Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely efficient in reproducing complex responses observed in experiments. Additionally, in their discretized form, they are computationally very efficient, often resulting in a simple algebraic relation, and therefore they have been extensively used within large-scale explicit and implicit finite element models. However, it is very challenging to formulate new constitutive models, particularly for materials with complex microstructures such as composites. A recent trend in constitutive modeling leverages complex neural network architectures to construct complex material responses where a constitutive model does not yet exist. Whilst very accurate, they suffer from two deficiencies. First, they are interpolation models and often do poorly in extrapolation. Second, due to their complex architecture and numerous parameters, they are inefficient to be used as a constitutive model within a large-scale finite element model. In this study, we propose a novel approach based on the physics-informed learning machines for the characterization and discovery of constitutive models. Unlike data-driven constitutive models, we leverage foundations of elastoplasticity theory as regularization terms in the total loss function to find parametric constitutive models that are also theoretically sound. We demonstrate that our proposed framework can efficiently identify the underlying constitutive model describing different datasets from the von Mises family.

翻译：典型地说,材料的机械反应是通过结构模型描述的,往往以限制的普通差异方程式的形式描述的。这些模型的参数数量非常有限,但它们在复制实验中观察到的复杂反应方面极为高效。此外,它们以分解的形式计算非常高效,往往导致简单的代数关系,因此在大规模、明确和隐含的有限要素模型中广泛使用。然而,制定新的结构模型,特别是具有复杂微结构(如复合材料)的材料,是非常困难的。在结构模型中,一个复杂的神经网络结构结构最近的趋势是建立复杂的材料反应,而结构模型尚不存在。虽然非常准确,但它们有两种缺陷。首先,它们是相互交错的模型,往往在外推法方面做得很差。第二,由于其结构复杂和参数众多,它们被广泛用于在大规模模式确定要素模型(如复合材料)中作为一个组成模型的构成模式。我们提议以物理知情学习机器为基础,在结构模型总体特征特征和发现时,采用新的方法来构建复杂的神经网络结构结构结构结构。我们并不理解,因此,在结构模型中采用正确的组织结构模型中,我们可找到可靠的结构模型的分类结构模型。