Dynamic Mechanical Analysis and Optimization of Vibration Damping in Epoxy-Based Nano Cement Composite Dampers for Sustainable Structures

Abstract

Traditional cement-based materials often fall short in delivering both high mechanical strength and effective vibration damping. Although nano-modified composites have shown promise, a gap remains in understanding the interaction between nanofillers and polymeric phases in epoxy-based cement systems. This study investigates the development of epoxy-based cement composite dampers with enhanced mechanical strength and vibration damping for structural applications. The composite integrates nano-SiO₂ and graphene to improve the energy dissipation, structural integrity, and long-term performance. A comprehensive experimental and mathematical modeling approach was employed to evaluate the storage modulus, loss modulus, and damping factor (tan δ) using Dynamic Mechanical Analysis (DMA). The results indicated that incorporating 2.0 wt.% nano-SiO₂ and 0.05 wt.% graphene leads to an optimum increase in both mechanical and damping properties, achieving a 92% enhancement in compressive strength and a 38% improvement in damping factor compared to conventional cement composites. Beyond this optimal composition, agglomeration effects reduce the reinforcement efficiency. Microstructural investigations using TEM and EDX confirmed the homogeneous dispersion of the nanofillers, leading to enhanced matrix densification and improved interfacial bonding. A validated mathematical model was proposed to predict viscoelastic behavior, correlating well with experimental findings. These results highlight the potential of epoxy-based cement composites for high-performance damping applications in sustainable infrastructures.

1. Introduction

Structural vibration attenuation is significantly influenced by the damping properties of cement-based materials, which play a critical role in improving the mechanical performance and longevity of infrastructure. Extensive research has been devoted to enhancing both the mechanical strength and damping capabilities of cement-based materials by incorporating advanced nanomaterials and modified cementitious matrices [1,2].

The damping behavior of cementitious materials is commonly characterized using the damping ratio and loss factor, both of which directly correlate with the ability of the material to dissipate vibrational energy. An increase in the damping ratio and loss factor improves the overall damping performance of a material [3,4,5]. Various experimental methodologies, such as the free vibration method, have been employed to determine the damping ratio of cement-based composites. In this approach, a specimen was subjected to a dynamic excitation load, and the attenuation of acceleration during free vibration decay was recorded. This dataset was subsequently used to compute the damping ratio mathematically [6,7,8].

Several techniques exist for determining the material damping ratio using the free-vibration method. Li et al. [9] designed a simply supported beam with polyurethane-treated coarse aggregates, which were then subjected to mechanical tapping to measure the damping ratio. Wang et al. [10] utilized a cantilever beam subjected to impact excitation to quantify the damping ratio of recycled aggregate concrete. In addition to the free-vibration method, DMA is frequently used to determine the loss factor, which is another crucial damping parameter.

Additional approaches exist for conducting loss factor measurements. Bahari-Sambran et al. [11] employed a three-point bending mode to measure the loss factor of a montmorillonite-modified cement paste. Similarly, cement pastes reinforced with graphene oxide and PVA fibers were tested for the loss factor using the tension-compression mode [12]. One of the primary challenges in damping ratio assessment is the difficulty of applying a controlled artificial load without introducing bearing deformation or external perturbations. To overcome these challenges, the DMA technique provides a highly controlled and automated approach for precisely measuring the loss factor variations under different loading conditions. This has led to an increased preference for DMA-based damping analysis [13,14,15].

Among the advanced nanomaterials, carbon nanotubes (CNTs) have been widely explored for their exceptional mechanical and physical properties when incorporated into cement-based composites. However, owing to their strong van der Waals interactions, CNTs tend to agglomerate, limiting their uniform dispersion in cement matrices [16,17]. To counteract this, researchers have employed surfactants (e.g., Polycarboxylate Superplasticizer (PCE), sodium dodecyl sulfate (SDS)) and ultrasonic dispersion techniques to enhance CNT dispersion [18,19]. Studies have demonstrated that CNT incorporation improves the cement composite strength, reduces creep and shrinkage, and enhances durability [20,21,22].

The damping properties of CNT-reinforced cementitious materials have attracted significant attention in recent years. Assi et al. [23] utilized aromatic-modified polyethylene glycol ether and polyvinylpyrrolidone (PVP) to achieve homogeneous dispersion of CNTs in cement matrices. Their experimental findings revealed that CNTs increased the loss factor of cement by 25.9%, signifying an improvement in the damping capacity of the cementitious structures. Other experimental investigations have also confirmed that CNTs significantly enhance the damping performance and energy dissipation [24,25,26].

Luo et al. [27] and Wang et al. [28] demonstrated that graphene oxide-coated steel fibers could enhance the interfacial transition zone (ITZ), leading to improved mechanical and damping behavior in ultra-high-performance concrete (UHPC). Similarly, Avil et al. [29] and Zheng et al. [30] compared damping properties of epoxy nanocomposites reinforced with graphene nanoplatelets and carbon nanotubes, emphasizing the role of filler dispersion in energy dissipation. Furthermore, the incorporation of nano-alumina and nano-titania has been shown to refine pore structures and improve energy absorption under dynamic loading conditions [31,32].

