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Learning constitutive relations from experiments: II. dynamic indentation
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DOI：10.1016/j.jmps.2026.106629.png)
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Abstract
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We continue the development of a method to accurately and efficiently identify the constitutive behavior of complex materials through experimental observations that we started in Akerson et al. (2025). We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to the model using the adjoint method. In this paper, we extend the approach to include contact and study dynamic indentation. Contact is a nonholonomic constraint, and we introduce a Lagrange multiplier and a slack variable to address it. We demonstrate the method on synthetic data before applying it to experimental observations on rolled homogeneous armor steel and a polycrystalline aluminum alloy.
Keywords:
Indentation
Dynamics
Plasticity
Experimental inference
Inverse problems
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