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          <h2 class="h2 article-title">Multiscale Modeling of SPS with Direct FE2 Framework</h2>
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          <h4 class="h4">Direct FE2 Framework for Multiscale SPS Simulations</h4>

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            <ul class="author-info-box">
              <li class="author-info-item">
                <span class="info-label">Main Author:</span>
                <span class="info-value">Ashwani Kumar</span>
              </li>
              <li class="author-info-item">
                <span class="info-label">Affiliation:</span>
                <span class="info-value">ETH Zurich</span>
              </li>
              <li class="author-info-item">
                <span class="info-label">Online:</span>
                <a href="https://doi.org/10.1016/j.jmapro.2025.07.006" target="_blank"
                  class="info-value text-link">ScienceDirect</a>
              </li>
              <li class="author-info-item">
                <span class="info-label">Co-Authors:</span>
                <span class="info-value">Z. Zhang, M. Afrasiabi, M. Bambach </span>
              </li>
              <li class="author-info-item">
                <span class="info-label">Date:</span>
                <span class="info-value">2025</span>
              </li>
              <li class="author-info-item">
                <span class="info-label">Journal:</span>
                <span class="info-value">Journal of Manufacturing Processes</span>
              </li>
            </ul>

            <h4 class="h4">Project Overview</h4>
            <p>
              This project focuses on improving the simulation of spark plasma sintering (SPS), a key process in
              advanced materials manufacturing.
              Traditional finite element models either miss microscale powder interactions or become too
              computationally
              expensive.
              To address this, a Direct FE2 multiscale framework was developed that directly integrates microscale
              powder behavior into macroscale electro-thermal-mechanical simulations.
            </p>

            <h4 class="h4">Problem & Motivation</h4>
            <p>
              SPS involves complex electrical, thermal, and mechanical interactions across different scales.
              Existing models either treat powder as a continuum (ignoring particle-level detail) or use
              particle-based
              methods (accurate but computationally prohibitive).
              This gap made it difficult to simulate large-scale SPS with both accuracy and efficiency.
            </p>

            <h4 class="h4">Research Contributions</h4>
            <ul class="feature-list">
              <li>Designed a Direct FE2 approach for fully coupled electro-thermal-mechanical SPS simulations.
              </li>
              <li>Achieved temperature & displacement error below 1% compared to full FE analysis.</li>
              <li>Reduced computational cost by factors up to 70x, with degrees of freedom reduced up to 44x.</li>
              <li>Demonstrated flexibility in handling different powder morphologies (SC, BCC, FCC).</li>
              <li>Validated the model against the Heckel equation.</li>
            </ul>

            <h4 class="h4">Technical Highlights</h4>
            <ul class="tech-list">
              <li>Tools & Platforms: Abaqus FE solver, Python scripting for automation.</li>
              <li>Methods: Finite Element Analysis (FEA), multiscale FE2 coupling, representative volume elements
                (RVEs), periodic boundary conditions, multi-point constraints.</li>
              <li>Models Used: Coupled electro-thermal-mechanical FE models, Johnson–Cook material law for copper
                powders.</li>
              <li>Performance: Demonstrated scalable efficiency with 8–70x faster runtime compared to full FE
                methods.
              </li>
            </ul>

            <h4 class="h4">Results & Impact</h4>
            <p>
              The Direct FE2 framework produced results nearly identical to full FE simulations while drastically
              lowering computational cost.
              It revealed how powder morphology, mesh scaling, and current intensity affect densification during
              SPS.
              The method makes it feasible to simulate realistic SPS geometries that were previously
              computationally
              intractable.
              This work advances multiscale modeling in materials processing and provides a foundation for future
              studies on non-spherical powders and complex geometries.
            </p>

            <h4 class="h4">Publication Details</h4>
            <p>
              <strong>Journal:</strong> Journal of Manufacturing Processes<br>
              <strong>Year:</strong> 2025<br>
              <strong>DOI:</strong> <a href="https://doi.org/10.1016/j.jmapro.2025.07.006" target="_blank"
                class="text-link">10.1016/j.jmapro.2025.07.006</a>
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