Relaxation Tests Research Articles

Programable shape recovery properties and snap-through instabilities of viscoelastic and shape-memory NS metamaterials

The combination of smart material and mechanical metamaterial has the potential to bring novel properties and additional functionalities, which, however, has been ignored for a long time. This work numerically, experimentally, and analytically examines the negative stiffness (NS) metamaterials based on shape memory polymers (SMPs) with a focus on the tunable and temperature-dependent properties induced by the interaction of material and geometry nonlinearity. A universal discrete model of a series of shape-memory NS metamaterial is developed by separating the bending effect and stretching effect, where the viscoelastic material is described by the generalized Maxwell-Wiechert model, and an SMP constitutive model is proposed based on multiplicative decomposition of the deformation gradient. The mechanical and shape-memory properties influenced by temperature, geometry, material and loading rate are experimentally observed through relaxation tests and cyclic compression tests. Then the discrete model and finite element analysis (FEA) is adopted to examine the novel mechanical responses in a wide range of parameters. Results show that viscoelasticity and loading rate play a significant role in mechanical responses, and tunable load-capacity and stability can be achieved for shape-memory metamaterial. A phase diagram of different stabilities is constructed showing strictly monotonic, S-shaped, and snapping responses. Additionally, repeated compression and recovery performance proves the possibility of reusable applications. This work provides new opportunities for functional metamaterial to obtain programmable shape recovery and mechanical responses.

Time-dependent constitutive behaviors of a dynamically crosslinked glycerogel governed by bond kinetics and chain diffusion

Soft materials featuring dynamic networks represent a burgeoning frontier in materials science, offering multifaceted applications spanning soft robotics, biomaterials, and flexible electronics. Unraveling the time-dependent constitutive behavior of these materials, rooted in dynamic networks, stands as a pivotal pursuit for engineering advancements. Herein, we fabricate a tough and extreme-temperature-tolerant glycerogel with a polymer network crosslinked by metal-coordination crosslinkers and conduct a thorough analysis of its intricate mechanical responses across monotonic loading, relaxation, creep, and cyclic tests. We then develop a physically grounded constitutive model integrating the dynamics of crosslinker association/dissociation and polymer chain diffusion, furnishing a holistic framework to elucidate their interplay. We employ a statistical description, using density functions of chains in terms of end-to-end vectors, to characterize network reconfiguration. The evolution of chain density under external load, mediated by crosslinker kinetics and chain diffusion in a viscous medium, leads to intriguing variations in elastic energy and stress responses. Through meticulous experimental validation and numerical simulations, we demonstrate the efficacy of the model in forecasting the mechanical behavior of dynamic polymer networks under diverse loading scenarios, encompassing strain rate effects, stress relaxation, Mullins effect, and self-recovery phenomena. Our findings provide valuable insights into the design and optimization of dynamic network-based materials for diverse applications in biomedical and engineering fields.

Frequency Range Optimization for Linear Viscoelastic Characterization of Burger's Model

