We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation, and a momentum equation constraint. Numerical results on model problems show that the formulation is capable handling discontinuous, and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

中文翻译：

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平面应力反弹性问题本构方程公式的直接误差

我们提出了一种新的计算公式，用于解决具有全场数据的弹性反问题。该公式是本构方程公式中误差的变体，但允许直接求解模量场并适应不连续的应变场。该公式的开发是由于目前的直接公式在处理应变和材料特性分布的不连续性方面的性能相对较差，目前文献中已有报道。该公式依赖于最小化本构方程中的误差和动量方程约束。模型问题的数值结果表明，该公式能够处理不连续和嘈杂的应变场，并且还可以收敛于连续和不连续材料属性分布的网格细化。