Nonlinear Stress-strain Response Research Articles

Contribution of geometrical infill pattern on mechanical behaviour of 3D manufactured polylactic acid specimen: Experimental and numerical analysis

Additive manufacturing is regarded as a very efficient fabrication technique since it permits the manufacturing of any three-dimensional product. The present work determines the effect of various infill pattern on the mechanical properties in term of tensile strength, yield strength and hardness of poly-lactic acid (PLA) samples fabricated by fused deposition modeling method. The mechanical behaviour of the 3D-printed PLAs investigated using dog-bone specimens with six distinct infill patterns: line, triangle, tri-hexagon, cubic, octet, and gyroid. The mechanical characteristics were evaluated using the uniaxial tensile test and shore D type hardness tester. The strain and deformation criteria were employed to substantiate the ductile and brittle characteristics. The fractural surface morphology analyzed using the field emission scanning electron microscope. Nonlinear Finite Element Analysis (FEA) was employed to simulate the uniaxial tensile test and establish a Yeoh third order hyperelastic material model for the predictions of the stress-strain response. This model is chosen for its precise ability to predict the nonlinear stress-strain responses for significant deformation and is crucial in applications that involve high degrees of flexibility and elasticity, such as in tire modeling, polymer and elastomer analysis, sports equipment designing, 3D printed components etc. Results revealed that the cubic infill had a maximum tensile strength 32.648 ± 1.42 MPa and octet infill had a minimum tensile strength 22.373 ± 0.79 MPa. The majority of experimental data indicated a brittle behaviour for line-infilled, but triangular, trihexagonal, cubic, octet, and gyroid infill patterns demonstrated ductile behaviour. In comparison to other geometrical infills, cubic shown relatively superior mechanical responses. Consequently, the geometrical infill effect plays a significant role in finding the appropriate mechanical property for industrial applications. The developed material model possesses potential utility in non-linear FEA investigations pertaining to 3D printed PLA objects that are predicted to sustain tensile strength.

A multiaxial thermo-mechanical damage model for concrete including Load Induced Thermal Strain (LITS)

In the current study, a multiaxial LITS model of concrete was innovatively developed. This model can predict the behavior of concrete subjected to wide applied load level ranges from 20 % to 80 % and temperatures up to 800 °C. A 3D LITS model is developed through a triaxial compression stress confinement implementation and Poisson's ratio. Considering the water evaporation of concrete under high temperature, a third order polynomial LITS derivative function and an exponential derivative function were proposed to characterize the effects of the stress confinement and thermal effect. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete is developed. The effect of LITS on the multiaxial stress-strain response was considered in the multiaxial model. The coupling thermo-mechanical contributions containing the development of LITS among thermal effect, stress confinement, damage and plastic hardening evolution were creatively considered in the potential function within thermodynamics framework. The numerical calculations of this proposed model were conducted for validation. The effect of LITS on the multiaxial stress-strain response was studied. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranges from 20 °C to 1000 °C through the comparative study with test results in literatures, which indicates the accuracy and applicability of the proposed model.

Giant mechanical energy storage capacity and long-term mechanical cyclability in a fine-grained Heusler-type Co51V33Ga16 shape memory alloy

Shape memory alloys can be exploited for the storage of mechanical energy by utilizing the stress-driven superelasticity. However, the intrinsic hysteresis and non-linear stress-strain response endowed by the first-order martensitic transformation cripple the efficient utilization and controllable release of stored energy. Here, we demonstrate an effective strategy to realize stable linear superelasticity with low hysteresis and giant mechanical energy storage capacity. By utilizing rapid solidification to engineering grain size and crystallographic orientation, a fine-grained Co51V33Ga16 alloy with weakly preferred orientation was synthesized through suction casting. Such microstructure enables large amounts of residual martensite to be trapped by mechanical training, yielding a rate-independent linear superelasticity in a wide temperature range from 290 K to 400 K. Moreover, under a maximum strain of 4.5 %, giant stored energy higher than 20.5 MJ m−3 and small dissipated energy lower than 0.5 MJ m−3 can be retained for more than 200,000 cycles of superelastic deformation, being superior to those in most shape memory alloys reported so far.