From a materials modeling standpoint, researchers have adopted viscoelastic models, including Standard Linear Solid (SLS) and Voigt models, to simulate frequency-dependent damping behavior in nano-modified composites [33,34]. These models facilitate the prediction of mechanical responses under varying loading frequencies and support the experimental observations made through DMA. Moreover, polymer-modified cementitious systems, especially those using bisphenol-A epoxy resins, are increasingly preferred due to their superior cross-linking, adhesion, and damping properties [35,36].

Although nano-reinforced cement composites show promise, the scientific understanding of how nanofillers interact with epoxy–cement matrices to influence damping behavior remains limited. Practically, there is a need for materials that combine high mechanical strength with effective vibration damping for structural applications. This study systematically investigated the synergistic effects of nano-SiO₂ and graphene (1–3% by cement weight) on the damping capacity of cementitious mortar composites. The loss factors of nano-SiO₂ and graphene-modified mortar composites were evaluated using DMA. Additionally, advanced microstructural characterization techniques, such as Transmission Electron Microscopy (TEM) and Energy Dispersive X-ray Spectroscopy (EDX), were employed to gain deeper insights into the distribution, interfacial bonding, and morphological changes in the cementitious matrix. A mathematical modeling approach was also implemented to predict and compare the loss factor values with the experimental results. By integrating nanoengineered cementitious materials with superior damping properties, this study contributes to the development of high-performance vibration-resistant cement composites for structural applications.

2. Materials and Methods

2.1. Materials Used in the Study

Ordinary Portland Cement (OPC) Grade 53, conforming to IS:269-2015 [37], was procured from Ultratech Cement Pvt. Ltd., Hubli, Karnataka, India, with a specific surface area of 340 m²/kg. This cement was selected for its high-strength development properties, making it suitable for high-performance composite applications. River sand with a specific gravity of 2.60 was utilized as the fine aggregate to ensure optimal particle gradation and workability. Both coarse and fine aggregates complied with IS:383-2016 [38] specifications. The coarse aggregate used in the mix consisted of 5 mm particles, which were chosen to enhance the packing density and mechanical interlocking characteristics of the composite. A polycarboxylate ether-based (PCE) superplasticizer meeting IS:9103-2018 [39] standards was incorporated to enhance the workability and dispersion of cementitious particles while reducing water demand, thus ensuring improved rheological behavior of the mix.

The selection of materials was based on their established performance in high-strength and multifunctional cementitious systems. OPC Grade 53 was chosen due to its high early strength and wide availability, making it ideal for developing structural composites with enhanced mechanical properties. River sand was used as the fine aggregate for its natural gradation and good compaction characteristics, which support matrix densification. Nano-silicon dioxide (nSiO₂) was selected for its high surface area and pozzolanic reactivity, which contribute to additional calcium silicate hydrate (C-S-H) formation and pore refinement. Graphene oxide was incorporated for its exceptional mechanical properties and high aspect ratio, which are known to improve interfacial bonding and crack-bridging behavior. Bisphenol-A epoxy resin was used as the polymer matrix due to its superior adhesion, cross-linking density, and viscoelasticity, all of which support energy dissipation and improve damping performance. The combination of these materials was specifically tailored to address both mechanical reinforcement and vibration damping requirements in sustainable structural applications.

The nanomaterials used in this study included graphene oxide (GO) nanopowder and silicon dioxide (nSiO₂) nanopowder, both acquired from Intelligent Materials Pvt. Ltd., Punjab, India (https://www.nanoshel.in/) on 12 February 2024. These nanomaterials were selected because of their ability to enhance the mechanical properties, reduce the porosity, and improve the damping performance of cementitious composites. The detailed specifications of these materials are listed in

Table 1. Specifications of silicon dioxide nano powder (nSiO₂).

Product Description	Silicon Dioxide Nano Powder Properties
Purity	99.9%
Average Size of Particles	60–70 nm
Molecular Formula	SiO2
Molecular Weight	60.08 g/mol
Form	Powder
Color	White
Density	2.4 g/cm
Bulk Density	0.10 g/cm3
Specific Surface Area (SSA)	190–600 m2/g
Melting Point	1600 °C
Solubility	Insoluble in Water

and

Table 2. Specifications of graphene oxide (GO) nano powder.

Product Description	Graphene Oxide Nano Powder Properties
Purity	99.99%
Lateral size	10 µm
Thickness	1.6 nm
Molecular Weight	12.01 g/mol
Form	Powder
Color	Black
Density	1.9–2.2 g/cm3
Boiling Point	4830 °C
Specific Surface Area (SSA)	550–580 m2/g
Melting Point	3452–3697 °C
Solubility	Slightly soluble in Water

.

Figure 1 shows the experimental workflow and study design for the development and evaluation of epoxy-based nano cement composite dampers.

Table 3. Material formulations and designations.

Sl No	Designation	Filler wt.% (nSiO2)	Filler wt.% (Graphene)	Filler wt.% (Epoxy)
1	pPC	--	--
2	nSPC1	1.0	0.05	10
3	nSPC2	1.5	0.05	10
4	nSPC3	2.0	0.05	10
5	nSPC4	2.5	0.05	10
6	nSPC5	3.0	0.05	10

presents the material formulations and designations of the different compositions used in this study. It provides the percentage weight of nano-silicon dioxide (nSiO₂), graphene, and epoxy incorporated into the specimens. The composition was designed to systematically evaluate the effect of varying the nSiO₂ concentration while maintaining a constant graphene and epoxy content. The reference mix, designated as pPC, did not contain any fillers, while the nano-modified composites (nSPC1–nSPC5) incorporated increasing amounts of nSiO₂ up to 3.0 wt.%. A uniform graphene content of 0.05 wt.% ensures a controlled variable across different formulations.

