profile. Optimized IMNs with porous, high surface area features achieve 50% decrease in IMN stiffness over 6 months recovery time and complete in vivo degradation in 24 months. DISCUSSION/SIGNIFICANCE: Our TOF reduces “stress-shielding” effects via design for controlled IMN biodegradation to gradually increase fracture zone loading, stimulating remodeling and reducing current risk of post-operative fracture and surgical removal in ~15k cases/yr. in the U.S. In vitro mechanical and in vivo clinical testing is required to validate design results.

Characterisation of Bio composites for Bio-Manufacturing: Jute-reinforced Bacterial Cellulose for Construction

This research investigates the biological, mechanical and thermal characterisation of the jute-reinforced bacterial cellulose biocomposites to forecast their potential and performance in bio-manufacturing for architectural construction. The experimental trial-and-error-based methodology involves seven stages: Material formulation, manufacturing of biocomposite samples, mechanical testing, scanning electron microscopy analysis, thermogravimetric analysis, and biodegradation assessment. The results indicated that the use of biobased construction materials has a potential to reduce carbon footprint, while the addition of jute fibres resulted in enhanced mechanical properties such as higher elasticity and desirable stiffness compared to pure bacterial cellulose. Moreover, slight distinctions in thermal property analysis and biodegradation assessments across the specimens are observed. The findings contribute valuable data for material selection, design optimization, and structural considerations in the integration of these biopolymers into construction practices. Overall, this research aligns with the broader objective of advancing ecological construction starting from the material formulations, thus addressing the scalability of these materials, considering their potential for large-scale adoption in the construction industry.

Seismic effect of steel bracing systems in RC frame models

A bracing system is a common type of construction used in multi-storyed buildings for strengthening the structure. This type of technique may be used for retrofitting of existing building. Steel braced frame is used to resist earthquake loads in multistoried buildings. Steel bracing systems are affordable, simple to install, take up less space and may be designed in a variety of ways to achieve the desired strength and stiffness. In this study, three different heights of building model were considered to analyze the effect of bracing systems. For the study, each model is considered to be different bracing system viz. X-bracing, diagonal bracing, inverted V-bracing, eccentric bracing. The bracing is provided for peripheral columns of each model. Using STAAD Pro software, the building models were analyzed for seismic zone IV according to IS 1893: 2002. According to the results, the X type of steel bracing significantly increases structural rigidity and reduces the maximum interstorey drift of the frames. Global and story drifts are used to analyze the building's performance.

Physical learning of stiffness tensors by self-activated solids

Unlike plastic deformations, elastic deformations usually cannot change mechanical properties of materials under different loading conditions. In this talk, we suggest a class of self-activated solids and derive a local learning rule so that the solid can learn the desired stiffness tensors through repeated elastic deformations it experienced. The local learning rule is inspired by contrastive Hebbian learning, which guides the learning process by modulating the bond stiffness of the solid based on its local stain. Extensive numerical tests are performed to validate the design and learning rule. We show that the self-activated solid can be physically trained to display the desired bulk, shear, and coupling moduli and to manifest uni-mode and bi-mode materials. The solid can also realize time-varying moduli to function as time-modulated materials. The material design and learning strategy introduced are scalable and applicable to arbitrary lattice geometries and other discrete material systems. The study could lead to new physical learning systems, beneficial to autonomous materials, machines, and robots.

Optimization of Gelatin Methacryloyl Hydrogel Properties through an Artificial Neural Network Model.