A 3D thermo-mechanical damage model for concrete including Short-Term Thermal Creep Strain (STTCS)

In the current study, a Short-Term Thermal Creep Strain (STTCS) model of concrete was innovatively developed. This model can predict the time-dependent deformation of concrete subjected to wide applied load level ranging from 20 % to 60 % and temperatures up to 900 °C. A creep compliance function was developed to study the nonlinear creep characteristics of concrete with creep parameters. The definition and sensitivity of the creep parameters were investigated. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete is developed. The influence of STTCS on the multiaxial stress-strain behaviors was taken into account in the multiaxial model. The coupling thermo-mechanical contributions containing the development of STTCS with thermal effect, stress confinement, plastic damage and hardening evolution were creatively considered in the potential function within thermodynamics framework. The sensitivity of yield surface was discussed. The numerical operations of this proposed model were conducted for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranging from 20 °C to 800 °C through the comparative study with test results in literatures, which indicates the accuracy and applicability of the proposed model.

Inverse design of functionally graded porous structures with target dynamic responses

Although functionally graded porous structures (FGPS) have been studied comprehensively due to their excellent mechanical and functional properties, the design process of FGPS with target stress response still dependent on continuous trial and error, which is not only time-consuming but also heavily relies on experience and intuition. This study proposes a novel inverse design framework of 2D FGPS with targeted dynamic stress-strain responses via a combination of conditional diffusion model and a residual neural network. Unlike traditional binary pixel representations, this approach utilizes nuclei position maps and color mapping technique to represent the structure configurations and cell wall thicknesses to improve the efficiency and performance of the model. Firstly, various functionally graded porous structures were constructed by employing Voronoi diagram techniques, and finite element simulations were conducted to calculate the nonlinear responses subjected to dynamic loadings. A dataset comprising 2100 FGPS and corresponding nonlinear stress-strain responses was established. Then, an inverse design framework is formulated by integrating a generator that uses a diffusion model to synthesize structures conditioned on specific target responses, with a predictor that employs a residual neural network to assess the responses of these structures. Finally, to demonstrate the effectiveness of the approach, the performance of the predictor and generator was thoroughly investigated. Structures with various target stress-strain responses were generated through the proposed method, and validated by finite element analysis. A detailed impact experiment was also carried out to verify the effectiveness of the proposed methods. The result shows that the framework can effectively generate new structures with objective nonlinear responses. This work offers a fast and efficient way to design FGPS that meet specific performance objectives.

A multiaxial multiscale compressive thermo-mechanical damage model for Fiber Reinforced Cementitious Composites (FRCC)

In the current study, a multiaxial multiscale compressive stress-strain model for Fiber Reinforced Cementitious Composites (FRCC) was innovatively developed. The proposed model was on the basis of the theory of thermodynamics, multiscale theory and internal variable theory. The free energy function and dissipation function were established to characterize the elastic and plastic deformation of FRCC, respectively. The multiscale behaviors of FRCC in meso-scale and macro-scale was taken into account. In meso-scale, the energy dissipation functions of fiber in tension and bond-slip deformation in the interface transition zone (ITZ) were established. The resistance to cracking of cementitious matrix through the fiber bond stress were taken into account. In macro-scale, the thermo-mechanical coupling contributions of plastic damage, thermal damage, yield surface and hardening evolution were creatively considered in the potential function within thermodynamics framework. The influence of types and volume fractions of fibers on the reinforcement mechanism was discussed. When the temperature is higher than the melting point of fiber, the fiber influence coefficients was employed. The sensitivity of yield surface was discussed. The numerical predictions of this developed model were carried out for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranges from 20 °C to 800 °C compared with the experimental data, which indicates the accuracy and applicability of the proposed model.

Design of non-linear, viscoelastic architected foams

Flexible viscoelastic foams with relative density in the range of 5-50% are widely used to control interaction forces, notably in cushions for impact protection, shoes, mechanical grippers, etc. The design of new foams to improve performance is challenging, due to the lack of efficient models to connect cellular architecture, viscoelasticity of the base resin, and non-linear responses that stem from large deformation of open pores. This paper presents highly efficient solutions for the response of linearly viscoelastic, kinematically non-linear and shear-deformable struts that are loaded at an oblique angle to their axis. The models can be used to predict structure-property relationships for strut-based metamaterials, including non-linear stress-strain response and accompanying hysteresis. To illustrate this, the entire design space of a simple unit cell is mapped in terms of a broad range of strut angles and thicknesses; the unit cell is inspired by features in stochastic foams that dominate their response. An enormous range of stress-strain responses can be obtained from this single foam-like cell, including purely softening, purely stiffening, and non-monotonic stiffness with adjustable tangent moduli. The model is also used to illustrate connections between viscoelastic material parameters, loading rate, and hysteresis for two distinct classifications of non-linear stress-strain response.