2.2. Characteristics of Resin

Bisphenol-A (BPA) epoxy resin was used as the primary polymer matrix in this study. The chemical structure of the epoxy monomer is shown in Figure 2. BPA epoxy is a thermosetting polymer that is widely utilized owing to its high mechanical strength, chemical resistance, and excellent adhesion properties. It has a molecular weight of 340 g/mol and contains two highly reactive epoxy functional groups that facilitate cross-linking during the curing process. A 4,4′-sulfonyldianiline (DDS) curing agent with a molecular weight of 248 g/mol was used to initiate and complete the polymerization reaction [40,41]. The curing reaction occurs via epoxide ring opening, where the epoxy groups interact with the amine groups of the curing agent, forming a highly cross-linked network. During this reaction, each epoxy group must break the C–O–C bond to generate a reactive CH₂ site, which plays a crucial role in cross-link formation and determines the final mechanical properties of the cured epoxy composite.

2.3. Preparation of Epoxy-Based Nano SiO₂ and Graphene Nano Powder Mortar Composites

Epoxy-based cement composites were formulated by blending resin, cement powder, and water to achieve a homogeneous matrix with enhanced damping characteristics. The formulation process was optimized to ensure the uniform dispersion of the nanofillers and effective cross-linking of the epoxy network. For each cement composition, the fixed epoxy content of 10 wt.% relative to cement weight was used to balance structural rigidity and damping efficiency. The epoxy system comprised bisphenol-A epoxy resin and DDS curing agent in a stoichiometric ratio of 4:1, ensuring superior mechanical performance.

2.3.1. Material Mixing and Composite Preparation

The preparation process began with precise weighing of all components, including cement, sand, epoxy resin, curing agent, and nanomaterials (nano-SiO₂ and graphene oxide). The epoxy resin was pre-mixed with nano-SiO₂ and graphene oxide at low speeds (500–1000 rpm) for 10–15 min using a mechanical stirrer (REMI Motors, Mumbai, India). To further enhance deagglomeration and achieve nano-scale homogeneity, ultrasonication (40 kHz) was performed for 30–60 min, followed by vacuum degassing to remove entrapped air and prevent porosity. Ethanol was added as a dispersing agent to stabilize the nanoparticles [42,43].

In parallel, the cement and fine aggregates were dry-mixed using a planetary mixer at 1000 rpm for 2–3 min. The epoxy–nano solution was gradually introduced into the dry mixture while stirring at 1500–2000 rpm for 5–10 min to ensure thorough binding. The curing agent was added in the final stage, followed by mixing for 2–5 min to achieve complete polymerization. A polycarboxylate ether-based (PCE) superplasticizer, conforming to IS:9103-2018, was incorporated to enhance workability and rheological stability. To prevent air entrapment during mixing, an antifoaming agent (AFA) was used to mitigate the formation of voids, which could compromise the mechanical integrity and damping performance. The epoxy-to-cement ratio (E/C ratio) played a crucial role in defining the load-bearing capacity, energy-dissipation properties, and interfacial adhesion [44,45]. A higher cement content provided greater compressive strength, while an increased epoxy fraction enhanced the viscoelasticity, promoting improved damping behavior.

2.3.2. Casting and Curing of Specimens

The composite mixture was poured into 50 mm × 10 mm × 5 mm molds to ensure uniform compaction. The cast samples (5 replicates) were stored in sealed plastic bags at 100% relative humidity for 24–48 h, followed by autoclaving at 175 °C for 8 h to enhance the mechanical and thermal stability. Finally, the specimens were oven-dried at 116 °C for 24 h to remove the residual moisture and stabilize the microstructure.

DMA was conducted to determine the storage modulus, loss modulus, and loss factors and quantify the damping capabilities of the composites under dynamic loading conditions. The final formulations and mix proportions for 100% are summarized in

Table 4. Mix design for cement mortar 1:1 with epoxy 10% by weight of cement.

Mix Id	Ingredient(g)		FOR Cement Mortar 1:1
	Cement	Sand	Nano SiO2	Graphene	W/C	Epoxy
pPC	43.87	49.28	0	0	0.45	0
nSPC1	43.87	49.28	0.44 (1%)	0.0044 (0.01%)	0.45	4.387
nSPC2	43.87	49.28	0.66 (1.5%)	0.0044 (0.01%)	0.45	4.387
nSPC3	43.87	49.28	0.88 (2.0%)	0.0044 (0.01%)	0.45	4.387
nSPC4	43.87	49.28	1.108 (2.5%)	0.0044 (0.01%)	0.45	4.387
nSPC5	43.87	49.28	1.32 (3.0%)	0.0044 (0.01%)	0.45	4.387

, and Figure 3 illustrates the mold and specimen configurations used for DMA testing. The experimental procedure, from material selection to the final casting process, is summarized in the graphical abstract shown in Figure 4.

