In this dissertation, two main topics will be discussed. First, a novel approach to computational mechanics via a Domain Specific Language(DSL) with a syntax to facilitate new model development will be presented. Second, discrete element multiphysical models will be proposed to study powder based additive manufacturing processes. The DSL presented is a tool for computational mechanics which is designed to allow an engineer to focus more on model development and investigation by providing a syntax which makes it easier to define new discretizations and test different constitutive models. In order to achieve this, a system for managing data and specifying models is created around the Python development environment. There are three powerful features of the DSL. First, the language provides a syntax for creating objects which describe the fundamental physical objects and numerical elements in the problem and facilitates the allocation, management and modification of the data allocated for these objects. Second, all constitutive models are input using symbolic notation allowing for the language of math, rather than raw code, to be used to describe interactions. Third, low level code is automatically generated for the models and their gradients(via symbolic differentiation) for use with linear and non-linear solvers and time-stepping methods, both explicit and implicit. Also, Python wrappers are automatically generated so the high performance implementations can be used in the Python environment without additional work by the user. The discrete element method is a Lagrangian technique which uses interactions of spherical elements to model material behaviors. In the past, it has been most commonly used in the study of granular media such as sands and soils. Here, extensions to the method to model heat transfer, thermal expansion and interactions with non-spherical objects will be discussed for simulating additive manufacturing processes. The formulation, implemented with the DSL, is used to study powder packing in a manner that is physically consistent with Selective Laser Sintering/Melting machines. Also, the dynamics of powders subjected to a heat source are investigated. Additional multiphysics behavior is incorporated through a temperature dependent bonding model to create an efficient simulation for studying Laser Metal Deposition. Finally, a method for using discrete elements to enhance Eulerian finite elements to efficiently prevent advection welding is proposed.