Skip to content

Visco-Hyperelastic Material Modeler App

During the fall 2022 term, while serving as a post‑baccalaureate research assistant in the Boğaziçi University Vibrations Laboratory, I developed the MATLAB Visco‑Hyperelastic Material Modeler App. My role focused on restructuring Prof. Cetin Yilmaz’s analysis code, standardising the parameter set for automated runs, and building a researcher‑friendly GUI for streamlined optimisation and prediction.

Model Overview

Characterizing visco-hyperelastic materials is essential for applications such as automotive damping systems and biomedical devices. These materials exhibit both viscoelastic and hyperelastic properties, resulting in complex nonlinear and frequency-dependent mechanical behaviors. The paper by Ozcan. et al. presents a mechanical model consisting of nested linkage mechanisms with linear lumped elements (springs and dashpots) to replicate these behaviors using constant system parameters. Unlike traditional models requiring parameter adjustments over time or varying strain conditions, this model achieves accurate predictions using fixed parameters.

The mechanism, illustrated below1, consists of two nested parallelogram linkages interconnected by linear springs and dashpots. The outer linkage angles are denoted by $\alpha$, and the inner linkage angles by $\beta$. Forces within the mechanism result from spring elongation or compression and dashpot velocity-dependent damping:

  • Horizontal forces arise from horizontal springs $(k_{hs}, k_{h})$ and dashpot $(c_h)$.
  • Vertical forces are derived from vertical springs $(k_{vs}, k_{v})$ and dashpot $(c_v)$.

The total force acting on the left-most joint $F_t(t)$ is:

$$ F_t(t) = \bigl[k_{hs}u_t(t) + k_{h}u_s(t)\bigr]\tan\beta(t)\cot\alpha(t) \;+\; \bigl[k_{vs}v_t(t) + k_{v}v_s(t)\bigr]\cot\alpha(t) $$

This force is essentially the force exerted by the material as response to the strain. Here, $u_t(t)$ and $v_t(t)$ represent total horizontal and vertical displacement extensions, respectively, while $u_s(t)$ and $v_s(t)$ are corresponding spring displacements. These forces collectively simulate the nonlinear, frequency-dependent behaviors of visco-hyperelastic materials.

Proposed nested linkage model to mimic hyper-viscoelastic behavior
Figure 1: Proposed nested linkage model to mimic hyper-viscoelastic behavior

MATLAB App Development

The MATLAB‑based visco‑hyperelastic material modeler app facilitates the practical application of this mechanical model. In order to streamline parameter optimization and prediction, I re‑engineered and optimized the underlying MATLAB codebase and wrapped it in an intuitive graphical user interface (GUI). The app allows researchers to load experimental data, calibrate the model’s constant parameters, and generate predictions without writing any code.

App Interface

Below is a screenshot illustrating the MATLAB app's user-friendly interface for inputting experimental data and optimizing model parameters:

MATLAB App Home Screen
Figure 2: MATLAB App Home Screen

App Workflow

  1. Experimental Data Input: Users upload their data corresponding to one or more of four distinct experiment types:

    • Quasi-Static Loading – slow loading to measure nonlinear stiffness.
    • Hysteresis – cyclic loading to assess energy dissipation.
    • Ramp-and-Hold – rapid loading followed by a constant strain to observe stress relaxation.
    • Dynamic Stiffness – sinusoidal loading at different frequencies to evaluate frequency-dependent behavior.

  2. Parameter Initialization Using Latin Hypercube Sampling (LHS): Each optimization iteration begins by initializing model parameters with LHS—a statistical technique that distributes sample points evenly across the entire parameter space—providing a robust starting set for optimization.

  3. Optimization Procedure:

    • Kinematic variables (displacement and velocity) are computed from input data.
    • Forces are then calculated through the linkage mechanism (see Model Overview).
    • Parameters are refined by minimizing residuals between experimental and predicted forces using either constrained nonlinear optimization (fmincon) or nonlinear least-squares minimization (lsqnonlin). Both techniques iteratively adjust parameters until convergence.

  4. Predictive Capability: After optimization, the constant parameters are used to predict responses for additional experiments. In the example below, parameters fitted to the first four experiments accurately predict outcomes for two unseen tests.

Results Visualization

The figure compares optimized model predictions with experimental data. Parameters were tuned using the first four experiments and then used to predict the last two (bottom-middle and bottom-right plots):

Model Prediction vs. Experimental Data
Figure 3: Model Prediction vs. Experimental Data

Conclusion & Availability

The app offers researchers a streamlined, code-free pathway for calibrating the constant-parameter visco-hyperelastic model and generating reliable predictions from new experimental data. At present, the MATLAB GUI is maintained internally in the Boğaziçi University Vibrations Laboratory and is not available online. Interested collaborators may request access by reaching out to me.

  1. M. Umut Ozcan, Cetin Yilmaz, and Fazil O. Sonmez. Visco-hyperelastic material modeling using nested linkage mechanisms. International Journal of Solids and Structures, 193–194:393–404, 2020. doi:10.1016/j.ijsolstr.2020.02.035. ↩