2.4. Testing Methods

2.4.1. Flexural and Compressive Strength

The compressive and flexural strengths of the epoxy-based cement composites were evaluated using a compression-testing machine as shown in Figure 5a and Figure 5b, respectively. The loading rate for the compressive strength test was maintained at 20 N/s and the specimen dimensions were 50 mm × 50 mm × 50 mm. For the flexural strength test, the specimen dimensions were 80 × 20 × 20 mm, and the loading rate was set to 2.4 kN/s. These tests were conducted under controlled conditions to assess the mechanical behavior and structural integrity of the composites.

2.4.2. Damping Property Evaluation

DMA was performed to characterize the viscoelastic behavior of the epoxy-based nano cement composites (ENCs). This technique provides critical insights into the storage modulus (E₁), loss modulus (E₂), damping factor (tan δ), and glass transition temperature (Tg), which are essential for evaluating the mechanical stability and long-term performance of a material. DMA is particularly advantageous over conventional vibration-based damping tests because it ensures a controlled load application and eliminates human-induced errors. DMA was performed using a TA Instruments Q800 in dual cantilever mode. The test was conducted at a controlled temperature of 30 ± 1 °C with a frequency sweep from 0.5 to 20 Hz. Prior to testing, the instrument was calibrated using standard reference materials as per the manufacturer’s protocol. The system offered a force sensitivity of 0.0001 N and displacement resolution of 1 nm, ensuring high accuracy in detecting viscoelastic behavior.

The damping properties of the epoxy–cement mortar samples were assessed using a TA Q800 Dynamic Thermal Mechanical Analyzer (TA Instruments, New Castle, Delaware, USA) in tension-compression mode. The DMA test involved applying a sinusoidal force to measure the storage modulus (E₁), loss modulus (E₂), and loss factor (tan δ), which were calculated using the following equations:

$$E_1={\displaystyle \raisebox{1ex}{${\sigma }_0\cos \delta $}\!\left/ \!\raisebox{-1ex}{${\epsilon }_0$}\right.}$$

(1)

$$E_2={\displaystyle \raisebox{1ex}{${\sigma }_0\sin \delta $}\!\left/ \!\raisebox{-1ex}{${\epsilon }_0$}\right.}$$

(2)

$$\tan \delta =E_2/E_1$$

(3)

where δ represents the phase angle, tan δ is the loss factor, σ₀ and ε₀ are the stress and strain, respectively, and E₁ and E₂ correspond to the storage and loss moduli, respectively. The test was conducted on 50 mm × 10 mm × 10 mm specimens at temperatures of up to 300 °C, with frequency variations ranging from 0.5 Hz to 2.5 Hz. The results obtained from DMA enabled the identification of the damping capacity and thermo-mechanical stability of ENCs, confirming their applicability in high-performance structural and vibration-damping applications.

2.4.3. Microstructural and Elemental Analysis

Energy Dispersive X-ray Spectroscopy (EDX) was used to determine the elemental composition and dispersion of nano-SiO₂ and graphene within the cement matrix. This technique provides a detailed chemical profile, ensuring the uniform distribution, purity, and integration of the nanofillers in the composite. EDX analysis was conducted using a Bruker XFlash® 6-30 Detector (Bruker Nano GmbH, Berlin, Germany), which operated at an accelerating voltage of 20 kV and had an energy resolution of 125 eV at Mn Kα. This system allows for precise quantitative and qualitative identification of elemental constituents, ensuring the effective incorporation of nanofillers within the cementitious matrix.

TEM was employed to examine the hydrated phases of the cementitious matrix, focusing on the calcium silicate hydrate (C-S-H) gel structure and its interaction with nano-SiO₂ and graphene. The analysis was performed using a JEOL JEM-2100F TEM (JEOL Ltd., Tokyo, Japan) microscope operating at an accelerating voltage of 200 kV, equipped with a field-emission gun (FEG) for high-resolution imaging. This system offers a spatial resolution of 0.19 nm, enabling the visualization of nano-scale dispersion, interfacial bonding, and structural integrity of the composite. TEM investigation provided insights into the morphology, particle dispersion, and chemical interactions of the nanofillers within the cementitious matrix. Additionally, selected-area electron diffraction (SAED) patterns were used to confirm the crystalline phases present in the cement composite, further validating the integration of nano-SiO₂ and graphene into the matrix.

2.5. Viscoelastic Damping Model for Epoxy-Based Composites

The study of vibration damping in epoxy-based nano cement composites requires a robust mathematical model to describe the viscoelastic behavior and damping properties (Equations (4)–(14)). This section presents a comprehensive mathematical framework for the DMA results, loss modulus, storage modulus, and the influence of nano-SiO₂ and graphene on the mechanical properties [46,47,48,49,50,51,52]. The model was validated against the experimental results of the study.

Viscoelastic materials exhibit both elastic and viscous behaviors. The stress–strain relationship is governed by the following constitutive equation:

$$\sigma \left(t\right)=E_1ϵ\left(t\right)+\eta {\displaystyle \frac{dϵ\left(t\right)}{dt}}$$

(4)

where $\sigma \left(t\right)$ is the applied stress, $ϵ\left(t\right)$ is the strain response, $E_1$ is the storage modulus, $\eta$ is the viscosity coefficient of the epoxy nanocomposites.