The linear viscoelastic behavior of materials is represented using mechanical models of choice, which are further utilized in different numerical investigations, such as finite element simulations and discrete element simulations. Burger's model is one of the widely adopted mechanical models and remains highly favored in contemporary research due to its multiple advantages. Specifically, it excels in representing long-term creep and stress relaxation behavior in a relatively simplified manner. Accurate identification of the long-term behavior for the viscoelastic material, particularly asphalt concrete, is crucial, as it serves as a key indicator of asphalt pavement performance over its service life. However, past research studies show that the parameters of Burger's model should be back-calculated from experimental data only within a limited range of frequency, otherwise, the parameters fail to represent the true material behavior. To the best of the authors’ knowledge, there is no approach for researchers to obtain the critical frequency range in which the experiments should be performed. Therefore, this study proposes a novel framework to find the critical frequency range to obtain appropriate model parameters of Burger's model, to better characterize the viscoelastic behavior of the materials. To examine the framework, asphalt concrete mixtures are used as examples in this study. Necessary laboratory tests including complex modulus tests and stress relaxation tests, are performed on two distinctive types of asphalt concrete mixtures. The generalized Maxwell model with different number of Maxwell chains are used to evaluate the performance of Burger's model. Furthermore, since commercially available finite element packages generally do not have a direct built-in Burger's model, the article shows a way of implementing Burger's model in finite element simulation. The simulations corresponding to the laboratory tests are carried out in both frequency domain and time domain to thoroughly evaluate the performance of Burger's model. The optimal frequency range of 0.1-20 Hz for the examined mixtures is found to significantly improve the accuracy of the descriptive master curve. The results also suggest that the generalized Maxwell model requires a minimum of four Maxwell chains to maintain good performance in accurately characterizing the behavior of asphalt mixtures. However, adding more Maxwell chains beyond a critical limit may not provide significant benefits. Finite element simulations demonstrate that the stress relaxation behavior predicted by the obtained Burger's model parameters aligns more closely with experimental data over longer time intervals. This makes Burger's model a strong choice for aiding in the design of simulations for studies focused on the long-term behavior of materials.

Effect of Skeletal Muscle Immobilization on Regional Anisotropic Viscohyperelastic Properties Change in a Rat Model

Passive mechanical properties in three different zones (distal, proximal, and medial) of biceps brachii immobilized in short position and its free contralateral were investigated. For that, in vitro equibiaxial relaxation tests were performed with samples harvested from skeletal muscles of immobilized rats during one or two weeks. From data obtained in two plane axes of loading, a viscohyperelastic anisotropic model described by a strain energy function coupled with second order Maxwell's model, was used to identify the material parameters. It has been shown that the zone influences the material parameters of the hyperelasticity behavior while the immobilization acts rather on the viscoelasticity response. Based on measurements of histological parameters from flexor carpi ulnaris muscles, we observed that immobilization produced contractile tissue atrophy and connective tissue thickening. The muscle atrophy caused by immobilization could lead to a more linear mechanical behavior along the axis of the muscle fibers. Furthermore, fibrosis, quantified by histological analysis on flexor carpi ulnaris muscles, could result in highly non-linear behavior along the other axis. These structural changes also contribute to an increase in relaxation following immobilization along both axes (+11.7% and +15.5% on average with p < 0.001 and p < 0.01 respectively for each axis). Statement of significanceTo our best knowledge, this work is the first to investigate the anisotropic, viscohyperelastic and heterogeneous properties within a passive skeletal muscle immobilized in a short position. For that, from a rat model, equibiaxial relaxation tests were performed and material parameters were found from a strain energy function coupled with a Maxwell's model. We showed that excising zone of samples greatly influences the parameters of the hyperelastic behavior while the immobilization influences the viscoelasticity response instead. Furthermore, histological analysis permitted to quantify fibrosis in the skeletal muscle and bear out, at least in part, changes in relaxation behavior following immobilization.

Flash Sintering of Bimetallic Assemblies for Turbine Disks in Next‐Generation Jet Engines

René 77 and another advanced powder metallurgy nickel‐based superalloy are flash‐sintered and joined to produce a dual‐alloy assembly. This innovative process allows for the sintering of powders to achieve high relative densities or the formation of solid joints in a shorter time than is feasible with conventional diffusion bonding techniques. Examination of the microstructure after heat treatments reveals that diffusion and recrystallization phenomena can modulate the transition zone. The creep properties of both alloys, evaluated using stress relaxation tests, do not seem to differ by more than an order of magnitude, while the higher thermal stability of René 77 compared to Alloy B at 800 °C tips the scales. In tension, base materials show very high properties, while bimetallic specimens exhibit at least higher properties than René 77. However, failure occurs at the bond at high temperatures due to the formation of an oxide film during the bonding process. These encouraging results illustrate the potential and constraints of the flash‐sintering process for producing dissimilar assemblies, which may enhance the properties of next‐generation aero‐engine turbine disks.