Gelatin methacryloyl (GelMA) hydrogels are promising materials for tissue engineering applications due to their biocompatibility and tunable properties. However, the time-consuming process of preparing GelMA hydrogels with desirable properties for specific biomedical applications limits their clinical use. Visible-light-induced cross-linking is a well-known method for the preparation of GelMA hydrogels; however, a comprehensive investigation on the influence of critical parameters such as Eosin Y (EY), triethanolamine (TEA), and N-vinyl-2-pyrrolidone (NVP) concentrations on the stiffness and gelation time has yet to be performed. In this study, we systematically investigated the effect of these critical parameters on the stiffness and gelation time of GelMA hydrogels. We developed an artificial neural network (ANN) model with three input variables, EY, TEA, and NVP concentrations, and two output variables, Young's modulus and gelation time, derived from our experimental design. Through the alteration of individual chemical concentrations, [EY] between 0.005 and 0.5 mM and [TEA] and [NVP] between 10 and 1000 mM, we studied the impact of these alterations on the real-time values of stiffness and gelation time. Furthermore, we demonstrated the validity of the ANN model in predicting the properties of GelMA hydrogels. We also studied cell survival to establish nontoxic concentration ranges for each component, enabling safer use of GelMA hydrogels in relevant biomedical applications. Our results showed that the ANN model can accurately predict the properties of GelMA hydrogels, allowing for the synthesis of hydrogels with desirable stiffness for various biomedical applications. In conclusion, our study provides a comprehensive library that characterizes the stiffness and gelation time and demonstrates the potential of the ANN model to predict these properties of GelMA hydrogels depending on the critical parameters. The ANN models developed here can facilitate the optimization of GelMA hydrogels with the most efficient mechanical properties that resemble a native extracellular matrix and better address the need in the in vivo microenvironment. The approach of this study is to bring research about the synthesis of GelMA hydrogels to a new level where the synthesis of these hydrogels can be standardized with minimum cost and effort.

Modelling and continuous stiffness control of robot with compliant wrist for misalignment shaft-hole assembly

In this paper, a continuously variable stiffness control strategy for shaft-hole assembly with a compliant wrist is proposed. The compliant wrist adjusts stiffness by changing the cantilever length of a super-elastic Ni-Ti wire. Its core idea is that when the contact force of the robot exceeds a particular value, the wrist adjusts the stiffness and can deform in a specific direction that guarantees assembly, allows a relatively significant misalignment, and produces a small force. The advantage of the proposed strategy is that the shaft-hole assembly status is supervised by calculating the deformation of compliant wrist based on contact force information, this significantly decrease the requirements of shaft-hole alignment accuracy. On this basis, the kinetostatic coupling kinematic and static force model is built and the fuzzy PD stiffness control strategy is designed to realize the desired stiffness of the wrist in various directions. Finally, the shaft-hole assembly experiments under different misalignment error demonstrates the reliability of the wrist, indicating the efficacy of the control method.

Microstructure evolution and mechanical properties of a cast and heat-treated Al–Li–Cu–Mg alloy: Effect of cooling rate during casting

As a kind of cast aluminum alloy with high strength, Al–Li–Cu–Mg series alloys exhibit desirable stiffness and formability, while a limited investigation has discussed the influence of cooling rate on microstructure and mechanical properties of these alloys. In this work, the effect of cooling rate during casting on microstructure evolution and mechanical properties of cast Al–2Li–2Cu-0.5Mg-0.15Sc-0.1Zr-0.1Ti alloy was investigated using a step-like iron mold. The results showed that the increased cooling rate refined the grain size and augmented the volume fraction of second phase in the as-cast microstructure. In the aging process, the rapid cooling rate markedly promotes precipitation and suppresses coarsening of the δˊ(Al3Li), T1(Al2CuLi) and Sˊ(Al2CuMg) phases, which plays a vital role in enhancing strength of the peak-aged alloy. In addition to diffusion and vacancy mechanisms, a Li-rich zone offers a new precipitation pathway for T1 precipitates. Notably, the rapid cooling rate of 16.1 °C/s significantly facilitated the formation and inhomogeneous distribution of the cubic σ(Al6Cu5Mg2) phase, which competed with the T1 and Sˊ phases for Cu and Mg atoms. Finally, the formation mechanism of the σ phase under different cooling rates was discussed, and the strengthening and fracture mechanisms were quantified. The present work is expected to enlighten the understanding of the microstructure evolution of Al–Li alloys with varied cast cooling rates.