For sinusoidal loading:

$$ϵ\left(\mathrm{t}\right)={ϵ}_0{\mathrm{e}}^{\mathrm{i}\mathsf{\omega }\mathrm{t}}$$

(5)

where ω is the angular frequency of the applied stress. Substituting this into the constitutive equation gives

$$\sigma \left(t\right)=E_1{ϵ}_0{e}^{𝓲\omega t}+𝓲\omega \eta {ϵ}_0{e}^{𝓲\omega t}$$

(6)

which leads to the complex modulus:

$$E^{*}=E_1+𝓲E_2$$

(7)

where E₁ = E is the storage modulus (elastic component), E₂ = ωη is the loss modulus (viscous component).

The loss factor (damping property) is then defined as

$$\tan \left(\delta \right)={\displaystyle \frac{E_2}{E_1}}={\displaystyle \frac{\omega \eta }{E_1}}$$

(8)

2.5.1. Effect of Nano-SiO₂ and Graphene on Damping Ratio

Nano-SiO₂ and graphene enhance damping by increasing the interaction between the cement hydration products and the epoxy phase. The improved damping ratio can be represented as

$$\xi ={\xi }_0+{\alpha }_1{V}_{nSi{O}_2}+{\alpha }_2{V}_{Graphene}$$

(9)

where $\xi$ is the effective damping ratio, ${\xi }_0$ is the base cement damping ratio, $V_{nSi{O}_2}$ and $V_{Graphene}$ are the volume fractions of nano-SiO₂ and graphene, respectively, ${\alpha }_1$, ${\alpha }_2$ are material-dependent coefficients.

For a standard linear solid (SLS) model, which better approximates the viscoelastic behavior of nano-modified composites, the constitutive equation is

$$\sigma +{\lambda }_1\dot{\sigma }=E_0ϵ+E_1\dot{ϵ}+{\lambda }_2\ddot{ϵ}$$

(10)

where ${\lambda }_1$ and ${\lambda }_2$ are relaxation constants, and $E_0 \mathrm{and}$ $E_1$ are elasticity parameters. Using the Boltzmann Superposition Principle, the creep compliance can be expressed as

$$J\left(t\right)=J_0+{{\displaystyle \sum }}_{i=1}^n{J}_i(1-e^{{\displaystyle \raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{${\tau }_i$}\right.}}$$

(11)

where $J_0$ is the instantaneous compliance, $J_i$ are retardation parameters, τ_i are relaxation times.

2.5.2. Frequency-Dependent Modulus and Damping Behavior

For dynamic testing in DMA, the frequency-dependent modulus follows

$$E_1\left(\omega \right)=E_0+{\displaystyle \frac{E_{\infty }-E_0}{1+{\left(\omega \tau \right)}^n}}$$

(12)

where $E_0$ and $E_{\infty }$ are the low- and high-frequency moduli, respectively, and τ\tauτ is the relaxation time.

Using Voigt Model, the effective modulus can be computed as

$$E_{eff}={\displaystyle \frac{E_1{E}_2}{E_1+E_2}}$$

(13)

The phase lag δ is derived as

$$\tan \left(\delta \right)={\displaystyle \frac{C\left(\omega \right)}{2\sqrt{K\left(\omega \right)M\left(\omega \right)}}}$$

(14)

where $C\left(\omega \right)$ is the damping coefficient, $K\left(\omega \right)$ is stiffness, and $M\left(\omega \right)$ is mass.

3. Results and Discussion

3.1. Flexural and Compressive Strength

The flexural and compressive strength results of the epoxy-based nano cement composites (ENCs) are presented in Figure 6a,b. These results demonstrate the impact of nano-SiO₂ and graphene incorporation on the mechanical performance of the composites. The compressive strength of the control sample (pPC) was 25 MPa, which significantly improved with the addition of nano-SiO₂ and graphene. The highest compressive strength was observed for the nSPC3 sample (48 MPa), containing 2.0 wt.% nano-SiO₂ and 0.05 wt.% graphene, showing a 92% increase compared to the control mix. The enhancement in compressive strength can be attributed to the pozzolanic activity of nano-SiO₂, which reacts with the calcium hydroxide (CH) formed during cement hydration, leading to the generation of additional calcium silicate hydrate (C-S-H), the primary strength-contributing phase in cementitious composites.

Beyond 2.0 wt.% nano-SiO₂, a slight reduction in compressive strength was observed in nSPC4 (45 MPa) and nSPC5 (42 MPa). This can be attributed to particle agglomeration at higher nano-SiO₂ concentrations, which may lead to a heterogeneous distribution, reduced interfacial bonding, and localized stress concentrations. An optimal balance between nano-SiO₂ dispersion and reactivity was achieved at 2.0 wt.%, corresponding to the maximum compressive strength in nSPC3.