Instrumented assessment of lower and upper motor neuron signs in amyotrophic lateral sclerosis using robotic manipulation: an explorative study

BackgroundAmyotrophic lateral sclerosis (ALS) is a lethal progressive neurodegenerative disease characterized by upper motor neuron (UMN) and lower motor neuron (LMN) involvement. Their varying degree of involvement results in a clinical heterogenous picture, making clinical assessments of UMN signs in patients with ALS often challenging. We therefore explored whether instrumented assessment using robotic manipulation could potentially be a valuable tool to study signs of UMN involvement.MethodsWe examined the dynamics of the wrist joint of 15 patients with ALS and 15 healthy controls using a Wristalyzer single-axis robotic manipulator and electromyography (EMG) recordings in the flexor and extensor muscles in the forearm. Multi-sinusoidal torque perturbations were applied, during which participants were asked to either relax, comply or resist. A neuromuscular model was used to study muscle viscoelasticity, e.g. stiffness (k) and viscosity (b), and reflexive properties, such as velocity, position and force feedback gains (kv, kp and kf, respectively) that dominated the responses. We further obtained clinical signs of LMN (muscle strength) and UMN (e.g. reflexes, spasticity) dysfunction, and evaluated their relation with the estimated neuromuscular model parameters.ResultsOnly force feedback gains (kf) were elevated in patients (p = 0.033) compared to controls. Higher kf, as well as the resulting reflexive torque (Tref), were both associated with more severe UMN dysfunction in the examined arm (p = 0.040 and p < 0.001). Patients with UMN symptoms in the examined arm had increased kf and Tref compared to controls (both p = 0.037). Neither of these measures was related to muscle strength, but muscle stiffness (k) was lower in weaker patients (p = 0.012). All these findings were obtained from the relaxed test. No differences were observed during the instructions comply and resist.ConclusionsThis findings are proof-of-concept that instrumented assessment using robotic manipulation is a feasible technique in ALS, which may provide quantitative, operator-independent measures relating to UMN symptoms. Elevated force feedback gains, driving larger reflexive muscle torques, appear to be particularly indicative of clinically established levels of UMN dysfunction in the examined arm.

Long-term viscoelastic behavior and evolution of the Schapery model for mirror epoxy

Abstract Mirror epoxy, used in its pure form with a resin-to-hardener ratio of 100:50, is emerging as an innovative material widely used in modern flooring. Its appeal lies in its smooth, shiny surface, offering a unique and contemporary aesthetic. However, understanding its long-term viscoelastic behavior is essential to ensure the durability and performance of floor coverings under various conditions of use. This study examines the evolution of the Schapery model for mirror epoxy, focusing on its long-term viscoelastic behavior. Creep tests at constant loads and ambient temperature are carried out in order to numerically determine the static nonlinearity factors g and g 0 formulated in the Schapery model. To validate this model, other relaxation tests at constant deformations are carried out under the same conditions, which allowed us to determine the nonlinearity factors h and h 0 formulated in this model using the same method. A remarkable consistency between the variations in the experimental and numerical values of the model programmed on MATLAB allows us to conclude that the Schapery model describes the real behavior of the mirror epoxy in a satisfactory manner.

Polymerization-Induced Self-Assembly Providing PEG-Gels with Dynamic Micelle-Crosslinked Hierarchical Structures and Overall Improvement of Their Comprehensive Performances.