Seismic Behaviour of Multistorey Steel Framed Tall Buildings Using Intentionally Eccentric Braces

Braces with intentional eccentricity (BIE) are recently proposed to improve the seismic behaviour of conventional buckling braces (CBBs) by inserting intentional eccentricity along the brace length. Due to this eccentricity and the resultant bending moment, the BIE bends uniformly from small storey drifts and moves smoothly into the postbuckling behaviour under compression and sustains trilinear behaviour under tension. This behaviour delays the appearance of midlength local buckling which causes unstable energy dissipation. BIEs have a desirable postyielding stiffness which results in stable energy dissipation during cyclic loading and are capable of dissipating energy during low-intensity earthquakes. The seismic behaviour of structures with BIEs for use in buildings has not yet been investigated, specifically in tall buildings. Therefore, this study concentrates on investigating the seismic behaviour of tall buildings equipped with BIEs that uses a 3-dimensional (3D) finite element model in ETABS. In the first step, a 20-storey structure is designed using both eccentric brace frame (EBF) and BIE system and their seismic performance under the TABAS earthquake record is compared. In the second step, the seismic performance of a 25-storey irregular structure is assessed to evaluate the efficiency of the BIE system in irregular structures. Results show the desirable performance and energy dissipation capacity of the BIE system but it also shows large out-of-plane deformation in some cases.

Prescribing Cartesian Stiffness of Soft Robots by Co-Optimization of Shape and Segment-Level Stiffness.

Soft robots aim to revolutionize how robotic systems interact with the environment thanks to their inherent compliance. Some of these systems are even able to modulate their physical softness. However, simply equipping a robot with softness will not generate intelligent behaviors. Indeed, most interaction tasks require careful specification of the compliance at the interaction point; some directions must be soft and others firm (e.g., while drawing, entering a hole, tracing a surface, assembling components). On the contrary, without careful planning, the preferential directions of deformation of a soft robot are not aligned with the task. With this work, we propose a strategy to prescribe variations of the physical stiffness and the robot's posture so to implement a desired Cartesian stiffness and location of the contact point. We validate the algorithm in simulation and with experiments. To perform the latter, we also present a new tendon-driven soft manipulator, equipped with variable-stiffness segments and proprioceptive sensing and capable to move in three dimensional. We show that, combining the intelligent hardware with the proposed algorithm, we can obtain the desired stiffness at the end-effector over the workspace.

Additive manufacturing of silicone composite structures with continuous carbon fiber reinforcement

AbstractAs a relatively new material deployed in additive manufacturing (AM), silicone and its composites have the potential to realize tunable functionality and heterogeneous, architected properties for a number of applications requiring low modulus, elastic materials. Continuous fiber reinforced composites have been developed for AM to achieve various complex structures that are lightweight with high mechanical properties. AM of silicone‐based composites with direct ink writing (DIW) technology has potential application in medical devices, gasket components, flexible soft electronics, and food packaging. However, DIW printed materials have mechanical anisotropy since the extrusion‐based printing process creates small changes in geometry during the material deposition process. In addition, silicone elastomers are relatively low modulus in tension and can be reinforced with woven cloth or fibers. In this work, a continuous fiber AM machine is developed to manufacture silicone composite structures with continuous fiber reinforcing the printed silicone. Tensile tests show that the anisotropic property of the perpendicular printed specimens, relative to the tension direction, has been significantly improved by continuous carbon fiber reinforcements. This continuous fiber silicone reinforcement printing technique can be applied to tune fiber volume ratios and orientations for different silicone composite structures to meet the desired strength and stiffness.

Computer-Aided Design of A-Trail Routed Wireframe DNA Nanostructures with Square Lattice Edges.