The flexural strength results revealed a trend similar to that of the compressive strength. The plain cement composite (pPC) exhibited a flexural strength of 6.6 MPa, which increased with the incorporation of nano-SiO₂ and graphene. The highest flexural strength of 7.5 MPa was recorded for the nSPC3 sample, representing a 13.6% increase compared to that of the control mix. The improved flexural strength is attributed to the ability of nano-SiO₂ to refine the pore structure and enhance matrix densification, along with the exceptional tensile properties of graphene, which improve crack-bridging and load transfer mechanisms Beyond 2.0 wt.% nano-SiO₂, a declining trend in flexural strength was observed in nSPC4 (6.8 MPa) and nSPC5 (6.5 MPa). This reduction could be due to nanoparticle clustering, which leads to weakened interfacial bonding and stress concentration sites under flexural loads.

The enhancement in both compressive and flexural strengths can be attributed to the synergistic effects of nano-SiO₂ and graphene: nano-SiO₂ accelerates cement hydration, forming higher amounts of C-S-H gel, which leads to increased strength and reduced porosity. Graphene improved the interfacial bonding, prevented crack propagation, and enhanced the tensile resistance of the composite. The combination of nano-SiO₂ and graphene reinforces the cement matrix, providing a densified microstructure and improved load transfer properties [53,54]. However, excessive nano-SiO₂ concentration (>2.0 wt.%) led to particle agglomeration, reducing the available reactive surface area and negatively impacting the mechanical performance.

3.2. Damping Characteristics

The damping characteristics of epoxy-based nano cement composites were analyzed through DMA, focusing on the loss factor (tan δ) and storage modulus (E₁) to evaluate the viscoelastic behavior and energy dissipation properties. These parameters play a crucial role in determining the mechanical stability and damping efficiency of the hybrid composites under cyclic loading. The results presented in Figure 7 and Figure 8 illustrate the influence of nano-SiO₂ and graphene incorporation on the damping performance of the composites.

The loss factor (tan δ), which represents the energy dissipation capability, exhibited a significant enhancement in the hybrid composite samples (nSPC1–nSPC5) compared with plain cement concrete (pPC). The control mix (pPC) displayed the lowest damping capacity, whereas the nSPC3 sample (2.0 wt.% nano-SiO₂ and 0.05 wt.% graphene) recorded the highest loss factor, indicating an optimized balance between rigidity and energy absorption. The increase in the nano-SiO₂ content contributed to improved interfacial bonding and microstructural flexibility, enhancing the ability to dissipate vibrational energy. However, after 2.0 wt.% nano-SiO₂, a slight decline in the loss factor was observed in nSPC4 and nSPC5, likely due to nanoparticle agglomeration and reduced efficiency in energy dissipation. The superior damping performance of nSPC3 can be attributed to the synergistic reinforcement of nano-SiO₂ and graphene, which modified the cement–polymer interface and enhanced the energy-absorption mechanisms within the composite matrix.

The storage modulus (E₁), which indicates the stiffness and elastic response of the material, showed a progressive increase with nano-SiO₂ incorporation up to 2.0 wt.%, as observed in Figure 8. The nSPC3 sample exhibited the highest storage modulus, confirming an optimal enhancement in the load-bearing capacity owing to improved matrix densification and interfacial bonding. However, similar to the trend in the loss factor, the storage modulus declined slightly beyond 2.0 wt.% nano-SiO₂, suggesting that excessive filler content led to clustering effects, reducing its reinforcing efficiency. The increase in the storage modulus of nSPC3 suggested that the combination of nano-SiO₂ and graphene strengthened the microstructure, leading to a more compact and resilient composite capable of withstanding dynamic loading.

The overall relationship between damping capacity and structural stiffness indicates that nSPC3 achieves an optimal balance between high-energy dissipation and mechanical strength, making it an ideal candidate for vibration-damping applications. The results confirm that nano-SiO₂ plays a critical role in matrix reinforcement, whereas graphene enhances interfacial bonding, crack resistance, and stress distribution under cyclic loads. However, an excessive amount of nano-SiO₂ beyond 2.0 wt.% negatively affected both damping efficiency and stiffness, most likely due to non-uniform dispersion and filler aggregation.

The nSPC3 composite (2.0 wt.% nano-SiO₂, 0.05 wt.% graphene) exhibited the best combination of damping capacity and structural stiffness, proving to be an efficient solution for vibration control in cementitious materials.

3.3. Energy Dispersive X-Ray Spectroscopy, X-Ray Diffraction, and Transmission Electron Microscopy

The Energy Dispersive Spectroscopy (EDS) analysis, presented in Figure 9a,b, provides a comprehensive understanding of the elemental composition and distribution in the epoxy-based nano cement composite. EDS is a valuable technique for confirming the presence and integration of nano-reinforcements such as nano-SiO₂ and graphene within the cementitious matrix. The EDS spectrum (Figure 9b) displays prominent peaks corresponding to Oxygen (O), Carbon (C), Silicon (Si), Calcium (Ca), Aluminum (Al), Titanium (Ti), and Iron (Fe), indicating the chemical composition of the material. The corresponding elemental composition data (Figure 9a) showed that Oxygen (43.8 wt.%) and Calcium (20.6 wt.%) are the dominant elements, followed by Carbon (21.5 wt.%), Silicon (9.6 wt.%), Aluminum (2.2 wt.%), Titanium (0.3 wt.%), and Iron (2.1 wt.%).

