Nonlinear Stress-strain Response Research Articles

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.

Designing Hierarchical Soft Network Materials with Developable Lattice Nodes for High Stretchability.

Soft network materials (SNMs) represent one of the best candidates for the substrates and the encapsulation layers of stretchable inorganic electronics, because they are capable of precisely customizing the J-shaped stress-strain curves of biological tissues. Although a variety of microstructures and topologies have been exploited to adjust the nonlinear stress-strain responses of SNMs, the stretchability of most SNMs is hard to exceed 100%. Designing novel high-strength SNMs with much larger stretchability (e.g., >200%) than existing SNMs and conventional elastomers remains a challenge. This paper develops a class of hierarchical soft network materials (HSNMs) with developable lattice nodes, which can significantly improve the stretchability of SNMs without any loss of strength. The effects of geometric parameters, lattice topologies, and loading directions on the mechanical properties of HSNMs are systematically discussed by experiments and numerical simulations. The proposed node design strategy for SNMs is also proved to be widely applicable to different constituent materials, including polymers and metals.

Modelling the Structure and Anisotropy of London Clay Using the SA_BRICK Model

Several constitutive models had been developed by other researchers to cover the main features of mechanical behaviour of natural overconsolidated clays, such as the nonlinear stress–strain response at small and large strains, and the recent stress history effect. Kinematic hardening models include these features to facilitate realistic predictions of soil–structure interaction. This paper presents the further development of a kinematic hardening model BRICK that includes anisotropy and the influence of soil structure on the mechanical behaviour of a natural clay. High quality laboratory tests were used to calibrate the input parameters of the model in a single element configuration, and a documented boundary value problem of tunnel excavation was used to validate the model in finite element calculations. A comprehensive comparative study between the predictions of different kinematic hardening models, using two different software packages, was carried out. It was observed that the SA_BRICK model is in fair agreement with the observed data and gives improved predictions in comparison to other kinematic hardening models, particularly in terms of narrowness of the settlement trough above the tunnel. Advanced predictions of ground deformations caused by tunnel excavations can be effectively used to mitigate possible damage of existing structures affected by tunnelling in an urban environment.

Characterisation of mechanical behaviour of fibre reinforced thermoplastic composites subjected to off-axis compressive loading

This paper presents an experimental and numerical investigation on the mechanisms of damage onset and evolution in unidirectional carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting and end collapsing of specimens during test. A series of compression tests were conducted with specimens of various off-axis angles. Different failure mechanisms and nonlinear stress-strain responses were observed and studied. The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented using finite element analysis and compared to experimental results. It is shown that the LaRC05 criterion can provide accurate predictions for matrix cracking failure mode of unidirectional thermoplastic composites controlled by compression-shear combined stresses.

Complex unloading behavior of titanium alloy in cold and thermal-mechanical working

Unloading behavior is of crucial importance in metal forming, which particularly creates challenges for springback analysis and control of shape and dimensional accuracies of the manufactured components. For the working with hard-to-form materials at elevated temperatures, the thermal-mechanical coupling effect makes the unloading process more complicated and thus more difficult to model and control. Establishing an insight into the thermal-mechanical unloading behavior is crucial for ultimately improving the shape and dimensional accuracy of formed components. In this research, by using a near-alpha high-strength titanium alloy as a case study material, a series of continuous loading-unloading-reloading experiments within cold and warm forming domains were designed and conducted. Through the experiments, the complex unloading behavior, specially for the temperature-dependent degradation effect of elastic modulus and nonlinear stress-strain response, was investigated. A physically-based model was developed to reproduce the temperature-dependent nonlinear reduction effect of elastic modulus. In this model, the reversible mobile dislocation density is particularly included and represented to describe the evolving nonlinear elastic strain component upon unloading affected by both plastic strain and deformation temperature. Based on the model-based analysis, the mechanism accounting for the complex unloading nonlinearity in thermal-mechanical working was discussed and revealed from different evolutions of dislocation behaviors depending on plastic deformation and temperature.

Off-Axis Compressive Behaviour of Fibre Reinforced Thermoplastic Composites.

This paper presents an experimental investigation on the mechanisms of damage onset and evolution in unidirectional PEEK/AS4 carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting, and end collapsing of the specimens during the test. A series of compression tests were conducted with specimens of various off-axis angles. The displacement and strain fields of all specimens during the tests were evaluated by the digital image correlation (DIC) method. In combination with the DIC results, the influence of the off-axis angles on the failure mechanisms and nonlinear stress–strain responses were analysed. The corresponding failure mechanisms were examined by scanning electron microscopy (SEM). The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented and compared to the experimental results. It was shown that the LaRC05 criterion can provide accurate predictions when the off-axis angle is larger than 15°. The complex failure mechanisms were analysed to better understand the effect of ductility of the thermoplastic matrix to the composites. The series of tests provide an experimental failure envelope in combined stress states and can be used for the evaluation of failure theories and the criteria of thermoplastic composites.

Numerical simulation of transverse compression and densification of wood

Densification is commonly adopted to increase the mechanical performance of wood, but research on the micromechanical behaviour of the material during transverse compression is limited. Robust numerical models will enable better predictions of the performance of wood during compression and optimise the manufacturing process of densified wood minimising experimentation. The densification stress–strain response of wood after chemical treatment is reported via numerical simulations. A 3D finite element model of wood microstructure is studied under transverse compression using ABAQUS/Explicit software. A lower cellulose, hemicellulose and lignin content in the chemically treated wood is considered in the material parameters of the cell wall, and an ideal elastoplastic material model is used to represent the nonlinear stress–strain response. Parametric studies regarding the cell wall thickness, yield stress and chemical treatment are also considered. The numerical predictions agree well with microscopy studies of densified wood, and the nominal stress–strain curve obtained is similar to experimental findings under transverse compression as found in the literature. The cell wall thickness and yield stress are found to significantly affect the compressive stress–strain response of wood.