Effect of recycled polymer fibre on dynamic compressive behaviour of engineered geopolymer composites

To enhance the cost-effectiveness and sustainability of engineered geopolymer composites (EGC), polyvinyl alcohol (PVA) fibres in EGC can be partially replaced with recycled tyre polymer (RTP) fibres. This paper presents a systematic experimental study on the effects of PVA fibre volume fraction (1.0%, 1.5% and 2.0%) and RTP fibre content (0.25%, 0.5%, 0.75% and 1.0%) on the dynamic compressive behaviour of EGC under various strain rates (54.43–164.13 s−1). Results indicate that the flowability, quasi-static compressive strength and elastic modulus of EGC reduce with the increase of PVA fibre content, where the reductions can be effectively mitigated by adding RTP fibres. The dynamic compressive properties of all investigated mixtures including dynamic compressive strength, dynamic increase factor (DIF) and energy absorption capacity show a pronounced strain rate dependency which can be well described using the proposed equations for DIF against strain rate ranging from 10−5 s−1 to 103 s−1 with values of mostly greater than 0.9. The dynamic compressive properties of EGC are enhanced with the increasing PVA fibre dosage under various strain rates while replacing PVA fibre with a certain amount of RTP fibre (0.25% and 0.5%) can result in better dynamic compressive properties compared to EGC with 2.0% PVA fibre. EGC containing 1.75% PVA fibre and 0.25% RTP fibre can be considered as the optimal mixture given its superior quasi-static and dynamic compressive properties in comparison with EGC with 2.0% PVA fibre

Dynamic splitting tensile behaviour of engineered geopolymer composites with hybrid polyvinyl alcohol and recycled tyre polymer fibres

Partial replacement of the widely used polyvinyl alcohol (PVA) fibre in engineered geopolymer composites (EGC) with recycled fibres can reduce the material cost and improve sustainability. This study investigates the effect of hybrid PVA and recycled tyre polymer (RTP) fibre content on the quasi-static and dynamic splitting tensile behaviour and microstructure of ambient-cured fly ash-slag based EGC through split Hopkinson pressure bar, scanning electron microscopy and X-ray computed tomography tests. Results indicate that the presence of PVA or RTP fibres can considerably improve the quasi-static and dynamic splitting tensile behaviour of geopolymers. All investigated mixtures are characterised by remarkable strain rate sensitivity within the considered test range, which can be well described using the proposed relationship between dynamic increase factor and strain rate for predictions of dynamic properties. Replacing PVA fibre with 0.25–0.5% RTP fibre can lead to better dynamic splitting tensile properties of EGC compared to that with 2.0% PVA fibre, which can be mainly ascribed to the improved synergistic effect of hybrid fibres in controlling the cracks. The microscopic images reveal that the failure mode of RTP fibres is not sensitive to the strain rate due to its hydrophobic surface feature, which could benefit the energy absorption capacity of EGC under dynamic loading. EGC containing hybrid PVA and RTP fibres holds promise as a cost-effective and sustainable material for applications against dynamic loadings

Existence and asymptotic behavior of normalized solutions for coupled critical Choquard equations

In this paper, we study the coupled critical Choquard equations with prescribed mass \begin{equation} \begin{aligned} \left\{ \begin{array}{lll} -\Delta u+\lambda_1u=(I_\mu\ast |u|^{2^*_\mu})|u|^{2^*_\mu-2}u+\nu p(I_\mu\ast |v|^q)|u|^{p-2}u\ & \text{in}\quad \mathbb{R}^N,\\ -\Delta v+\lambda_2v=(I_\mu\ast |v|^{2^*_\mu})|v|^{2^*_\mu-2}v+\nu q(I_\mu\ast |u|^p)|v|^{q-2}v\ & \text{in}\quad \mathbb{R}^N,\\ \int_{\mathbb{R}^N}u^2=a^2,\quad\int_{\mathbb{R}^N}v^2=b^2, \end{array}\right.\end{aligned} \end{equation} where $N\in\{3,4\}$, $0<\mu<N$, $\nu\in\mathbb{R}$, $I_\mu:\mathbb{R}^N\rightarrow\mathbb{R}$ is the Riesz potential, and $2_{\mu,*}:=\frac{2N-\mu}{N}<p,q<\frac{2N-\mu}{N-2}:=2^*_{\mu},$ with $2_{\mu,*}, 2^*_{\mu}$ called the lower and upper critical exponent in the sense of Hardy-Littlewood-Sobolev inequality respectively. We prove that no normalized ground state exists for $\nu0$, we study the existence, non-existence and qualitative behavior of normalized solutions by distinguishing three cases: $L^2$-subcritical case: $p+q<4+\frac{4-2\mu}{N}$; $L^2$-critical case: $p+q=4+\frac{4-2\mu}{N}$; $L^2$-supercritical case: $p+q>4+\frac{4-2\mu}{N}$. In particular, in $L^2$-subcritical and $L^2$-critical cases, we show the system has a radial normalized ground state for $0<\nu<\nu_0$ with $\nu_0$ explicitly given. In $L^2$-supercritical case, we prove the existence of two thresholds $\nu_2\geq\nu_1\geq0$ such that a radial normalized solution exists if $\nu>\nu_2$, and no normalized ground state exists for $\nu<\nu_1$. Moreover, we give the concrete ranges of $p$ and $q$ for $\nu_2=\nu_1=0$ and $\nu_2\geq\nu_1>0$.Comment: 37 page