On the dynamic performance of additively manufactured visco-elastic meta-materials

Additive manufacturing (AM) has revolutionized the production of structures with tailored material properties, including elastomer polyurethanes (EPU) which exhibit exceptional mechanical performance. EPU possesses unique characteristics, such as high elongation at break, efficient energy dissipation, and superior specific strength, making it well-suited for applications requiring resilience to dynamic loadings. By combining the advantages of AM and EPU, enhanced and customized meta-materials can be created, surpassing the mechanical performance of traditional bulk materials. However, because of the non-linear stress–strain response of both the constitutive material and the structure, designing such meta-materials for high strain-rates can be challenging. In this work, therefore, quasi-static and dynamic experiments were conducted to evaluate a meta-material architecture. The investigation revealed a strong positive rate dependency. The mechanical performances, including strength, and dissipated energy, increased with increasing loading rate. The EPU meta-materials demonstrate their suitability for dynamic applications where high energy dissipation is crucial for reducing transmitted loads.

A strain rate and temperature dependent model for describing nonlinear unloading stress-strain response after warm and hot compression deformation

For an accurate numerical simulation of springback behavior and control of shape and dimensional accuracies of the manufacture component under warm and hot precision plastic forming, the use of an appropriate material model dependent with strain, strain rate and temperature describing the nonlinear unloading process is vital, which is remained to be developed. The thermo-mechanical coupling effect in difficult-to-form material deformed at elevated temperature makes the unloading process more complicated and thus more difficult to model. In this paper, by using face-centered cubic (FCC) aluminum alloys as case study materials, loading-unloading experiments with different strains and strain rates at warm and elevated temperatures of 300 – 500 °C were conducted, the effects and contributions of strain, strain rate and temperature on unloading chord modulus (elastic modulus) and nonlinear unloading stress-strain response were quantified. A unique strain-, strain rate- and temperature-dependent nonlinear unloading coupled model was established. By validating and applying the nonlinear unloading coupled model in the both monotonous loading-unloading and cyclic loading-unloading warm and hot compression deformation, the calculation results agree well with experimental results, indicating that the model can describe perfectly the nonlinear unloading stress-strain responds and springback behavior. From the discussion on calculated results and capabilities of model, it was found that the proposed unified equation incorporating strain rate and temperature is also able to be coupled with the existing strain-dependent chord modulus model such as modified Yoshida-Uemori (Y-U) model. The capability of predicting nonlinear unloading curves and springback strains of aluminum alloys deformed at various strains, strain rates, and temperatures demonstrates the potential applicability of the model to a wide range of warm and hot forming process conditions.

Hierarchical Mechanical Transduction of Precision-Engineered DNA Hydrogels with Sacrificial Bonds.

Engineering the response to external signals in mechanically switchable hydrogels is important to promote smart materials applications. However, comparably little attention has focused on embedded precision mechanisms for autonomous nonlinear response in mechanical profiles in hydrogels, and we lack understanding of how the behavior from the molecular scale transduces to the macroscale. Here, we design a nonlinear stress-strain response into hydrogels by engineering sacrificial DNA hairpin loops into model network hydrogels formed from star-shaped building blocks. We characterize the force-extension response of single DNA hairpins and are able to describe how the specific topology influences the nonlinear mechanical behavior at different length scales. For this purpose, we utilize force spectroscopy as well as microscopic and macroscopic deformation tests. This study contributes to a better understanding of designing nonlinear strain-adaptive features into hydrogel materials.

Parameterization-based neural network: predicting non-linear stress–strain response of composites

Parameterization-based neural network: predicting non-linear stress–strain response of composites

Softening of the Hertz indentation contact in nematic elastomers

Polydomain liquid crystalline (nematic) elastomers have highly unusual mechanical properties, dominated by the dramatically nonlinear stress–strain response that reflects stress-induced evolution of domain patterns. Here, we study the classical Hertz indentation problem in such a material. Experimentally, we find that polydomain nematic elastomers display a smaller exponent than the classical 3/2 in the load vs. indentation depth response. This is puzzling: asymptotically a softer stress–strain response requires a larger exponent at small loads. We resolve this by theory where three regimes are identified — an initial elastic regime for shallow indentation that is obscured in experiment, an intermediate regime where local domain pattern evolution leads to a smaller scaling in agreement with experiments, and a final stiffening regime where the completion of local domain evolution returns the response to elastic. This three-regime structure is universal, but the intermediate exponent is not. We discuss how our work supports a new mechanism of enhanced adhesion for pressure-sensitive adhesion of nematic elastomers.