Polymer gels are fascinating soft materials and have become excellent candidates for wearable electronics, biomedicine, sensors, etc. Synthetic gels usually suffer from poor mechanical properties, and integrating good mechanical properties, adhesiveness, stability, and self-healing performances in one gel is more difficult. Herein, polymerization-induced self-assembly (PISA) providing PEG-gels with an overall improvement in their comprehensive performances is reported. PISA synthesis is carried out in PEG (solvent) to efficiently produce various nanoparticles, which are used as the nanofillers in the subsequent synthesis of PEG-gels with dynamic micelle-crosslinked hierarchical structures. Compared to hydrogels, PEG-gels show excellent long-term stability due to the nonvolatile feature of PEG solvent. The hierarchical PEG-gels (with nanofillers) exhibit better mechanical and adhesive properties than the homogeneous-gels (without nanofillers). The energy dissipation mechanism of the PEG-gels is analyzed via stress relaxation and cyclic mechanical tests. High-density hydrogen bonds between the micelles and PAA matrix can be broken and reformed, endowing better self-healing properties of the dynamic micelle-crosslinked PEG gels. This work provides a simple strategy for producing hierarchical structural gels with enhanced properties, which offers fundamentals and inspirations for the designing of various advanced functional materials.

Effective optimization method of asphalt binders and asphalt mixtures based on the two-parameter of contraction and relaxation

Thermal cracking is one of the primary distresses of asphalt pavement which is a complex process. Evaluating the Low-temperature Performance (LTP) of asphalt mixtures accurately and conducting material optimization analysis is not only crucial for understanding the thermal cracking mechanism of asphalt mixtures but also serve as the basis for enhancing their thermal cracking resistance performance. However, current research has not sufficiently interpreted the mechanism of thermal cracking. It is segmentary that optimizes asphalt mixtures solely based on their ultimate strength, strain, and so on at certain low-temperature points. Therefore, this study closely integrated the thermal cracking mechanism and proposed a two-parameter optimization method. Firstly, clarifying the decisive role of the contraction and relaxation relationship in determining LTP through the Thermal Stress Restrained Specimen Test (TSRST), thermal contraction test, and low-temperature relaxation test. Secondly, quantizing the impact of the aggregates skeleton and then using a two-parameter method to analyze the comprehensive effects on LTP of asphalt mixtures. Finally, summarizing the material optimization method of asphalt binder-first, aggregates-second based on the multiple linear regression method. This paper simplified the evaluation method and provided a basis for material selection and design for improving the thermal cracking resistance of asphalt mixtures.

Thermomechanical and Viscoelastic Characterization of Continuous GF/PETG Tape for Extreme Environment Applications

The thermomechanical and viscoelastic properties of a glass fiber polyethylene terephthalate glycol (GF/PETG) continuous unidirectional (UD) tape were investigated using differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical analysis (DMA). This study identified five operational conditions based on the Army Regulation 70-38 Standard. The DSC results revealed a glass transition temperature of 78.0 ± 0.3 °C, guiding the selection of temperatures for TMA and DMA tests. TMA provided the coefficient of thermal expansion in three principal directions, consistent with known values for PETG and GF materials. DMA tests, including strain sweep, temperature ramp, frequency sweep, creep, and stress relaxation, defined the material’s linear viscoelastic region and temperature-dependent properties. The frequency sweep indicated an increased modulus with rising frequency, identifying several natural frequency modes. Creep and stress relaxation tests showed time-dependent behavior, with strain increasing under higher loads and stress decreasing over time for all tested input values. Viscoelastic models fitted to the data yielded R2 values of 0.99, demonstrating good agreement. The study successfully measured thermomechanical and viscoelastic properties across various conditions, providing insights into how temperature influences the material’s mechanical response under extreme conditions.

Simple Aseismic Reinforcement of Steel Structures Using Knee Braces with High-Hardness Vises

A novel technique for upgrading the seismic resistance of steel buildings by adding knee braces to existing structures using vises was proposed by researchers in 2022. A feature of this retrofitting method is the easy setup owing to its use of vises made from high-hardness metal. Tests were conducted to investigate two main failure modes: slipping failure at the connection and yielding and buckling failure of the knee brace. The retrofitting design is discussed based on a comparison between the slipping strengths obtained through tests and calculations. Furthermore, an analytical study, using the finite element method (FEM), was conducted to evaluate the test results of retrofitted frames that failed in terms of the yielding and buckling of the knee braces. The findings of the analyses are consistent with the test results. This study included a stress relaxation test to assess the long-term performance of the vises.