In recent years, interest in wireframe DNA origami has increased, with different designs, software, and applications emerging at a fast pace. It is now possible to design a wide variety of shapes by starting with a 2D or 3D mesh and using different scaffold routing strategies. The design choices of the edges in wireframe structures can be important in some applications and have already been shown to influence the interactions between nanostructures and cells. In this work, we increase the alternatives for the design of A-trail routed wireframe DNA structures by using four-helix bundles (4HB). Our approach is based on the incorporation of additional helices to the edges of the wireframe structure to create a 4HB on a square lattice. We first developed the software for the design of these structures, followed by a demonstration of the successful design and folding of a library of structures, and then, finally, we investigated the higher mechanical rigidity of the reinforced structures. In addition, the routing of the scaffold allows us to easily incorporate these reinforced edges together with more flexible, single helix edges, thereby allowing the user to customize the desired stiffness of the structure. We demonstrated the successful folding of this type of hybrid structure and the different stiffnesses of the different parts of the nanostructures using a combination of computational and experimental techniques.

A Curved Compliant Differential Mechanism With Neutral Stability

AbstractDifferential mechanisms are remarkable mechanical elements that are widely utilized in various systems; nevertheless, conventional differential mechanisms are heavy and difficult to use in applications with limited design space. This paper presents a curved differential mechanism that utilizes a lightweight, compliant structure. This mechanism acquires its differential characteristic by having a high rotational stiffness when the mechanism is symmetrically actuated on two sides, while having a low rotational stiffness when actuated only on one side. To make the mechanism neutrally stable, the intrinsic elastic strain energy required for deformation of the compliant differential is compensated for by the reintroduction of potential energy, which is provided by two preloaded springs. The rotational stiffness of the one-sided actuation of the compliant differential mechanism around the neutral position is hypothesized to be adjustable by changing the preload of the springs. The stiffness can be positive, zero, or negative, indicating that the mechanism can be neutral or bistable. This hypothesis is investigated using a simulated model in Ansys Parametric Design Language (APDL) using optimized parameters to achieve the desired stiffness for the mechanism. The simulated model is validated using an experimental setup for both the one-sided and symmetrical actuation stages. The experimental results showed a high correlation with the simulation results. The mechanism with optimized dimensions and preload demonstrated neutral stability over a 16deg range. Bistability was discovered for preloads greater than the optimized preload. At θ = 0, a linear relationship was discovered between the spring preload and the rotational stiffness of the mechanism. Furthermore, an output/input kinematic performance of 0.97 was found for the simulated results and 0.95 for the experimental results.

Design Optimization of a Variable Stiffness Actuator for Knee Exoskeleton Application

The field of wearable devices and exoskeletons for rehabilitation and assistance is one of the main fields where variable stiffness actuators (VSAs) are continuously incorporated. This is due to the need for such devices to adapt to erratic environments and mimic human motions. Recently, a passive revolute joint design with controllable variable stiffness was proposed by the authors. However, the previous design was only introduced as a proof of concept, with no further investigation of the design stiffness change capabilities for application utilization. In this work, we introduce an extended analysis and comprehensive parametric study of the system’s main design parameters. Based on the performed analysis, we propose an optimization framework for this design concept that allows implementation in knee exoskeletons. The main design parameters that affect the stiffness performance are defined. The proposed method allows the identification of these design parameters, which enables the redesign of the system according to the predefined user requirements, such as size, desired stiffness range, and stiffness change rate. A bench-top experimental setup is constructed to validate the obtained optimal design parameters. Results show the ability to achieve the desired stiffness performance for the intended application.

Perturbation-Based Stiffness Inference in Variable Impedance Control

One of the major challenges in learning from demonstration is to teach the robot a wider set of task features than the plain trajectories to be followed. In this sense, one key parameter is stiffness, i.e., the rigidity that the manipulator should exhibit when performing a task. The required robot stiffness is often not known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> and varies along the execution of the task, thus its profile needs to be inferred from the demonstrations. In this work, we propose a novel, force-based algorithm for inferring time-varying stiffness profiles, leveraging the relationship between stiffness and tracking error, and involving human-robot interaction. We begin by gathering a set of demonstrations with kinesthetic teaching. Then, the robot executes a perturbed reference, obtained from these demonstrations by means of Gaussian process regression, and the human intervenes if the perturbation makes the manipulator deviate from its expected behaviour. Human intervention is measured and used to infer the desired control stiffness. In the experiments section, we show that our algorithm can be combined with different types of force sensors, and provide suitable processing algorithms. Our approach correctly infers the stiffness profiles from the force and electromyography sensors, their combination permitting also to comply with the physical constraints imposed by the environment. This is demonstrated in three experiments of increasing complexity: a motion in free Cartesian space, a rigid assembly task, and bed-making.

