  Deep learning and the collocation method are merged and used to solve partial
differential equations describing structures' deformation. We have considered
different types of materials: linear elasticity, hyperelasticity (neo-Hookean)
with large deformation, and von Mises plasticity with isotropic and kinematic
hardening. The performance of this deep collocation method (DCM) depends on the
architecture of the neural network and the corresponding hyperparameters. The
presented DCM is meshfree and avoids any spatial discretization, which is
usually needed for the finite element method (FEM). We show that the DCM can
capture the response qualitatively and quantitatively, without the need for any
data generation using other numerical methods such as the FEM. Data generation
usually is the main bottleneck in most data-driven models. The deep learning
model is trained to learn the model's parameters yielding accurate approximate
solutions. Once the model is properly trained, solutions can be obtained almost
instantly at any point in the domain, given its spatial coordinates. Therefore,
the deep collocation method is potentially a promising standalone technique to
solve partial differential equations involved in the deformation of materials
and structural systems as well as other physical phenomena.