Digital Representation of Materials Testing Data for Semantic Web Analytics: Tensile Stress Relaxation Testing Use Case

This study aims to represent an approach for transferring the materials testing datasets to the digital schema that meets the prerequisites of the semantic web. As a use case, the tensile stress relaxation testing method was evaluated and the testing datasets for several copper alloys were prepared. The tensile stress relaxation testing ontology (TSRTO) was modeled following the test standard requirements and by utilizing the appropriate upper-level ontologies. Eventually, mapping the testing datasets into the knowledge graph and converting the data-mapped graphs to the machine-readable Resource Description Framework (RDF) schema led to the preparation of the digital version of testing data which can be efficiently queried on the web.

Modelling the time-dependent mechanical properties of thermoplastic and thermosetting polymers with Gumbel distribution functions

In this paper, we propose a simple modelling method that accurately describes the time-dependent viscoelastic behaviour of thermoplastic and thermosetting solid polymers. We performed short-term creep and stress relaxation tests on representative samples of three major classes of polymers: an amorphous, a semi-crystalline thermoplastic and a thermosetting polymer. Then, to investigate the relationship between the model parameters and the material composition, we also tested thermoplastic matrix composites with different plasticiser contents. From the short-term tests, master curves were constructed with the use of the time–temperature superposition principle. Then, the temperature dependence of the obtained shift factors was described using the Arrhenius model. The resulting creep compliance and relaxation modulus master curves were normalised and modelled with a two-parameter cumulative Gumbel distribution function (CDF) and its complementary distribution function (CCDF). For the creep and stress relaxation master curves, the median error of modelling was less than 16 % and 16.5 % in all cases, respectively. Furthermore, it was less than 2 % for the thermosetting polymer, making this model an excellent tool for describing the creep and stress relaxation behaviour of thermosetting systems. In the case of the plasticised composites, we found a strong relationship between the material composition and the location parameter of the Gumbel model. Based on this, we developed a method that can be used to estimate the evolution of the creep compliance curve for any arbitrary OLA content (between 0 wt% and 16 wt%) at any desired temperature (between 22 °C and 70 °C).

On the experimental identification of equilibrium relations and the separation of inelastic effects in soft biological tissues

The mechanical characterization of vascular tissues has been mainly focused on the measurement of elastic properties, while the investigation of inelastic effects has received comparatively little attention. Even the relatively simple, purely elastic description of the material behavior requires an appropriate set of experimental data that cannot be easily isolated using standard testing procedures. The presence of viscous and damage-related phenomena poses some challenges in the definition of appropriate testing protocols capable of identifying an equilibrium response, which in general does not solely represent the elastic material behavior. The primary goal of the present study is therefore to devise an experimental procedure that can distinguish and evaluate the different constitutive phenomena separately. To this end, we apply methodologies widely used in the mechanical testing of rubber-like materials and transfer them to the field of biomechanics. We performed two types of experiments in equibiaxial extension on porcine thoracic aorta: a continuous cyclic test followed by a single-step relaxation test and a cyclic multi-step relaxation test, each at varying stretch rates. We demonstrate that the approximation of quasi-stationarity through continuous testing at slow rates is inadequate for the identification of an equilibrium relation. Alternatively, a step-wise protocol allows for the separation of equilibrium and viscous effects. This motivates a thermodynamic discussion of the experimental results in terms of energy dissipation and a closer look at the interplay of inelastic phenomena.

