## 1 Introduction  
The global energy paradigm is shifting from fossil fuels to eco-friendly alternatives, with hydrogen energy gaining prominence due to its high energy density and zero-emission characteristics [1]. For hydrogen fuel cell vehicle commercialization, 87.5 MPa ultra-high pressure hydrogen storage and control technology represents a critical enabling technology [2]. Within these applications, ultra-high pressure hydrogen solenoid valves serve as core components responsible for stable hydrogen control in high-pressure environments [3, 4]. Traditional sealing strategies in fluid control \(\square\) valves have predominantly relied on hard-to-hard material combinations with conforming contact geometries (\(R_{p}\) < \(R_{s}\)), developed primarily through empirical field testing approaches. This conventional paradigm, while effective for moderate pressure applications, encounters fundamental limitations in ultra-high pressure hydrogen environments where neither traditional hard-to-hard sealing nor superelastic sealing elements can adequately address the conflicting requirements of low-pressure sealing effectiveness and high-pressure structural integrity. The emergence of ultra-high-pressure pilot-operated valves necessitates a paradigm shift toward soft-to-hard material combinations with hydrogen-resistant engineering plastics, coupled with systematic theoretical frameworks to replace empirical design practices. These valves face a unique design challenge: operating reliably across pressure conditions from 2 MPa to 87.5 MPa. This broad operating range creates a fundamental design dilemma. At low pressures, sufficient contact pressure is necessary for effective sealing, while at high pressures, the maximum stress at the contact area must remain below the material's compressive strength to prevent permanent deformation. These requirements, low-pressure sealing performance and high-pressure structural integrity, often conflict, presenting a key challenge in contact geometry design [5; 6]. Conventional solenoid valve designs typically employ rectangular contact geometry, prioritizing manufacturability and cost-efficiency. This configuration, where plunger and seat meet at nearly right angles, provides effective sealing in low-pressure environments. However, under ultra-high-pressure conditions, severe stress concentration occurs at the edge, exceeding the material's compressive strength. This results in permanent deformation of the plunger material, significantly reducing valve lifespan and reliability [7; 8]. Hydrogen valve plungers commonly use engineering plastics such as polyamide-imide (PAI), which offer excellent hydrogen penetration resistance and dimensional stability but limited mechanical durability compared to metals. Under high-pressure conditions with stress concentration, these materials can easily exceed their compressive strength, leading to permanent deformation or cracking. Researchers have explored various approaches to address these limitations, including high-strength alloy materials, surface hardening treatments, and edge-rounding designs [9]. Recent structural mechanics studies have demonstrated that curved surface designs can improve contact stress distribution and enhance structural durability, yet most remain within the framework of existing rectangular contact geometry, failing to achieve the fundamental balance between low-pressure sealing and high-pressure durability required across broad pressure ranges [10; 11]. To fundamentally resolve this design challenge, we propose a novel soft-to-hard sealing approach that leverages hydrogen-resistant plastic materials in a non-conforming contact geometry (\(R_{p}>R_{s}\)). This approach applies Hertzian contact theory principles in an unconventional configuration that challenges traditional contact mechanics wisdom, establishing the first systematic theoretical framework for ultra-high-pressure pilot-operated valve sealing and moving beyond empirical design practices toward predictive modeling.