Tailoring superelastic and transformation-induced plastic response of shape memory multilayers with wavy architectures

The finite-volume direct averaging micromechanics (FVDAM) has been extended to simulate the superelastic and plastic response of shape memory composites. The homogenized stress–strain response and local field variables generated with FVDAM were first validated vis-à-vis the exact solution under axisymmetric loading conditions. Furthermore, an in-house finite-element code was developed to assess the FVDAM theory’s accuracy for simulating wavy multilayers. Parametric studies were conducted to quantify the effect of microstructural parameters on the nonlinear response of multilayers. The common mechanism is responsible for the differences in the nonlinear stress–strain response of multilayers is rooted in the effective stress differences that alter the phase transformation.

Damage and Fracture Mechanics of Porcine Subcutaneous Tissue Under Tensile Loading.

Subcutaneous injection, which is a preferred delivery method for many drugs, causes deformation, damage, and fracture of the subcutaneous tissue. Yet, experimental data and constitutive modeling of these dissipation mechanisms in subcutaneous tissue remain limited. Here we show that subcutaneous tissue from the belly and breast anatomical regions in the swine show nonlinear stress-strain response with the characteristic J-shaped behavior of collagenous tissue. Additionally, subcutaneous tissue experiences damage, defined as a decrease in the strain energy capacity, as a function of the previously experienced maximum deformation. The elastic and damage response of the tissue are accurately described by a microstructure-driven constitutive model that relies on the convolution of a neo-Hookean material of individual fibers with a fiber orientation distribution and a fiber recruitment distribution. The model fit revealed that subcutaneous tissue can be treated as initially isotropic, and that changes in the fiber recruitment distribution with loading are enough to explain the dissipation of energy due to damage. When tested until failure, subcutaneous tissue that has undergone damage fails at the same peak stress as virgin samples, but at a much larger stretch, overall increasing the tissue toughness. Together with a finite element implementation, these data and constitutive model may enable improved drug delivery strategies and other applications for which subcutaneous tissue biomechanics are relevant.

A computational building block approach towards multiscale architected materials analysis and design with application to hierarchical metal metamaterials

In this study we report a computational approach towards multiscale architected materials analysis and design. A particular challenge in modeling and simulation of materials, and especially the development of hierarchical design approaches, has been to identify ways by which complex multi-level material structures can be effectively modeled. One way to achieve this is to use coarse-graining approaches, where physical relationships can be effectively described with reduced dimensionality. In this paper we report an integrated deep neural network architecture that first learns coarse-grained representations of complex hierarchical microstructure data via a discrete variational autoencoder and then utilizes an attention-based diffusion model solve both forward and inverse problems, including a capacity to solve degenerate design problems. As an application, we demonstrate the method in the analysis and design of hierarchical highly porous metamaterials within the context of nonlinear stress–strain responses to compressive deformation. We validate the mechanical behavior and mechanisms of deformation using embedded-atom molecular dynamics simulations carried out for copper and nickel, showing good agreement with the design objectives.

A discrete element analysis for general failure behavior of basalt

Discrete element method is a commonly used numerical method in rock mechanics and rock engineering. In this research, the flat-joint contact bond model is used to reproduce the macro-properties of basalt on an assembly of particles. A series of laboratory tests, including uniaxial compression test, Brazilian tension test, and fracture toughness test are used to simulate progressive degradation of rock mass strength in a size-independent model with a unique set of micro-properties. The work involves a detailed analysis for estimating compressive elastic modulus, Poisson's ratio, bimodularity, mode I fracture toughness, crack closure, crack initiation, and crack damage thresholds, as well as the tensile and compressive strengths. The constructed flat-jointed material yields a realistic uniaxial compression to tensile strength ratio and nonlinear stress-strain response through sustaining adequate particle interlocking and embedded pre-existing microcracks. The role of sample size on the compressive elastic modulus, crack initiation and crack damage stress limits is demonstrated in detail. A model size-independency analysis was also performed to examine the effect of particle size on the results. The numerical results presented in this study are within 10% of the laboratory results.