Influence of Biaxial Geogrid at the Ballast Interface for Granular Earth Railway Embankment

The development of reinforcements for soil has made an impact in most of the civil engineering sectors especially transportation. The use of geogrids is frequent in roadways but they are also finding use in railways. The major impact that geogrids could have is providing desired stiffness to a section by reducing material and serving as a proper reinforcement material. In the current study, an attempt has been made to redesign the railway embankment economically with the help of geogrids. Biaxial geogrid is used to substitute the blanket layer (thickness up to 100 cm) in the railway embankment by fulfilling the strain modulus requirement of the embankment, calculated using a plate bearing test as per DIN 18134. The experiment is performed on the embankment replicated in a metallic test chamber with granular soil as subgrade and geogrid is placed beneath the ballast. The experimental study is validated by a 3-D numerical model using Midas GTS NX software. The experimental analysis shows an improvement of 31.47% in the second modulus of the earth embankment. For the implementation of this study, a design section of Indian railways is adopted. With the help of geogrid, a reduction of 50% is observed in the embankment height, thereby reducing the overall costs.

Effectiveness of cellulose and chitosan nanomaterial coatings with essential oil on postharvest strawberry quality

Polysaccharide materials, including bagasse cellulose nanocrystals (BCNCs), chitosan nanofibers (ChNFs), and sodium alginate (SA), were blended with oregano essential oil (OEO) to make single- and multi-polysaccharide edible coating suspensions. The prepared suspensions were spray-coated on strawberry surface to form thin films with thickness varying from about 570 to 790 nm for single-polysaccharide coatings and 690–930 nm for multi-polysaccharide coatings. The coatings made with multi-polysaccharide were more effective in inhibiting fungal growth compared with single-polysaccharide coatings. Strawberry treated with SA/BCNC/ChNF/OEO formulation had only 10.8 % weight loss after nine days of storage. In contrast, uncoated and single-polysaccharide coated strawberries had >37.0 % and 28.6 % weight loss, respectively. In addition, the SA/BCNC/ChNF/OEO coating retained desired moisture, respiration rate, stiffness, firmness, and appearance properties of strawberry due to its gas barrier properties resulting from the entangled matrix structure. These results suggest that the multi-polysaccharide suspensions with OEO have a high potential for application as edible coatings for retarding senescence of strawberries.

Synergistically program thermal expansional and mechanical performances in 3D metamaterials: Design-Architecture-Performance

Metamaterials, incorporating specific micro-architectures, could be purposely customized to export the programmability in both thermal expansional and mechanical performances, which are beneficial to obtain the thermal and structural stabilities in engineering devices. Here, by focusing on developing an original design strategy, multiple classes of metamaterials were devised and analyzed to integrate the programmable coefficient of thermal expansion (CTE) and mechanical performances (relative density, stiffness and strength). In detail, firstly, a series of the bi-material metaunits was devised, and a vector analysis method was proposed to analytically identify the CTE tensors. Then, an original design strategy, i.e., matrix transformation method, was developed to systematically devise multiple classes of 3D metamaterials with the unidirectional, transversal isotropic and isotropic CTEs. Besides, the mechanical performances, including the relative density, stiffness and strength, were theoretically established. It was identified that these metamaterials well balanced the directionality and programmability of the CTEs. Most importantly, by modulating the geometrical parameters, the desirable CTEs, light weight, high stiffness and strength could be synergistically achieved in these metamaterials. Eventually, a principle was established to guide the development of metamaterials. That was the original design strategy acted as the underlying foundation to map the specific architectures in metamaterials, correspondingly, to build the ability to synergistically program or customize the thermal expansional and mechanical performances.