A viscoelastic constitutive framework for aging muscular and elastic arteries

The evolution of arterial biomechanics and microstructure with age and disease plays a critical role in understanding the health and function of the cardiovascular system. Accurately capturing these adaptative processes and their effects on the mechanical environment is critical for predicting arterial responses. This challenge is exacerbated by the significant differences between elastic and muscular arteries, which have different structural organizations and functional demands. In this study, we aim to shed light to these adaptive processes by comparing the viscoelastic mechanics of autologous thoracic aortas (TA) and femoropopliteal arteries (FPA) in different age groups. We have extended our fractional viscoelastic framework, originally developed for FPA, to both types of arteries. To evaluate this framework, we analyzed experimental mechanical data from TA and FPA specimens from 21 individuals aged 13 to 73 years. Each specimen was subjected to a multi-ratio biaxial mechanical extension and relaxation test complemented by bidirectional histology to quantify the structural density and microstructural orientations. Our new constitutive model accurately captured the mechanical responses and microstructural differences of the tissues and closely matched the experimentally measured densities. It was found that the viscoelastic properties of collagen and smooth muscle cells (SMCs) in both the FPA and TA remained consistent with age, but the viscoelasticity of the SMCs in the FPA was twice that of the TA. Additionally, changes in collagen nonlinearity with age were similar in both TA and FPA. This model provides valuable insights into arterial mechanophysiology and the effects of pathological conditions on vascular biomechanics. Statement of significanceDeveloping durable treatments for arterial diseases necessitates a deeper understanding of how mechanical properties evolve with age in response to mechanical environments. In this work, we developed a generalized viscoelastic constitutive model for both elastic and muscular arteries and analyzed both the thoracic aorta (TA) and the femoropopliteal artery (FPA) from 21 donors aged 13 to 73. The derived parameters correlate well with histology, allowing further examination of how viscoelasticity evolves with age. Correlation between the TA and FPA of the same donors suggest that the viscoelasticity of the FPA may be influenced by the TA, necessitating more detailed analysis. In summary, our new model proves to be a valuable tool for studying arterial mechanophysiology and exploring pathological impacts.

Relaxation tests for the time dependent behavior of pharmaceutical tablets: A revised interpretation

Relaxation tests are often used in the pharmaceutical field to assess the strain rate sensitivity of pharmaceutical powders and tablets. These tests involve applying a constant strain to the powder in the die and then monitoring the stress evolution over time. Interpreting these tests is complicated because different physical phenomena, mainly viscoelasticity and viscoplasticity, occur simultaneously. These two phenomena cannot be distinguished by observing the evolution of the axial pressure alone, as it decreases in both cases. In this work, it was shown that monitoring the evolution of the die-wall pressure during relaxation can help separate the effects of these phenomena. Theoretical considerations revealed that during viscoplasticity, the die-wall pressure also decreases, whereas an increase in the die-wall pressure during relaxation indicates a viscoelastic relaxation. This was confirmed experimentally using specially designed compaction cycles on four different pharmaceutical excipients. Experimental results indicated that at low pressure, viscoplasticity was predominant, whereas at high pressure, viscoelasticity became more prominent. These results suggest that at low pressures, relaxation tests can be used to assess the viscoplastic properties of different products. However, the use of high pressure should always be avoided as viscoelastic phenomena might become more significant, and the combination of both phenomena might compromise the interpretation.

Assessment of various polymeric sulphur as soft bitumen improver for pavement applications

ABSTRACT In this study, five polymeric sulphurs are utilised, including polymeric sulphur based on both aliphatic copolymers and styrene copolymers, namely PS1 to PS5 correlated to amorphous poly alpha olefins (APAO) PS1, olefin residues from MAC carpet company PS2, Ethylene Vinyl Acetate (EVA) copolymer PS3, Styrene Butadiene Styrene (SBS) copolymer PS4 and Dicyclopentadiene monomer (DCPD) PS5. The five polymeric sulphur compounds were mixed by 25wt% with soft bitumen penetration grade (80/100) to produce five sulphur-extended asphalt binders, namely SEA1, SEA2, SEA3, SEA4, and SEA5. The physical properties, including softening point, viscosity, and penetration, are examined to characterise the consistency of SEA binder. The dynamic mechanical behaviour such as complex modulus, temperature sweep, and stress relaxation test was investigated for SEA binder and compared with a reference soft bitumen (Blank) using a dynamic mechanical analyzer (DMA). It is concluded that polymeric sulphur based on styrene compounds SEA2 and SEA4 binders have the highest resistance against cracking of the pavement at low temperatures according to penetration index readings, and have the least permanent (plastic) deformation at high temperatures according to temperature sweep from DMA data. It is noticed that SEA5 binder has a negative effect on the performance of soft bitumen.