The high oxygen and calcium contents confirmed the presence of calcium silicate hydrate (C-S-H) and calcium hydroxide (CH), which are the primary binding phases in cement hydration. The formation of these phases plays a crucial role in improving the mechanical properties and durability of the composites. The significant presence of silicon (Si) further suggests the successful incorporation of nano-SiO₂, which contributes to pozzolanic reactions, microstructural refinement, and enhanced matrix densification. A notable carbon content (21.5 wt.%) is attributed to the epoxy resin and graphene-based reinforcements, confirming their effective integration within the composite. The inclusion of graphene enhanced the tensile strength, crack resistance, and damping properties, whereas the epoxy phase contributed to flexibility and durability.

In addition, the presence of aluminum (2.2 wt.%) is linked to cementitious phases such as tricalcium aluminate (C₃A), which influences early strength development. The detection of titanium (0.3 wt.%) and iron (2.1 wt.%) suggests the presence of trace elements, likely originating from cement constituents or nano-additives, which may further contribute to thermal stability and mechanical reinforcement. These results confirmed that nano-SiO₂ and graphene were successfully incorporated into the cement composite, improving its microstructural integrity, mechanical strength, and damping efficiency. The combination of C-S-H formation, nanofiller dispersion, and polymeric reinforcement makes epoxy-based nano cement composites a promising material for advanced structural applications requiring high-performance properties.

For TEM analysis, small fragments of the hardened composite were gently ground and suspended in ethanol using ultrasonication for 20 min to achieve fine particle dispersion. A drop of the resulting suspension was placed onto a carbon-coated copper grid and allowed to dry under ambient conditions. The prepared grids were then examined under the TEM without additional staining or coating. The microstructural characteristics of the epoxy-based nano cement composites are shown in Figure 10a–f. TEM analysis provides high-resolution imaging of the nanomaterial dispersion, particle–matrix interactions, and phase morphology, offering critical insights into the structural reinforcement mechanisms observed in the mechanical and damping property evaluations. The TEM image of pPC (Figure 10a) reveals a relatively porous microstructure with a heterogeneous particle distribution and lower matrix density, which is consistent with the lower compressive and flexural strengths observed in previous studies. The absence of nano-reinforcements results in higher porosity and weaker interfacial bonding, contributing to reduced mechanical performance and damping efficiency.

In contrast, the nano-modified composites (Figure 10b–f) exhibited significant microstructural enhancement. The TEM images of nSPC1 and nSPC2 (Figure 10b,c) show partially dispersed nano-SiO₂ and graphene with some areas of agglomeration, suggesting an improved but non-uniform distribution within the cement matrix. The formation of additional calcium silicate hydrate (C-S-H) phases is visible, contributing to the early strength development and increased matrix densification. The most optimized structure was observed in nSPC3 (Figure 10d), where nano-SiO₂ and graphene were homogeneously dispersed, leading to a dense, well-integrated microstructure with minimal defects. The uniformity of the dispersion indicates strong interfacial bonding, which effectively contributes to the enhanced compressive strength (48 MPa) and flexural strength (7.5 MPa). The improved packing of nanoparticles within the cementitious matrix also explains the higher storage modulus and loss factor, confirming the balance between the stiffness and damping capacity.

However, in nSPC4 and nSPC5 (Figure 10e,f), agglomeration of nano-SiO₂ was evident, leading to localized stress concentrations and microstructural inconsistencies. These observations correlate well with the slight reduction in the mechanical properties and damping performance beyond 2.0 wt.% nano-SiO₂, as excess nanoparticles tend to cluster, reducing their reinforcing efficiency. The TEM analysis validates the findings from the mechanical, damping, and EDS characterizations, confirming that nSPC3 exhibits the most optimized microstructure, with superior nanoparticle dispersion, matrix densification, and interfacial bonding.

To further validate the microstructural and elemental analysis, X-ray diffraction (XRD) was performed on the hardened composite. The XRD spectrum (Figure 11) exhibits prominent peaks at 2θ ≈ 18.1°, 29.3°, and 32.1°, which correspond to calcium silicate hydrate (C–S–H), portlandite (Ca(OH)₂), and unreacted alite (C₃S), respectively. These crystalline phases are typical of well-hydrated Portland cement systems. The peak at 29.3° confirms the formation of portlandite, while the broad hump around 18–22° is indicative of the semi-crystalline nature of C–S–H. The presence of unhydrated C₃S at ~32° suggests incomplete hydration, which is expected in dense matrices, especially with the inclusion of nanofillers like nano-SiO₂ that accelerate localized hydration and densify the matrix. No additional peaks were observed for crystalline silica, indicating that the nano-SiO₂ was well dispersed or fully reacted within the system.

3.4. Comparison of Experimental and Modeled Results

Figure 12 presents the stress–strain phase lag (δ) obtained from DMA for different nano-modified cement composites. The phase lag δ represents the delay between the applied stress and resulting strain, which directly correlates with the energy dissipation and damping performance. The results indicated a progressive increase in δ with the addition of nano-SiO₂ and graphene, reaching a peak in the nSPC3 sample (δ = 2.58°), which aligns with the highest loss factor (tan δ) and loss modulus (E₂). The optimal composition (2.0 wt.% nano-SiO₂, 0.05 wt.% graphene) enhances the composite’s viscoelastic response, allowing superior vibration damping without compromising structural stiffness. Beyond this filler ratio, the phase lag slightly decreased (nSPC4, nSPC5) owing to nanofiller agglomeration, reducing the effective damping contribution.