An enhanced data-driven constitutive model for predicting strain-rate and temperature dependent mechanical response of elastoplastic materials

Data-driven and machine-learning based approaches provide a highly compatible and efficient fundamentals for the mechanical constitutive modeling of engineering materials. In this work, an enhanced data-driven constitutive model is developed to predict the stress–strain relationship of an elastoplastic material through the integration of a data-driven concept with fundamental plasticity theory. A novel strain reconfiguration strategy is proposed to improve the learning capability and predictability of the data-driven model, along with a two-step training method. A compatible numerical implementation algorithm is developed to incorporate the data-driven approach into a finite element calculation. This developed data-driven constitutive model is applied to learn and predict the mechanical response of Ti-6Al-4V titanium alloy under multiple loading conditions, including five different loading rates, four different temperatures, and thirteen different stress states. The excellent correlation with the experimental results demonstrates the high accuracy and generality of the presented approach, especially its capability for predicting unknown nonlinear stress–strain response. The presented theory reveals the great potential of employing such a data-driven approach in computational mechanics.

3D Printing of Poly‐ε‐Caprolactone (PCL) Auxetic Implants with Advanced Performance for Large Volume Soft Tissue Engineering

AbstractA successful 3D printing of a novel 3D architected auxetic for large‐volume soft tissue engineering is reported. The 3D auxetic design is analyzed through finite element (FE) simulation and created by selective laser sintering (SLS) of Poly‐ε‐caprolactone (PCL) for further in‐depth mechanical and biological analysis. High initial flexibility and nonlinear stress–strain response to the uniaxial compression are achieved despite the use of PCL, which is one of the biomaterials that is clinically approved but has the disadvantage of having relatively stiff and linear mechanical properties. The high mass transport properties of the 3D auxetic are also demonstrated by not only high cell viability but also cell functionality within a cell‐laden hydrogel in large sizes of the auxetic. The outstanding mechanical and biological performance of the 3D auxetic is a consequence of the synergistic effect of the novel architected auxetic design combined with the inherent printing characteristic of SLS. The current study demonstrates great potential of SLS‐based printing of 3D auxetics toward the development of clinically viable 3D implants for the reconstruction of large‐volume soft tissues.

Off-Axis Tension Behaviour of Unidirectional PEEK/AS4 Thermoplastic Composites

An experimental method for non-standard off-axis tension tests of unidirectional composites is developed. A new oblique end-tab is designed to eliminate stress concentration and in-plane bending moment induced by off-axis tension loading. Finite element analysis and experiments on Polyetheretherketone (PEEK)/AS4 unidirectional thermoplastic composites (CFRTP) were conducted to evaluate the effectiveness of the proposed testing method. Simulation and test results demonstrate that the use of oblique end-tabs eradicates stress concentration and bending movements. The digital image correlation (DIC) method was used to help investigate the full-field tension/shear coupling deformation response of the off-axis specimen. Test results show significant nonlinear behaviour and inhomogeneous strain distribution under tension/shear combined stresses. A fractographic study was carried out to study the damage mechanisms under a tension/shear combined stress state. Specimens with 30°, 45° and 60° off-axis angles, fail in tension/shear mixed failure mode. Fracture surface morphology indicates that matrix plastic deformation and ductile drawing under tension/shear coupled stress state induced the nonlinear stress-strain response.

Mass-producible near-body temperature-triggered 4D printed shape memory biocomposites and their application in biomimetic intestinal stents

Despite the burgeoning interest in manufacturing highly complex and dynamically reconfigurable implants using the 4D printing technique, one of the most critical challenges is to develop near-body temperature (NBT)-triggered 4D printing materials in a facile and scale-up manner. The currently reported 4D printed biomaterials for implants have inappropriate transition temperatures or are limited to demonstration production of small amounts of materials in the laboratory. Here, 4D printed shape memory biocomposites with controllable transition temperature were developed through facile manufacturing technology, and the shape memory process of triggering printed constructs under NBT was realized. Customized, reconfigurable, biodegradable, and biocompatible 4D printed biomimetic intestinal stents were developed using NBT-triggered biocomposites, filling the blank of 4D printed intestinal stents. The 4D printed biomimetic intestinal stents were designed based on wavy biomimetic networks that can mimic the nonlinear stress-strain response of biological tissues, demonstrating high flexibility and facilitating reduced irritation of the intestinal wall. More importantly, the biodegradability of the 4D printed biomimetic intestinal stent can avoid the secondary endoscope removal required by the metal intestinal stent. This work not only offers an efficient and facile methodology to fabricate NBT-triggered 4D printing shape memory biocomposites but also demonstrates the attractive application potential of 4D printed intestinal stents in next-generation intelligent implants.