Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into non-simple material models with higher-order gradients of deformations. This makes, however, numerical computations much more involved. Here we propose another approach relying on local minimizers of the simple-material model. Computational tests are provided showing a very good agreement between our model and the original one.
翻译:大型Kelvin-Voigt病理学菌株中简单粘结材料的计时最小化计划,由于消散功能不具有准混杂性,因此没有妥善安排。一种可能的解决办法是采用非简单材料模型,其变形梯度较高,但这种模型涉及的数值要多得多。我们在此提出另一种方法,即依靠简单材料模型的当地最小化器。计算测试显示我们的模型和原始模型之间非常一致。