Table 5. Comparison of experimental and modeled results.

Sample	Storage Modulus (Exp.) (GPa)	Storage Modulus (Model) (GPa)	Loss Modulus (Exp.) (GPa)	Loss Modulus (Model) (GPa)	Loss Factor (Exp.) (tan δ)	Loss Factor (Model) (tan δ)
pPC	6.5	6.4	0.75	0.73	0.0325	0.031
nSPC1	6	6.6	0.78	0.77	0.035	0.034
nSPC2	6.2	6.8	0.82	0.81	0.038	0.037
nSPC3	7.2	7.1	0.88	0.87	0.045	0.044
nSPC4	6.1	7	0.86	0.85	0.043	0.042
nSPC5	6	6.9	0.85	0.84	0.042	0.041

presents a comparison between the experimentally obtained and theoretically modeled values of the storage modulus, loss modulus, and loss factor (tan δ) across different composite formulations. The storage modulus (E₁) represents the stiffness of the material, whereas the loss modulus (E₂) indicates the energy dissipation due to internal friction. The loss factor (tan δ) serves as a measure of the damping efficiency and is derived from the ratio of the loss modulus to the storage modulus. The results indicated that the theoretical model accurately predicted the experimental data, with minor deviations. The nSPC3 sample (2.0 wt.% nano-SiO₂, 0.05 wt.% graphene) exhibits the highest storage modulus and loss factor, confirming its superior mechanical strength and damping capacity. Beyond this composition, slight reductions in damping efficiency are attributed to nanoparticle agglomeration, which affects interfacial bonding.

Table 6. Comparative data on nano-reinforced cementitious composites.

Study	Nano-Additive (wt.%)	Compressive Strength	Flexural Strength	Damping Factor	Processing and Modeling Notes
Khajeh et al. [55]	MWCNT (0.1–0.3%) + Nano-SiO2 (up to 7.5%)	↑25% (to ~84 MPa)	↑53%	↑24%	Surfactant-assisted CNT dispersion; no modeling.
Wang et al. [56]	Graphene Oxide (0.01–0.1%)	↑15–33%	↑41–59%	Qualitative ↑	Conventional mixing; free vibration damping.
Li et al. [9]	MWCNT (0–0.07%)	↑2–3%	↑5%	↑15–20%	DMA-based damping; no modeling.
Liew et al. [57]	MWCNT (0–0.1%)	≈same	↑5%	↑44%	Viscoelastic matrix + CNT; high damping.
Li et al. [58]	CNT in polymer emulsion (~0.1%)	≈same	Not Reported	↑148%	Surface damping via coated aggregates.
Present Study (Epoxy–Cement Hybrid)	Nano-SiO2 (2.0%) + Graphene (0.05%)	↑92% (48 MPa)	↑13.6% (7.5 MPa)	↑38% (tan δ = 0.045)	Epoxy–cement hybrid; DMA tested; validated viscoelastic model used.

presents a comparative summary of recent studies on nano-reinforced cementitious composites in terms of their mechanical and damping performance. The present study demonstrates a notable enhancement in both compressive strength (92%) and damping factor (38%), outperforming most conventional systems. Unlike previous works that focused either on mechanical improvement or damping enhancement, this study uniquely combines an epoxy–cement hybrid matrix with nano-silica and graphene to achieve balanced multifunctional performance. Additionally, the integration of a validated viscoelastic model adds scientific rigor, distinguishing this work from prior experimental-only approaches.

4. Conclusions

This research successfully demonstrated the enhanced mechanical and damping performance of epoxy-based cement composite dampers reinforced with nano-SiO₂ and graphene. An optimal composition of 2.0 wt.% nano-SiO₂ and 0.05 wt.% graphene resulted in a significant increase in both flexural and compressive strength, reaching 7.5 MPa and 48 MPa, respectively, along with a 38% enhancement in damping properties. These improvements stem from the enhanced interfacial bonding, increased C-S-H formation, and superior dispersion of nanofillers, as validated by microstructural analysis (TEM and EDX).

The mathematical modeling approach successfully correlates with the experimental findings, accurately predicting the storage modulus, loss modulus, and phase lag δ for different compositions. The model confirms that nano-reinforcement improves energy dissipation and mechanical stability, making epoxy-based nano cement composites promising materials for high-performance damping applications.

However, beyond the optimal nano-SiO₂ concentration, agglomeration effects lead to a reduction in both mechanical and damping properties, emphasizing the need for controlled nanofiller dispersion. The findings of this study suggest that these advanced composites can significantly enhance the durability, energy absorption, and vibration control of structural elements, thereby contributing to sustainable and resilient infrastructure. Future research could explore alternative nano-additives and hybrid polymeric modifications to further optimize material properties.

The present study opens scientific and engineering prospects for designing multifunctional cement composites through synergistic epoxy and nanofiller integration. However, limitations include the fixed epoxy ratio, limited filler types, and lack of long-term dynamic performance evaluation. Future work may explore multi-filler systems, varying polymer content, and real-time vibration testing. The developed composite dampers are suitable for applications such as base isolators, vibration control pads, and structural joints in sustainable infrastructure.