Integrating dynamic relaxation with inelastic deformation in metallic glasses: Theoretical insights and experimental validation

Metallic glasses (MGs), a metastable material far from equilibrium, exhibit intricate dynamic relaxation behaviors. The challenge lies in developing a model that accurately describes the dynamics and deformation mechanisms of MG. This paper introduces a model integrating dynamic relaxation with deformation behavior. Validation through dynamic mechanical analysis, stress relaxation, creep, and strain recovery tests confirm the existence of four deformation modes: elasticity, anelasticity from β relaxation, anelasticity from α relaxation at low temperatures, and viscoplasticity from α relaxation at high temperatures. The model captures all of these deformation modes. The dynamical mechanical spectrum and stress relaxation spectrum unveil dynamic features during glass to liquid transition, and a simple and effective experimental method was developed for identifying ultra-low-frequency dynamic relaxation. This work provides new perspectives on the study of relaxation dynamics in glassy states and establishes important connections between dynamic relaxation behavior and deformation mechanisms. These findings lay a theoretical and experimental foundation for the broad application of MGs.

Compressive behavior and visco-hyperelastic constitutive of polyurethane elastomer over a wide range of strain rates

Polyurethane elastomers (PUEs) will experience different strain rates in different application scenarios. Therefore, it is of great significance to study the mechanical properties of PUE under a wide range of strain rates and establish a constitutive model that considers strain rates with high accuracy and few parameters. In this study, the quasi-static and dynamic compression tests of two types of PUEs (PUE55 and PUE85) were carried out, and investigated the strain rate effect of the materials. Based on the Mooney-Rivlin hyperelastic model and the Prony series, a compressible visco-hyperelastic constitutive model for PUE was established. Different from the conventional constant relaxation time in Prony series, two relaxation times that vary exponentially with principal stretch were proposed based on the relaxation test to describe the strain rate effect of the material at low and high strain rate respectively. In addition, using the visco-hyperelastic constitutive model to obtain the model inputs of the Simplified rubber/foam model in LS-DYNA, the impact process of the Metal/PUE composite projectile was reproduced under different impact conditions through the finite element simulation. Simulation results verified the visco-hyperelastic model in generating numerical model material parameters and the rationality of the Simplified rubber/foam model in describing PUEs.

Reduced warpage in semiconductor packages: Optimizing post-cure temperature profile considering cure shrinkage and viscoelasticity of epoxy molding compound

Warpage in semiconductor packages is a critical issue that affects their reliability and performance. This study aims to minimize the warpage of a bi-material dummy package by optimizing the post-mold curing (PMC) temperature profile. A warpage simulation model was developed considering the viscoelastic properties and cure shrinkage behavior of the epoxy molding compound (EMC). A compression molding monitoring system was also developed to analyze the cure behavior of the EMC. The gelation point of the EMC during compression molding was determined using a dielectric sensor, while cure shrinkage behaviors were analyzed using a fiber Bragg grating sensor. Viscoelastic properties were characterized through stress relaxation tests, and thermal properties were measured using three-dimensional digital image correlation. The developed simulation model was used to optimize the PMC temperature profile using a genetic algorithm. Experimental validation showed that the optimized temperature profile reduced the warpage from ∼1519 μm to 486 μm compared to a linear profile. The findings of this study have broader implications for the design and manufacturing of semiconductor packages, as the proposed approach can be applied to minimize warpage and improve package reliability.